tag:blogger.com,1999:blog-55670271584913973212024-03-13T22:07:31.170+05:30MathByVemuriMathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.comBlogger264125tag:blogger.com,1999:blog-5567027158491397321.post-22551216244636475692015-12-09T21:12:00.000+05:302015-12-09T21:14:17.221+05:30Even-Odd car formula of Delhi Government<div dir="ltr" style="text-align: left;" trbidi="on">
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<a href="http://4.bp.blogspot.com/-kPM65SDasro/VmhLYiGFWoI/AAAAAAAAAsQ/T2qzrxkPeQ4/s1600/car-EvenOdd.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-kPM65SDasro/VmhLYiGFWoI/AAAAAAAAAsQ/T2qzrxkPeQ4/s1600/car-EvenOdd.jpg" /></a></div>
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The new initiative Even-Odd car formula of Delhi government to control traffic and</div>
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air pollution is making rounds in the news now-a-days. I just thought of simple</div>
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math behind this.</div>
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We can easily conclude that this initiative will bring down car traffic by 50%.</div>
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<br /></div>
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But how? This small write up is to bring out simple logic behind this conclusion.</div>
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The formula states that all even number registered cars are allowed to commute on</div>
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roads on even numbered days (2nd, 4th, 6th etc… of a month) and odd numbered cars</div>
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<br /></div>
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catch up on odd numbered days. Ideally, this should mean - on an odd numbered day,</div>
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<br /></div>
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all odd numbered cars commute on roads and the next day, which is eventually an</div>
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<br /></div>
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even numbered day, all even numbered cars commute on roads.</div>
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<br /></div>
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What does it mean?</div>
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I<b>f I consider any two consecutive days, “all odd” plus “all even” result in </b></div>
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<b style="text-align: left;">distribution of all cars in any two consecutive days. So it brings the day-average </b></div>
<b><br /></b>
<b>traffic to half proportion.</b></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com2tag:blogger.com,1999:blog-5567027158491397321.post-80373765510338380072013-08-18T17:50:00.000+05:302013-08-19T08:57:15.707+05:30My interview experiences with premier Indian B-schools<div dir="ltr" style="text-align: left;" trbidi="on">
I feel
privileged to have experience of competing in admission processes for Executive
MBA from premier Indian B-schools. Post CAT/GMAT, it starts with submitting papers on
SOP, Work-ex, Reco-letters, Questionnaires etc and ends with a crucial Personal
Interview. The whole process requires a lot of introspection. I feel it as a
rich experience to get involved in those processes with premier Indian
B-Schools like IIMs, XLRI, SP Jain’s, NMIMS, IMT etc., I would like to
summarize all my experiences here:<br />
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
I feel that the
following are three important qualities that are tested in the admission
process: <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">‘Clarity of thought’, ’Positive attitude’, ’Presentation skills’</i></b>.</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Clarity
on Career & Course:</i></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Clarity is
expected on “<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">why this course?</i></b>”. Different answers for this Q are like this:
For a working guy, MBA course may be useful for career progression.<span style="mso-spacerun: yes;"> </span>It may be useful in switching to new field of
work. For example, For an IT developer, it may be useful to switch over to
sales & marketing of IT products/services. </div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Introspection on
the following aspects is required:</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Your strengths
& weaknesses, Aligning of your career objectives with the course objectives,
Your achievements, Extra-curricular activities, Hobbies etc.</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br />
<a name='more'></a></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
A rigorous
course curriculum, learning from well reputed & experienced professors,
diverse mix of batch mates, assignments & case studies, international
immersion programmes give you a lot of exposure. A little study about the B-school
& the specified course is a bit useful. In this regard, the following
aspects are useful:</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Knowledge on
history of the B-school, it’s strengths & strategic location, information
on the specific course, core-topics & electives dealt in the course,
enquiries with alumni, a bit of R&D on placements.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
You
may be tested on your seriousness about joining the course. The interviewer may
suggest another course or career path and may strongly say that you are much
suitable for that. You need to be strong and clear to defend your stand.</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Some
Funda:</i></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Basic knowledge
on Finance fundamentals gives a lot of confidence to a typical
Engineering/Science graduate. <a href="http://www.scribd.com/doc/48898736/Niveshak-Interview-Booklet#outer_page_17">Check
out this document prepared by IIM Shillong</a>. I found it quite useful. You
may expect Q like: ‘How is inflation rate calculated?’ or ‘what is sensex?’
etc.</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Be clear and
submit facts while filling up application forms, writing SOP & other papers
etc., required in the admission process. Keep a copy of all those documents and
go through those docs carefully before the interview. You may expect some Q’s
from the documents submitted by you.<span style="mso-spacerun: yes;"> </span>Of
course, it is about you and prepared by you only.</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Most generally,
the interview starts with the question “<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Tell about you</i></b>”. Try to utilize it
cleverly. This may be the only direct question posed at you which can be used
by you to hint at your strong areas and thus leading the direction of interview
to your comfort zone. And of course there is a chance that it ends up as a
casual Q and may not have any impact on the next course of i/v. The
interviewers may follow strictly their agenda of Q’s. But keep one thing in
mind. Never lose confidence. Throughout the interview, make use of commonsense
and utilize every opportunity to pull the course of interview in to your
stronger zones.<span style="mso-spacerun: yes;"> </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
Don’t be much
afraid of Q’s from your graduation syllabus. On that aspect, you should be able
to give an overall picture. For example, let us suppose that you are an
Engineer in Electronics & Communications. Remember it’s not an interview
for scientist in DRDO or ISRO. No need of going deep in to the core engineering
topics but a quick outlook is enough. Look at the following questions:</div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
How Electronics
is relevant to the industry? What are analog and digital devices? Specify some
advantages of OFC? What are various modulation techniques in communication?
What is VLSI? Brief on microprocessors and its relevance in digital products? </div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
You are not expected
to draw a circuit diagram and explain its operation. Rather you are definitely expected
to sound some relevance and acquaintance with the topic. </div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
You may expect a
Q on <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">books
you read</i></b>. Prepare a brief on that front. Have a review of books you
read, author names, a little brief about. If you say that you don’t have book
reading habit, then you may expect an immediate Q: “You have already come out
of college long back. And you don’t have a book reading habit. You need to have
a lot of reading and case studies in MBA. How can you cope up with a rigorous
course curriculum?” </div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
The following
list is my answer for the Q on books:</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
‘Who
moved my cheese’, ‘The world is flat’, ‘Business Maharajas’, ‘Rich dad poor
dad’, ‘The monk who sold his Ferrari’, ‘Count your chickens before they hatch’,
‘My experiments with truth’.</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Prepare
well about your <b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">work-ex</i></b>. You are expected to know about your organization,
sector, and competitors of your organization etc. You may expect Q’s like: ‘Is
your organization listed?’, ‘What are the present prospects of your
organization?’, ‘With the similar work-ex which are the other companies you can
aim for?’. If you specify ‘Project Management’ in your work-ex, you may expect
a brief on PERT & CPM methods. <span style="mso-spacerun: yes;"> </span>Irrespective of whether you used these
techniques, you may be expected at least to expand the terms and a little brief
there on. </div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Being
from Telecom sector, I faced with the Q’s like ‘what is mobile VAS?’, ‘what is
MVNO?’, ‘Differentiate b/w 2G,3G and 4G technologies?’, ‘Expand CDMA/GSM/GPRS’,
‘Which companies use GSM and which use CDMA technology?’, ‘Tell about spectrum
allocation’, ‘What are the changes in Telecom sector after liberalization?’, ‘Out
of the following, which holds a key role in the present Telecom scenario: Telecom
Service Provider/Mobile Equipment manufacturer/Telecom S/W developer etc?’ </div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
You
need not be much worried if your acads are on lower side but get prepared for
the Q: ‘Why less marks in your graduation?’ or ‘Why are you not consistent in
studies?’. You may expect a Q like: ‘why this gap in your academic
career/work-ex career?’ in case it’s relevant to you.</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Don’t
get surprised and be ready for the following Q’s on numbers and names from ‘social
awareness’ front:</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
How
many states in India? How many Loksabha & Rajyasabha seats? Name the Chief
Ministers of all the border states of your state? Name the state in which the
B-School is located? For which your place/state is famous for? Name the cabinet
ministers of powerful portfolios (Finance, Commerce, External affairs, Home
etc)? How many cabinet ministers? Is there any limit on number of cabinet
ministers?</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Sometimes
your view on national integrity is tested. You may expect a Q like ‘Do you
support Naxal’s movement? Why or why not?’. They expect a balanced answer rather
than taking an extreme stance.</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
You
can expect the following Q’s from ‘current affairs’ front:</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
‘If
you are to decide, what is your stand on Pakistan?’, ‘What about depreciation of
Rupee value?’, ‘Who is the head of RBI or SEBI?’, ’What are the present rates
of RBI? (Repo, Reverse repo etc)’, ‘What does SEBI do?’ ‘What about Euro debt
crisis?’. It is advised to be in touch with the recent happenings on India and
world fronts. </div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
All
of a sudden some Q’s like the following may pop up for a surprise:</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
‘Tell
about T20?’, ‘Tell about Apple’s Ipod’ or ‘why Nandan Nilekani is in news?’.</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Another
frequent Q that needs to be taken care of is: ‘<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">What are your plans if you are
not placed after your MBA?</i></b>’ or ‘Do you understand the risks in taking
up the course?’ or ‘If you are selected, will you join after taking sabbatical
from your organization?’</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><i style="mso-bidi-font-style: normal;">Market
yourself:</i></b></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
‘Your
presentation of yourself’ is very important. Your exuberance of confidence
counts a lot. Don’t hesitate to showcase your strengths. I collected all my
write-ups from my blog on the theme ‘Math in Real life things’ and prepared a document
to present it to the interview board. My idea is to show case my analytical
skills. This type of preparation boosts your confidence levels. Try to be a
little different from conventional methods and I feel that <b style="mso-bidi-font-weight: normal;">a little crossing of border</b> may not be wrong as long as you have
clarity on what you do. </div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 142.35pt; text-align: justify;">
Be
positive. Don’t lose hope if you are faced with a Q that you can’t answer. For
example, if you are asked to name CM of Orissa state and if you forgot name of
the gentleman, then what will you do? You need not bluntly leave it. After you
politely say that you don’t remember the name of CM, at least you may tell
something that you know about Orissa. You may refer Chilka-lake or the capital
city Bhuvaneswar or famous classical dance mode of Orissa -Odissi or the famous
Puri-Jagannath temple. After all you are tested on social awareness front and
you know something related to that. This type of approach keeps your tempo on
top.</div>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com9tag:blogger.com,1999:blog-5567027158491397321.post-36718062504239106722013-08-11T19:46:00.000+05:302014-07-19T14:39:12.515+05:30A dream comes true…<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">My full-time MBA dream transforms in to reality now …</span></i><br />
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<i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">It’s a dream to be in top management institutes like IIMs…</span></i></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">It’s a fruitful year… First got admit offer from IIM Bangalore for Post
graduate Programme in Public Policy Management and then for EPGP from IIM
Indore. I prefer General Management to Public policy and opted for IIM Indore. </span></i></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">I am glad that, for the next one year, I will be put through rigorous
course curriculum in the form of “Executive Post Graduate Programme” in one of
the temples of management studies in India – IIM Indore. It’s rigorous in the
sense that typical two year MBA syllabus is completed in a span of hardly one
year. It consists of over 800 class room sessions, case studies, guest lectures by eminent professors, industrialists etc.
The class room is a mix of people with diverse work-ex backgrounds. The minimum
work-ex required is 5 years. It’s a rich experience to be part of such network
of work-ex pool. I am very much willing and eagerly waiting to pass through this
transformation phase… </span></i></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">My blog helped me a lot in my journey to IIM. First of all, I attempted
CAT-2012 to have a firsthand experience of online format of the prestigious
examination and utilize these inputs in building up my blog. My earlier stint
with CAT was in 2008, the last paper based format. I felt that, CAT-2012 would
give me some sort of real time exposure to analyze the toughest management
entrance test of India. But it gave me a lot more. It gave me two IIM calls. CAT/GMAT score is one of several parameters
for entry in to executive PG courses in IIMs. Work-ex, SOP, Interview etc., are
the other parameters being looked at in the admission process.</span></i></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<i style="mso-bidi-font-style: normal;"><span style="font-size: 12.0pt; line-height: 150%;">My blog not only keeps me in touch with the skills required to crack
competitive exams like CAT, but also with many other aspects. It helps to build
my confidence levels. It gives me a new lease of life and a lot of happiness. It
makes me very optimistic and open-minded. I feel that the time that I spend on building
my blog flows with positive energy. It reflected a lot in SOP papers and interview
process of my journey to IIM.</span></i></div>
<span style="font-family: Times, Times New Roman, serif; line-height: 115%;"><i>I am very much thankful to all the well wishers
and followers of my blog. All your wishes and acts make me to continue the
tempo…</i></span><br />
<i style="mso-bidi-font-style: normal;"><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"><a href="http://mathbyvemuri.blogspot.in/2013/08/my-interview-experiences-with-premier.html" target="_blank">check this post on my interview experiences with premier B-schools</a> </span></i><!--[if gte mso 9]><xml>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-29260803380100898072013-06-23T21:36:00.002+05:302013-06-25T19:43:25.647+05:30Math in Tenali Ramalinga’s puzzle on elephants<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> I
came to know about this story through my friend. This is about a problem solved
by the great Tenali Ramalinga. I always enjoy Ramalinga’s stories and this is
one among those tales:</span><br />
<div class="MsoNormal" style="line-height: 150%; text-align: justify; text-indent: 35.45pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify; text-indent: 35.45pt;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">An
old man had three sons. During his life time he acquired 17 elephants (Exactly do not remember whether they are elephants or horses. Let us consider elephants for example). He wrote
a note which specifies how these elephants shall be distributed among his three
sons after his death. The note says:</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“Half of the
elephants shall be given to the eldest son. Two third of the remaining shall be
give to the second son. <span style="mso-spacerun: yes;"> </span>Two third of the
remaining shall be give to the third son.” <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Finally the
day came and the elephants needed to be distributed among the sons according to
the note. But how can it be done? How can we divide 17 elephants such that the
eldest son gets half of the share?</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<a name='more'></a><br />
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">As usual,
Ramalinga has resolved the problem. This is how Ramalinga has solved the puzzle:</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">To this 17
elephants, Ramalinga added one elephant taken from King’s elephant force. This made
the count 18. Then he distributed 9 elephants (which is equivalent to half part)
to the eldest son. Then he distributed 6 out of the remaining 9 (which is
equivalent to 2/3 part) to the second son. Then he distributed 2 out of the
remaining 3 (which is equivalent to 2/3 part) to the third son. This exercise
left one elephant and that was given back to the king’s elephant force.</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Math in this puzzle:</span></b></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: HI; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt; mso-hansi-theme-font: minor-latin;">The fractions mentioned in
the note are 1/2, 2/3 and 2/3. So to evenly distribute, we need to have at least
2*3*3=18 elephants (these are the denominators of the fractions).</span></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-53227667096739780742013-05-27T21:20:00.001+05:302014-07-19T14:45:06.156+05:30CSAT 2013 Solved Paper (paper-II)<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">1</span>. In a rare coin collection, there is one gold coin
for every three non-gold coins. 10 more gold coins are added to the collection
and the ratio of gold coins to non-gold coins would be 1:2. Based on the
information, the total number of coins in the collection now becomes</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)90 (b)80 (c)60 (d)50<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Initial ratio =
G:N = 1:3 ---(1)</div>
<div class="MsoNormal" style="line-height: 150%;">
After adding 10
gold coins, the ratio becomes (10+G):N =
1:2 ---(2)</div>
<div class="MsoNormal" style="line-height: 150%;">
On solving (1)
& (2), we get, G=20 and N=60.</div>
<div class="MsoNormal" style="line-height: 150%;">
Presently, the
total number of coins in the collection = (10+G)+N= 10+20+60=90</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(a)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">2</span>. A gardener has 1000 plants. He wants to plant them
in such a way that the number of rows and the number of columns remains the
same. What is the minimum number of plants that he needs more for this purpose?
</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)90 (b)24 (c)32 (d)34<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
If the number of
rows and number of columns are to be equal, then the total number of trees will
be in the form of x<sup>2</sup>, which is nothing but a perfect square. As 1000
is not a perfect square, we need to check for a perfect square above and
nearest to 1000. </div>
<div class="MsoNormal" style="line-height: 150%;">
It’s 1024, which
is square of 32. So he needs to add 24 more trees to get 1024. </div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(b)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br />
<a name='more'></a><br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">3</span>. A Sum of Rs 700 has to be used to give 7 cash
prizes to the student of a school for their overall academic performance. If
each prize is Rs 20 less than its preceding
price, what is the least value of the price?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Rs
30 (b)Rs 40 (c)Rs 60 (d)Rs 80<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let the least
value price be X. Then the next value is X+20, and the next value is X+40 and
on and on up to 7 values.</div>
<div class="MsoNormal" style="line-height: 150%;">
It’s nothing but
an arithmetic Progression with sum 700.</div>
<div class="MsoNormal" style="line-height: 150%;">
X + X+20 + X+40
+… X+120=700 => 7X+(20+40+…+120)=700</div>
<div class="MsoNormal" style="line-height: 150%;">
=>
7X+20(1+2+3+…+6)=700 => 7X+20(21)=700 => 7X=280 =>X=40</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(b)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">4</span>. Out of 120 applications for a post 70 are male and
80 have a driver’s license. What is the ratio between the minimum to maximum
number of males having driver’s license?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)1
to 2 (b) 2 to 3 (c)3 to 7(d)5 to 7<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
70 male =>
120-70=50 female</div>
<div class="MsoNormal" style="line-height: 150%;">
For a maximum, all 70 male shall have driver’s
license</div>
<div class="MsoNormal" style="line-height: 150%;">
For a minimum:
If all 50 females posses driver’s license, then the remaining 30 licenses shall
be possessed by males. So minimum male-driver’s licenses = 30</div>
<div class="MsoNormal" style="line-height: 150%;">
Min to max = 30
to 70 = 3 to 7</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(c)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">5</span>. In a garrison, there was food for 1000 soldiers for
one month. After 10 days, 1000 more soldiers joined the garrison. How long
would the soldiers be able to carry on with the remaining food?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)25
days (b) 20 days (c) 15 days (d) 10 days<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
After 10 days,
the remaining food would be sufficient for the 1000 soldiers for 20 more days </div>
<div class="MsoNormal" style="line-height: 150%;">
=> If 1000
more soldiers are added, it shall be sufficient for only 10 days (as the no. of
soldiers is doubled, the days are halved)</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(d)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">6</span>. A tank-full petrol in Arun’s motor-cycle last for
10 days. If he starts using 25% more every day, how many days will the tank-full
petrol last?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)5
(b) 6 (c) 7 (d) 8<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
The analogy is
like this: Arun has 10 lt of petrol and he uses 1 lt per each day and consumes
it in 10 days. If he uses 1.25 lt every day, in how many days it will be
consumed?</div>
<div class="MsoNormal" style="line-height: 150%;">
We considered
1.25 lt here because it’s 25% more than 1 lt.</div>
<div class="MsoNormal" style="line-height: 150%;">
The answer would
be 10/1.25=8 </div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(d)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">7</span>. A person can walk a certain distance and drive back
in 6 hrs. He can also walk both ways in 10 hrs. How much time will he take to
drive both ways?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Two
hours (b) Two and a half hours (c) Five and a half hours (d) Four hrs<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
2-way walk = 10
hrs => 1-way walk = 5 hrs</div>
<div class="MsoNormal" style="line-height: 150%;">
1-way walk +
1-way Drive = 6 hrs => 1-way drive = 6-5= 1 hr</div>
<div class="MsoNormal" style="line-height: 150%;">
Hence, 2-way
drive = 2 hrs </div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(a)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">8</span>. Consider the following matrix:</div>
<div class="MsoNormal" style="line-height: 150%;">
<o:p></o:p></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 47.95pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
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3<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
370<o:p></o:p></div>
</td>
<td style="border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
7<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
2<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
224<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
6<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
1<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
730<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
X</div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
What is the
number at X in the above matrix?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)5
(b) 8 (c) 9 (d) 11<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Consider 2<sup>nd</sup>
element in each row. Sum up the digits of each number. </div>
<div class="MsoNormal" style="line-height: 150%;">
3+7+0=10</div>
<div class="MsoNormal" style="line-height: 150%;">
2+2+4=8</div>
<div class="MsoNormal" style="line-height: 150%;">
7+3+0=10</div>
<div class="MsoNormal" style="line-height: 150%;">
Now re draw the
table like this:<o:p></o:p></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 51.0pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
3<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
10<o:p></o:p></div>
</td>
<td style="border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
7<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
2<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
8<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
6<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
1<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
10<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
X</div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
Now each row
follows this: sum of 1<sup>st</sup> and 3<sup>rd</sup> elements is equal to 2<sup>nd</sup>
element.</div>
<div class="MsoNormal" style="line-height: 150%;">
1+X=10 => X =
9</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(c)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">9</span>. Examine the following three figures in which the
numbers follow a specific pattern:<o:p></o:p></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 41.7pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: 15.0pt; mso-row-margin-right: 1.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
84<o:p></o:p></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; height: 15.0pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="height: 15.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
81<o:p></o:p></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; height: 15.0pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="height: 15.0pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
88<o:p></o:p></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; height: 15.0pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border: none; mso-cell-special: placeholder;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
14<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
12<o:p></o:p></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; height: 15.0pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
18<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
9<o:p></o:p></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; height: 15.0pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<br /></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
?<o:p></o:p></div>
</td>
<td colspan="2" style="border: solid black 1.0pt; height: 15.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 49.0pt;" valign="bottom" width="65"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
11</div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
The missing
number (?) in the third figure above is</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)7
(b) 16 (c) 21 (d) 28<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Observe the
first two figures carefully:</div>
<div class="MsoNormal" style="line-height: 150%;">
2*(84/12)=14</div>
<div class="MsoNormal" style="line-height: 150%;">
2*(81/9)=18</div>
<div class="MsoNormal" style="line-height: 150%;">
Hence for the
third figure, 2*(88/11)=X=> X=2*8 => X=16 </div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(b)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">10</span>. Four
friends A,B,C and D distribute some money among themselves in such a manner
that A gets one less than B, C gets 5 more than D and D gets 3 more than B. Who
gets the smallest amount? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)A
(b) B (c) C (d) D<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
A=B-1 =>
B=A+1</div>
<div class="MsoNormal" style="line-height: 150%;">
C=D+5</div>
<div class="MsoNormal" style="line-height: 150%;">
D=B+3</div>
<div class="MsoNormal" style="line-height: 150%;">
If we see these
equations, we can find that - every one except A has got some thing more than
some other (+ indicates more than). So answer must not be B,C or D. So A is the
choice</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(a)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">11</span>. There are five hobby clubs in a college viz., photography,yachting,chess,electronics
and gardening. The gardening group meets every second day,the electronics group
meets every third day, the chess group meets every fourth day, the yachting
group meets every fifth day and the photography group meets every sixth day.
How many times do all the five groups meet on the same day with in 180 days? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)3
(b) 5 (c) 10 (d) 18<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
It's a simple
LCM problem. Find out LCM of 2,3,4,5 and 6. </div>
<div class="MsoNormal" style="line-height: 150%;">
It's 60. SO
every 60<sup>th</sup> day all the five groups meet. So in a period of 180 days
they meet thrice ie., on 60<sup>th</sup> day, 120<sup>th</sup> day and 180<sup>th</sup>
day.</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(a)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">12</span>. In a class of 45 students, a boy is ranked 20<sup>th</sup>
. When two boys joined, his rank was dropped by one. What is his new rank from
end? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)25<sup>th</sup> (b) 26<sup>th</sup> (c) 27<sup>th</sup> (d) 28<sup>th</sup> <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
After two boys
are added the class strength become 47. </div>
<div class="MsoNormal" style="line-height: 150%;">
The boy's rank
is dropped by one => his rank becomes 21<sup>st</sup> </div>
<div class="MsoNormal" style="line-height: 150%;">
=> There are
47-21=26 below his rank </div>
<div class="MsoNormal" style="line-height: 150%;">
=> He is
ranked 27<sup>th</sup> from end</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(c)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">13</span>. A thief running at 8km/hr is chased by a policeman
whose speed is 10km/hr. If the thief is 100m ahead of policeman, then the time
required for the policeman to catch the thief will be? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)2
(b) 3 (c) 4 (d) 6<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
If we consider
the difference of speeds, policeman is at 2 km/hr leading speed and hence he
can catch the thief at 100m ahead by 100m/2kmph = 100/2000 hr = 3 min</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(b)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">14</span>. A train travels at a certain average speed for a
distance of 63 km and then travels a distance of 72 km at an average speed of 6
km/hr more than its original speed. If it takes 3 hours to complete the total
journey, what is the original speed of the train in km/hr? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)24
(b) 33 (c) 42 (d) 66<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let the original
speed be ‘S’.</div>
<div class="MsoNormal" style="line-height: 150%;">
Total time taken
= 3 hr => 63/S + 72/S+6 = 3</div>
<div class="MsoNormal" style="line-height: 150%;">
Let us try with
answer options. As we have 63 in the numerator, we can assume that S may be a
multiple of 7. The only option available
is 4. So, let us try with that.</div>
<div class="MsoNormal" style="line-height: 150%;">
63/42 + 72/48 =
3/2 + 3/2 = 3 => this suits</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(c)</span><span style="color: red;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">15</span>. Four cars are hired at the rate of Rs 6 per km
plus the cost of diesel at Rs 40 a litre. In this context, consider the details
given in the following table:<o:p></o:p></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 86.75pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr style="height: 45.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td style="border-right: none; border: solid black 1.0pt; height: 45.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.4pt;" valign="top" width="62"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
Car<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 45.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.9pt;" valign="top" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
Mileage (km/l)<o:p></o:p></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; height: 45.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.2pt;" valign="top" width="63"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
Hours<o:p></o:p></div>
</td>
<td style="border: solid black 1.0pt; height: 45.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 51.0pt;" valign="top" width="68"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
Total Payment (Rs)<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.4pt;" valign="top" width="62"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
A<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.9pt;" valign="top" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
8<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.2pt;" valign="top" width="63"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
20<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 51.0pt;" valign="top" width="68"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
2120<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.4pt;" valign="top" width="62"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
B<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.9pt;" valign="top" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
10<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.2pt;" valign="top" width="63"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
25<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 51.0pt;" valign="top" width="68"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
1950<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.4pt;" valign="top" width="62"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
C<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.9pt;" valign="top" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
9<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.2pt;" valign="top" width="63"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
24<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 51.0pt;" valign="top" width="68"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
2064<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.4pt;" valign="top" width="62"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
D<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.9pt;" valign="top" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
11<o:p></o:p></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 47.2pt;" valign="top" width="63"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
22<o:p></o:p></div>
</td>
<td style="border-top: none; border: solid black 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-right-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 51.0pt;" valign="top" width="68"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
1812</div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
</div>
<div class="MsoNormal" style="line-height: 150%;">
Which car
maintained the maximum speed?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
Car A (b) Car B (c) Car C (d) Car D<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let the
distances travelled by cars A,B,C and D be a,b,c and d respectively.</div>
<div class="MsoNormal" style="line-height: 150%;">
Then, total payment for car A = 6a+40(a/8) =
11a=2120 => a=2120/11</div>
<div class="MsoNormal" style="line-height: 150%;">
It is mentioned
that car A travels for 20 hr</div>
<div class="MsoNormal" style="line-height: 150%;">
=> The
average speed of A= a/20 = 2120/11*20 = 106/11 > 9</div>
<div class="MsoNormal" style="line-height: 150%;">
Equation for B: 6b+40(b/10)=1950 => b=195</div>
<div class="MsoNormal" style="line-height: 150%;">
=> The
average speed of B= b/25 = 195/25 = 39/5=7.8 </div>
<div class="MsoNormal" style="line-height: 150%;">
Equation for C:
6c+40(c/9)=2064 => c=9*1032/47</div>
<div class="MsoNormal" style="line-height: 150%;">
=> The
average speed of C= c/24 = 9*43/47 < 9 </div>
<div class="MsoNormal" style="line-height: 150%;">
Equation for D:
6d+40(d/11)=1812 => d=11*906/53</div>
<div class="MsoNormal" style="line-height: 150%;">
=> The
average speed of D= d/22 = 453/53 < 9 </div>
<div class="MsoNormal" style="line-height: 150%;">
All speeds
except for A are less than 9 where as seed for A is greater than 9 and hence
it’s the greatest value.</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #0070c0;">(a)</span><span style="color: #b80047;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #b80047;">16</span>. The music director of a film wants to select
four persons to work on different aspects of the composition of a piece of
music. Seven persons are available for this work; they are Rohit,Tanya,Shobha,Kaushal,Kunal,Mukesh
and Jaswant. Rohit and Tanya will not work together. Kunal and Shobha will not
work together. Mukesh and Kunal want to work together.</div>
<div class="MsoNormal" style="line-height: 150%;">
Which of the
following is the most acceptable group of the people that can be selected by
the music director? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Rohit,Shobha,Kunal
and Kaushal</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)Tanya,
Kaushal,Shobha and Rohit</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)Tanya,Mukesh,Kunal and Jaswant</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)Shobha,Tanya,Rohit and Mukesh <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:</u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let us check the
answer options one by one.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) is
not possible as Shobha and Kunal shall not work together</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (b) is
not possible as Rohit and Tanya shall not work together</div>
<div class="MsoNormal" style="line-height: 150%;">
Option
(d) is not possible as Rohit and Tanya shall not work together </div>
<div class="MsoNormal" style="line-height: 150%;">
Hence
we shall go with option (c)</div>
<div class="MsoNormal" style="line-height: 150%;">
Ans: <span style="color: #004586;">(c)</span><span style="color: #b80047;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #b80047;">17</span>. Geeta is older than her cousin Meena. Meena's
brother Bipin is older than Geeta. When Meena and Bipin visit Geeta they want
to play chess. Meena wins the game more than Geeta. Based on the above
information, four conclusions as given below, have been made. Which one of
these logically follows from the information given above? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)While
playing chess with Geeta and Meena, Bipin often loses</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)Geeta
is the oldest among the three</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)Geeta hates to lose the game</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)Meena
is the youngest of the three <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let us try to
write the given conditions in the form of equations:</div>
<div class="MsoNormal" style="line-height: 150%;">
Geeta is older
than her cousin Meena => G > M</div>
<div class="MsoNormal" style="line-height: 150%;">
Meena's brother
Bipin is older than Geeta => B > G</div>
<div class="MsoNormal" style="line-height: 150%;">
From these two
we can easily say that B > G > M => Bipin is eldest and Meena is
youngest among the three. So we can take option (d) as right option. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)</span><span style="color: #002060;"><o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #b80047;">18</span>. A,B,C,D and E belong to five different cities
P,Q,R,S and T (not necessarily in that order). Each one of them comes from a
different city. Further it is given that:</div>
<div class="MsoNormal" style="line-height: 150%;">
1. B and C do
not belong to Q</div>
<div class="MsoNormal" style="line-height: 150%;">
2. B and E do
not belong to P and R</div>
<div class="MsoNormal" style="line-height: 150%;">
3. A and C do
not belong to R,S and T</div>
<div class="MsoNormal" style="line-height: 150%;">
4. D and E do
not belong to Q and T</div>
<div class="MsoNormal" style="line-height: 150%;">
Which one of the
following statement is not correct? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)C
belongs to P</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
D belongs to R</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c) A belongs to Q</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
B belongs to S <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
From the first
two conditions it is clear that, B does not belong to P,Q and R => B belongs
to either S or T</div>
<div class="MsoNormal" style="line-height: 150%;">
From the first
and third conditions it is clear that, C does not belong to Q,R,S and T => C
belongs to P</div>
<div class="MsoNormal" style="line-height: 150%;">
From the second
and fourth conditions it is clear that, E does not belong to P,Q,R and T =>
E belongs to S</div>
<div class="MsoNormal" style="line-height: 150%;">
=> B belongs
to T</div>
<div class="MsoNormal" style="line-height: 150%;">
=> Answer
option (d) is wrong</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #b80047;">19</span>. Seven men A,B,C,D,E,F and G are standing in a
queue in that order. Each one is wearing a cap of different colour like
violet,indigo,blue,green,yellow,orange and red. D is able to see in front of
him green and blue, but not violet. E can see violet and yellow but not red. G
can see caps of all colours other than orange. If E is wearing an indigo
coloured cap, then the colour of cap worn by F is </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Blue
(b)Violet (c) Red (d) Orange <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Order: A,B,C,D,E,F, G</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>The point is</b> – A person can see caps of
all persons standing in front of him but can’t see his own cap and caps of
persons standing behind him.</div>
<div class="MsoNormal" style="line-height: 150%;">
D is able to see
in front of him green and blue, but not violet => The people in front of D
ie., A or B or C worn green or blue and people after D and including himself
ie., D or E or F or G worn violet</div>
<div class="MsoNormal" style="line-height: 150%;">
E can see violet
and yellow but not red => From this and above statements, we can fix violet
cap for D. and A/B/C worn green/blue/yellow not necessarily in that order</div>
<div class="MsoNormal" style="line-height: 150%;">
G can see caps
of all colours other than orange => As he is the last person in the row, he
can see all caps except his. So we can fix Orange cap for G</div>
<div class="MsoNormal" style="line-height: 150%;">
Given that E
wears indigo cap.</div>
<div class="MsoNormal" style="line-height: 150%;">
The summary is:</div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 84.0pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 191px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b>Person<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 95.0pt;" valign="bottom" width="127"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
<b>Cap<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
A/B/C<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 95.0pt;" valign="bottom" width="127"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
green/blue/yellow<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
D<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 95.0pt;" valign="bottom" width="127"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
violet<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
E<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 95.0pt;" valign="bottom" width="127"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
indigo<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
G<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 95.0pt;" valign="bottom" width="127"><div class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: justify;">
orange<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
Finally, we are
left with red cap and so we can fix this to F</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #b80047;">20</span>. There are some balls of red,green and yellow
colour lying on a table. There are as many red balls as there are yellow balls.
There are twice as many yellow balls as there are green ones. The number of red
balls </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)is
equal to the sum of yellow and green balls</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)is
double the number of green balls</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
is equal to yellow balls minus green balls</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)cannot
be ascertained <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Let us write as
equations:</div>
<div class="MsoNormal" style="line-height: 150%;">
R=Y and Y=2G
=> R=2G</div>
<div class="MsoNormal" style="line-height: 150%;">
=> The number
of red balls is equal to double the number of green balls</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Directions for the following 4 items:<o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Read the
following statements and answer the four items that follow:</div>
<div class="MsoNormal" style="line-height: 150%;">
Five cities
P,Q,R,S and T are connected by different modes of transport as follows:</div>
<div class="MsoNormal" style="line-height: 150%;">
P and Q are
connected by boat as well as rail.</div>
<div class="MsoNormal" style="line-height: 150%;">
S and R are
connected by bus and boat.</div>
<div class="MsoNormal" style="line-height: 150%;">
Q and T are
connected by air only.</div>
<div class="MsoNormal" style="line-height: 150%;">
P and R are
connected by boat only.</div>
<div class="MsoNormal" style="line-height: 150%;">
T and R are connected
by rail and bus.</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">21</span>. Which mode of transport would help one to reach R
starting from Q, but without changing the mode of transport?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Boat
(b)Rail (c) Bus (d) Air <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
We have the
following transport options:</div>
<div class="MsoNormal" style="line-height: 150%;">
Q to P and P to
R: Here boat is a common mode of transport and this seems to be the correct
answer. But let us check the other transportation.</div>
<div class="MsoNormal" style="line-height: 150%;">
Q to T and T to
R : Here Q and T are connected by air only and T and R are connected by rail
and bus To make a complete trip there is no single mode of transport. So, this option is ruled out.</div>
<div class="MsoNormal" style="line-height: 150%;">
Here we have
only one rout Q-P-R which has a single mode of transportation ie., Boat </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">22</span>. If a person visits each of the places starting
from P and gets back to P, which of the following places must he visit twice?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Q
(b)R (c) S (d) T <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
With the given
options, we have the following two possibilities:</div>
<div class="MsoNormal" style="line-height: 150%;">
P -> Q ->
T -> R -> S -> R -> P </div>
<div class="MsoNormal" style="line-height: 150%;">
P -> R ->
S -> R -> T -> Q -> P </div>
<div class="MsoNormal" style="line-height: 150%;">
In both the
cases, R should be visited twice. (This is because, S is connected only to R)</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">23</span>. Which one of the following pairs of cities is
connected by any of the routes directly without going to any other city?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)P
and T (b)T and S (c) Q and R (d) None of these <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
None of the
cities in the given pairs (in options A,B and C) are directly connected. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">24</span>. Between which two cities among the pairs of cities
given below are there maximum travel options available?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Q
and S (b)P and R (c) P and T (d) Q and R <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Q and S: <o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Q -> T ->
R -> S : For Q to T we have air mode. For T to R we have rail/bus and for R
to S, we have bus/boat => all the options available are air,rail,bus and
boat. Here we have all modes of options and hence this is the correct answer.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Directions for the following 3 (three)
items:<o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Read the
following statements and answer the three items that follow:</div>
<div class="MsoNormal" style="line-height: 150%;">
A tennis coach
is trying to put together a team of four players for the forthcoming
tournament. For this 7 players are available: males A,B and C; and females
W,X,Y and Z. All players have equal capability and at least two males will be
there in the team. For a team of four, all players must be able to play with
each other. But B cannot play with W, C cannot play with Z and W cannot play
with Y. </div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">25</span>. If Y is selected and B is rejected, the team will
consist of which one of the following groups?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)A,C,W
and Y (b) A,C,X and Y (c) A,C,Y and Z (d) A,W,Y and Z <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
If Y is
selected, W shall not be selected. So options (a) and (d) are out. As C cannot
play with Z, option (c) is also out.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">26</span>. If B is selected and Y is rejected, the team will
consist of which one of the following groups?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)A,B,C
and W (b) A,B,C and Z (c) A,B,C and X (d) A,W,Y and Z <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
If B is
selected, W shall not be selected. So options (a) and (d) are out. As C cannot
play with Z, option (b) is also out.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">27</span>. If all the three males are selected, then how many
combinations of four member teams are possible?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)1
(b) 2 (c) 3 (d) 4 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
If males A,B,C
are selected, we need to select only one more person to make up a four member
team. </div>
<div class="MsoNormal" style="line-height: 150%;">
As B is
selected, W cannot be selected and as C is selected, Z cannot be selected. So
the choice is between X and Y. Then we can have the following possibilities:</div>
<div class="MsoNormal" style="line-height: 150%;">
(A,B,C,X) or
(A,B,C,Y) . SO we have two options of teams.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Directions for the following 3 (three)
items:<o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Examine
carefully the following statements and answer the three items that follow:</div>
<div class="MsoNormal" style="line-height: 150%;">
Out of four
friends A,B,C and D,</div>
<div class="MsoNormal" style="line-height: 150%;">
A and B play
football and cricket,</div>
<div class="MsoNormal" style="line-height: 150%;">
B and C play
cricket and hockey,</div>
<div class="MsoNormal" style="line-height: 150%;">
A and D play
basketball and football,</div>
<div class="MsoNormal" style="line-height: 150%;">
C and D play
hockey and basketball.</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">28</span>. Who does not play hockey? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)D
(b) C (c) B (d) A <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Just check the
sentences containing hockey. </div>
<div class="MsoNormal" style="line-height: 150%;">
B and C play
cricket and hockey, C and D play hockey and basketball => B,C and D play
hockey</div>
<div class="MsoNormal" style="line-height: 150%;">
=> A does not
play hockey </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">29</span>. Who plays football, basketball and hockey? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)D
(b) C (c) B (d) A <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Just check individually
(player wise). </div>
<div class="MsoNormal" style="line-height: 150%;">
A plays
football, cricket and basketball</div>
<div class="MsoNormal" style="line-height: 150%;">
B plays
football, cricket and hockey</div>
<div class="MsoNormal" style="line-height: 150%;">
C plays cricket,
hockey and basketball</div>
<div class="MsoNormal" style="line-height: 150%;">
D plays
basketball, football and hockey</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">30</span>. Which game do B,C and D play? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)Basketball
(b) Hockey (c) Cricket (d) Football <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Check these two:</div>
<div class="MsoNormal" style="line-height: 150%;">
B and C play
cricket and hockey</div>
<div class="MsoNormal" style="line-height: 150%;">
C and D play hockey
and basketball</div>
<div class="MsoNormal" style="line-height: 150%;">
=> B,C and D
play hockey</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">31</span>. Consider
the following statements:</div>
<div class="MsoNormal" style="line-height: 150%;">
(1)A primary
group is relatively smaller in size. </div>
<div class="MsoNormal" style="line-height: 150%;">
(2) Intimacy is an essential characteristic of
a primary group.</div>
<div class="MsoNormal" style="line-height: 150%;">
(3) A family may
be an example of a primary group</div>
<div class="MsoNormal" style="line-height: 150%;">
In the light of
above statements, which one of the following is true?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)All
families are primary groups</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
All primary groups are families</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
A group of smaller size is always a primary group</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
Members of a primary group are known each other intimately <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Avoid sharp
conclusions.</div>
<div class="MsoNormal" style="line-height: 150%;">
(a), (b) and (c)
are sharp conclusions. It cannot be concluded either all primary groups are
families or all families are primary groups. Characteristic of a Primary group
is intimacy and it may not be a characteristic of a family. Similarly, a group
of small size may not guarantee intimacy and hence may not be a Primary group.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (d)
reiterates the essential characteristic of a primary group and hence is the
correct option.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="color: #004586;">English Passage
–1<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Seven
year old Jim came home from the park without his new bicycle. “An old man and a
little boy borrowed it”, he explained. “They are going to bring it back at four
o’clock.” His parents were upset that he has given his expensive new bicycle,
but were secretly proud of his kindness and faith. Came four o’clock, no
bicycle. The parents were anxious. But at 4:30, the door bell rang, and there
stood a happy man and a boy, with a bicycle and a box of chocolates. Jim
suddenly disappeared in to bed room, and then came running out. “All right” he
said after examining the bicycle. “You can have your watch back!”</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">32</span>. When Jim came home without his bicycle, his
parents</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) were angry with him.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
were worried.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
did not feel concerned.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
were eager to meet the old man and the little boy. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
The given
options are easy to eliminate.</div>
<div class="MsoNormal" style="line-height: 150%;">
When Jim came
home without bicycle, his parents were not angry with him, but they are worried
that he has given his expensive bicycle.
Answer option (b) is correct. Options c and d are very easy to
eliminate.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">33</span>. Jim returned the watch to the old man and the
little boy because</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) they gave him chocolates.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
his father was proud of him.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
he was satisfied with the condition of his.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
they were late only by 30 minutes. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
“All right” he
said after examining the bicycle. “You can have your watch back!” => this is
implies that he is satisfied with the condition of bicycle and returned
the watch</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="color: #004586;">English Passage
–2<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
It
was already late when we set out for the next town, which according to the map
was about fifteen kilometers away on the other side of the hills. There we felt
that we would find a bed for the night. Darkness fell soon after we left the
village but luckily we met no one as we drove swiftly along the narrow winding
road that led to the hills. As we climbed higher, it became colder and rain
began to fall, making it difficult at times to see the road. I asked John , my
companion to drive slowly. After we had travelled for about twenty kilometers,
there was still no sign of the town which was marked on the map. We were
beginning to get worried. Then without warning the car stopped and we found we
had run out of petrol. </div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">34</span>. The author asked John to drive more slowly because</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) the road led to the hills.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
John was an inexperienced driver. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
the road was not clearly visible.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
they were in wilderness. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
“As we climbed
higher, it became colder and rain began to fall, making it difficult at times
to see the road. I asked John , my companion to drive slowly.” => As ‘the
road was not clearly visible’, he asked John to drive slowly. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">35</span>. The travelers set out for the town although it was
getting dark because </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) they were in a hurry.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
the next town was a short distance away and was a hill resort. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
they were in wilderness.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
the next town was a short distance away and promised a good rest for the night.
<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
“There we felt
that we would find a bed for the night” => This sentence is hinting at
option (d) </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">36</span>. The travellers were worried after twenty
kilometers because </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) it was a lonely country side.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
they probably feared of having lost their way. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
the rain began to fall.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
it was getting colder as they drove. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
They anticipated
that next town is at 15 km away. But even after travelling 20 km, they could
not find traces of it. This suggests that their worry is because they were
feeling that they lost their way. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="color: #004586;">English Passage
–3<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
A
stout old lady was walking with her basket down the middle of a street in
Petrograd to the great confusion of traffic and no small peril of herself. It
was pointed out to her that the pavement was the place for foot-passengers, but
she replied, “I am going to walk where I like. We have got liberty now.” It did
not occur to the dear lady that if the liberty entitled the foot-passenger to
walk down the middle of the road, it also entitled the taxi driver to drive on
the pavement, and that the end of such liberty would be universal chaos.
Everything would be getting in everybody else’s way and nobody would get
anywhere. Individual liberty would have become social anarchy. </div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">37</span>. It was pointed out to the lady that she should
walk on the pavement because she was</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) a pedestrian.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
carrying a basket. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
stout.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
an old lady. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Pavement is for
pedestrians. As she is walking, she is pointed to use pavement. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">38</span>. The lady refused to move from the middle of the
street because</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) she was not afraid of being killed.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
she felt that she is entitled to do whatever she liked. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
she did not like walking on the pavement.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
she was confused. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
The tone of the
reply she gave suggests that she felt that she is entitled to do whatever she
liked.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) and
(c) cannot be considered as those were not exclusively mentioned and they
cannot be implied.</div>
<div class="MsoNormal" style="line-height: 150%;">
Coming to option
(d): Actually, it can be understood that, she was not confused but her walking
in the middle of the road had confused the traffic. So option (d) is also
wrong. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">39</span>. The old lady failed to realize that</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) she was not really free.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
her liberty was not unlimited. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
she was an old person.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
roads are made for motor vehicles only. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option (c) is
irrelevant. </div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) is
not correct as it is an extreme sentence. She is free to do any work but there
are limits in exercizing those works. </div>
<div class="MsoNormal" style="line-height: 150%;">
Option (d) looks
very particular, but most part of the passage suggests a general sense. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Direction for the following two(2) items:<o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Read the
following passage and answer the two items that follow Your answers to these
questions should be based on the passage only.</div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Crude
mineral oil comes out of the earth as a thick brown or black liquid with a
strong smell. It is a complex mixture of many different substances, each with
its own individual qualities. Most o them are combinations of Hydrogen and
Carbon in varying proportions. Such hydrocarbons are also found in other forms
such as Bitumen, Asphalt and natural gas. Mineral oil originates from the carcasses
of tiny animals and plants that live in the sea. Over millions of years, these
dead creatures form large deposits under the sea bed; and ocean currents cover
them with a blanket of sand and silt. As this mineral hardens, it becomes
sedimentary rock and effectively shut out the oxygen, so preventing the
complete decomposition of the marine deposits underneath. The layers of
sedimentary rock become thicker and heavier. Their pressure produces heat,
which transforms the tiny carcasses in to crude oil in a process that is still
going on today.</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">40</span>. Mineral oil deposits under the sea do not get
completely decomposed because they</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) are constantly washed by the ocean
currents.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
become rock and prevent oxygen from entering them. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
contain a mixture of hydrogen and carbon.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
are carcasses of organisms lying in saline conditions. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
”As this mineral
hardens, it becomes sedimentary rock and effectively shut out the oxygen, so
preventing the complete decomposition of the marine deposits underneath.” => as per this quote from the passage, we
can choose option (b)</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">41</span>. Sedimentary rock leads to the formation of oil
deposits because</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) there are no saline conditions below it.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
it allows some dissolved oxygen to enter the dead organic matter below it. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
weight of overlying sediment layers causes the production of heat.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in;">
(d)
it contains the substances that catalyze the chemical reactions required to
change the dead organisms into oil. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
” The layers of
sedimentary rock become thicker and heavier. Their pressure produces heat,
which transforms the tiny carcasses in to crude oil in a process that is still
going on today.” => as per this quote
from the passage, we can choose option (c)</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">42</span>. Five people A,B,C,D and E are seated about a round
table. Every chair is spaced equidistant from adjacent chairs.</div>
<div class="MsoNormal" style="line-height: 150%;">
(i) C is seated
next to A</div>
<div class="MsoNormal" style="line-height: 150%;">
(ii) A is seated
2 seats from D</div>
<div class="MsoNormal" style="line-height: 150%;">
(iii) B is not
seated next to A</div>
<div class="MsoNormal" style="line-height: 150%;">
Which of the
following must be true?</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.75in; text-indent: -0.5in;">
<!--[if !supportLists]-->(I)<span style="font-size: 7pt; line-height: normal;">
</span><!--[endif]-->D is seated next to B</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.75in; text-indent: -0.5in;">
<!--[if !supportLists]-->(II)<span style="font-size: 7pt; line-height: normal;">
</span><!--[endif]-->E is seated next to A</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
Select the correct answer from the codes given below:</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) I only (b) II only (c) Both I and II (d) Neither
I nor II <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Draw a circle
and try out positions.</div>
<div class="MsoNormal" style="line-height: 150%;">
If I translate
the circular positions in to linear, the following are the two possibilities:</div>
<div class="MsoNormal" style="line-height: 150%;">
CAEDB (or) ACBDE</div>
<div class="MsoNormal" style="line-height: 150%;">
In both the
cases, D is placed next to B. And this is true for A and E (even though, it
won’t look like that, it is evident if we translate CAEDB or ACBDE in to
circular positions)</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Direction for the following two(2) items:<o:p></o:p></b></div>
<div class="MsoNormal" style="line-height: 150%;">
Read the
following passage and answer the two items that follow. Your answers to these
items should be based on the passage only.</div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Ecological
research over the last quarter of the century has established the deleterious
effects of habitat fragmentation due to the mining, highways and such other
intrusions on forests. When a large block of forests gets fragmented into
smaller bits, the edges of all these bits come into contact with human
activities resulting in the degradation of the entire forests. Continuity of
forested landscapes and corridors gets disrupted affecting several extinction
prone species of wild life. Habitat fragmentation is therefore considered as
the most serious threat to biodiversity conservation. Ad hoc grants of forest
lands to mining companies coupled with rampant illegal mining is aggravating
this threat. </div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">43</span>. What is the central focus of the passage?</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) Illegal mining in forests</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
Extinction of wild life </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
Conservation of nature</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
Disruption of habitat <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
The essence of
the passage is:</div>
<div class="MsoNormal" style="line-height: 150%;">
Due to some
activities like mining, highways etc, there is disruption in landscapes and
corridors. This is affecting several species of wild life.</div>
<div class="MsoNormal" style="line-height: 150%;">
The central
theme may be “disruption of habitat” </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">44</span>. What is the purpose of maintaining the continuity
of forested landscapes and corridors?</div>
<div class="MsoNormal" style="line-height: 150%;">
1. Preservation of biodiversity</div>
<div class="MsoNormal" style="line-height: 150%;">
2. Management of mineral sources</div>
<div class="MsoNormal" style="line-height: 150%;">
3. Grant of forest lands for
human activities</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) 1
only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
1 and 2 </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
2 and 3</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
1,2 and 3 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option 2 is out
of the scope of the passage. Option 3 has a negative tinge where as the
maintaining of the continuity of forested landscapes and corridors is for a
good purpose. Option 1 only is correct. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)</span></b> </div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage-3<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Malnutrition
most commonly occurs between the ages of six months and two years. This happens
despite the child’s food requirements being less than that of an older child.
Malnutrition is often attributed to poverty, but it has been found that even in
households where adults eat adequate quantities of food, more than fifty
percent of children-under-five do not consume enough food. The child’s
dependence on someone else to feed him/her is primarily responsible for the
malnutrition. Very often the mother is working and the responsibility of
feeding the young child is left to an older sibling. It is therefore crucial to
increase awareness regarding the child’s food needs and how to satisfy them.</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">45</span>. According to the passage, malnutrition in children
can be reduced </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
if the children have regular intakes of food</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
after they cross the age of five </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
if the food needs of younger children are known</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
if the responsibility of feeding younger children is given to adults <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
It is no where
mentioned that malnutrition can be reduced after age of five. So option (b) can
be avoided.</div>
<div class="MsoNormal" style="line-height: 150%;">
Even if the
children have regular intakes, it may not suffice. The quantity and quality of
food may be more important. Option (a) can be avoided.</div>
<div class="MsoNormal" style="line-height: 150%;">
No where it is
suggested that the responsibility of younger children shall be given to adults.
So answer option (d) can be avoided.</div>
<div class="MsoNormal" style="line-height: 150%;">
“It is therefore crucial to increase awareness
regarding the child’s food needs and how to satisfy them” => this sentence
of the passage hints at answer option (c). </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">46</span>. According to the author, poverty is not the main
cause of malnutrition, but the fact that</div>
<div class="MsoNormal" style="line-height: 150%;">
1. taking care of younger ones
is not a priority for working mothers.</div>
<div class="MsoNormal" style="line-height: 150%;">
2. awareness of nutritional needs
is not propagated by the public health authorities</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Select
the correct answer using the code given below:</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
1 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
2 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
Both 1 and 2</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
Neither 1 nor 2 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Both the given
options 1 and 2 are extreme and derogatory and are no where hinted in the
passage.</div>
<div class="MsoNormal" style="line-height: 150%;">
There is no mention about Public Health
authorities in the passage and hence option (2) can be straight away rejected.</div>
<div class="MsoNormal" style="line-height: 150%;">
It is mentioned
that “Very often the mother is working and the responsibility of feeding the
young child is left to an older sibling” => This does not mean that “taking
care of younger ones is not a priority for working mothers”. In this way it is
an extreme statement and hence option(2) can also be avoided.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">47</span>. You are the head of your office. There are certain
houses reserved for the allotment to the office staff and you have been given
the direction to do so. A set of rules for the allotment of houses has been
laid down by you and has been made public. Your personal secretary who is very
close to you, comes to you and pleads that as his father is seriously ill, he
should be given priority in allotment of a house. The office secretariat that
examined the request as per the rules turns down the request and recommends the
procedure to be followed according to the rules. You do not want to annoy your
personal secretary. In such circumstances, what would you do? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(a) Call him over to your room and personally explain why the allotment
cannot be done.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(b) Allot the house to him to win his loyalty.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) Agree with the office note to show that you are not biased and that
you do not indulge in favouritism.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(d) Keep the file with you and not pass any orders. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option (d) can’t
be selected as it shows indecisiveness.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (b) can’t
be selected as it leads to totally against to the rules.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option(c)
suggests the straight-forward procedure. But as it is mentioned not to annoy
the personal secretary, it is better to personally explain him, why can’t the
allotment be made to him. This little personal attention is not wrong and it
will help to clear the air. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">48</span>. While travelling in a Delhi-registered commercial
taxi from Delhi to an adjacent city (another state), your taxi driver informs
you that as he has no permit for running the taxi in that city, he will stop at
its transport office and pay the prescribed fee of Rs forty for a day. While
paying the fee at the counter you find that the transport clerk is taking an
extra fifty rupees for which no receipt is being given. You are in a hurry for
your meeting. In such circumstances, what would you do? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(a) Go up to the counter and ask the clerk to give back the money which
he has illegally taken.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(b) Do not interfere at all as this is a matter between the taxi driver
and the tax authorities.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) Take note of the incident and subsequently report the matter to the
concerned authorities.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(d) Treat it as a normal affair and simply forget about it. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Options (b) and
(d) can’t be selected as it shows irresponsibility on part of a citizen.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) can’t
be selected as it is mentioned that you are in hurry to attend a meeting and
may not take risk of wasting time as it may lead to an argument etc.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option(c) is
suitable option. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">49</span>. A person lives in a far off village which is
almost two hours by bus. The villagers neighbor is a very powerful landlord who
is trying to occupy the poor villager’s land by force. You are the district
magistrate and busy in a meeting called by a local minister. The villager has
come all the way, by bus and by foot, to see you and give an application
seeking protection from the powerful landlord. The villager keeps on waiting
outside the meeting hall for an hour. You come out of the meeting and are
rushing to another meeting. The villager follows you to submit his application.
What would you do? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(a) Tell him to wait for another two hours till you come back from your
next meeting.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(b) Tell him that the matter is actually to be dealt by a junior officer
and that he should give the application to him.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) Call one of your senior subordinate officers and ask him to solve the
villager’s problem.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(d) Quickly take the application from him, ask him a few relevant
questions regarding his problem and then proceed to the meeting. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Direct interaction with the villager may be
more soothing to him and hence options (b) and (c) are ruled out. Option (a)
can also be avoided as it makes further inconvenience to the villager.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">50</span>. There is a shortage of sugar in your district
where you are the district Magistrate. The government has ordered that only a
maximum amount of 30 kg sugar is to be released for wedding celebrations. A son
of your close friend is getting married and your friend requests you to release
at least 50 kg sugar for his son’s wedding. He expresses annoyance when you
tell him about the Government’s restrictions on this matter. He feels that since
you are the district magistrate you can release any amount. You do not want to
spoil your friendship with him. In such circumstances how would you deal with
the situation? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
(a) Release the extra amount of sugar which your friend has requested for.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(b) Refuse your friend the extra amount and strictly follow the rules.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) Show your friend the copy of the Government instructions and then
persuade him to accept the lower amount as prescribed in the rules.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(d) Advise him to directly apply to the allotting authority and inform
him that you do not interfere in this matter. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution: <o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is similar
to the question on “allotment of houses” (Q.47). </div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) is
ruled out as it is against the rules.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (b) is a
straight-forward approach but is ruled out as it is a harsh way to deal with as
you do not want to spoil relationship with your friend. Option (d) also looks a
bit harsh and indicates that you are running away from the problem. Option (c) looks more appropriate. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">51</span>. You are in-charge of implementing the Family
Planning Programme in an area where there is a strong opposition to the present
policy. You want to convince the residents of the need for keeping small
families. What would be the best way of
communicating this message?</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(a) By logically explaining to the residents the need for family planning
to improve the health and living standards.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(b) By encouraging late marriages and proper spacing of children.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) By offering incentives for adopting family planning devices.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(d) By asking people who have been sterilized or are using contraceptives
to directly talk to the residents. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution: <o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
The point here
is to convince the residents for keeping small families. Options (b) and (c)
are not about the methods to convince but rather these are methods for
implementation. Option (d) may be useful as a supporting method but not as a
direct method for convincing. </div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) looks
more suitable option. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">52</span>. You are a teacher in a university and are setting
a question paper on a particular subject. One of your colleagues whose son is
preparing for the examination on that subject, comes to you and informs you
that it is his son’s last chance to pass that examination and whether you could
help him by indicating what questions are going to be in the examination. In
the past your colleague has helped you in another matter. Your colleague
informs you that his son will suffer from depression if he fails in the
examination. In such circumstances, what would you do?</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(a) In view of the help he had given you, extend your help to him.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(b) Regret that you cannot be of any help to him.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(c) Explain to your colleague that this would be violating the trust of
the university authorities and you are not in a position to help him.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
(d) Report the conduct of your colleague to the higher authorities. <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution: <o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option (a) is
out of question as it is a violation of conduct rules. Option (b) is straight
forward but little rude given the sensitivities involved and hence may be
avoided. </div>
<div class="MsoNormal" style="line-height: 150%;">
Option (c) looks
more suitable option.</div>
<div class="MsoNormal" style="line-height: 150%;">
Option (d) is
not the immediate solution given the sensitivities involved. It may be used
only if you are very much compiled to commit a mistake. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Financial
markets in India have acquired greater depth and liquidity over the years.
Steady reforms since 1991 have led to growing linkages and its financial system
with the global economy. Weak global economic prospects and continuing
uncertainties in the international financial markets therefore, have had their
impact on the emerging market economies. Sovereign risk concerns particularly
in the Euro area, affected financial markets for the greater part of the year
with contagion of Greece’s sovereign debt problem spreading to India and other
economies by way of higher-than-normal levels of volatility. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
The
funding constraints in international financial markets could impact both the
availability and cost of foreign funding for banks and corporates. Since the
Indian financial system is bank dominated , banks ability to withstand stress
is critical to overall financial stability. Indian banks, however remains
robust, not withstanding a decline in capital to risk weighed assets ratio and
a raise in nonperforming asset levels in the recent past. Capital adequancy
levels remain above the regularity requirements. The financial market
infrastructure continues to function without any major disruption. With further
globalization, consolidation, deregulation and diversification of these
financial systems, the banking business may become more complex and riskier.
Issues like risk and liquidity management and enhancing skill therefore assume
greater significance.</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">53</span>. According to the passage, the financial markets in
the emerging market economies including India had the adverse impact in recent
years due to</div>
<div class="MsoNormal" style="line-height: 150%;">
1. Weak global economic prospects</div>
<div class="MsoNormal" style="line-height: 150%;">
2. Uncertainties in the international
financial markets</div>
<div class="MsoNormal" style="line-height: 150%;">
3. Sovereign
risk concerns in the Euro area.</div>
<div class="MsoNormal" style="line-height: 150%;">
4. Bad monsoons and the resultant crop
loss</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Select
the correct answer using the code given below:</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
1 & 2 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
1, 2 and 3 </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
2 & 3 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
2, 3 and 4 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is a straight forward question. The
factors can be taken directly from lines 2 to 5 of 1<sup>st</sup> paragraph.
Option (4) is out of scope of the para and all other options are mentioned.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">54</span>. The Indian
financial markets are effected by global changes mainly due to the </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
Increased inflow of remittances from abroad </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
Enormous increase in the foreign exchange reserves</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
Growing global linkages and integration of the Indian financial markets</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
Contagion of Greece’s sovereign debt problem</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is again a straight forward question. </div>
<div class="MsoNormal" style="line-height: 150%;">
“Sovereign risk
concerns particularly in the Euro area, affected financial markets for the
greater part of the year with contagion of Greece’s sovereign debt problem
spreading to India and other economies by way of higher-than-normal levels of
volatility”=> this sentence of 1<sup>st</sup> para hints at answer option
(d) </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">55</span>. According
to the passage, in the Indian financial system, banks ability to withstand
stress is critical to ensure overall financial stability because Indian
financial system is </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
controlled by the Government of India</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
less integrated with banks</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
controlled by Reserve Bank of India</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)dominated
by banks</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is again a
straight forward question. </div>
<div class="MsoNormal" style="line-height: 150%;">
“Since the
Indian financial system is bank dominated , banks ability to withstand stress
is critical to overall financial stability”=> this sentence of 2<sup>nd</sup>
para hints at answer option (d) </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">56</span>. Risk and liquidity management assumes more
importance in the Indian banking system in future due to</div>
<div class="MsoNormal" style="line-height: 150%;">
1. further globalization</div>
<div class="MsoNormal" style="line-height: 150%;">
2. more consolidation and deregulation of
the financial system</div>
<div class="MsoNormal" style="line-height: 150%;">
3. further
diversification of the financial system</div>
<div class="MsoNormal" style="line-height: 150%;">
4. more financial inclusion in the economy</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Select
the correct answer using the code given below:</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
1, 2 & 3 </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
2, 3 & 4 </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
1 & 2 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d) 3 & 4 only<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is a
straight forward question. The factors can be taken directly from lines 6 to 8
of 2<sup>nd</sup> paragraph. Option (4) is out of scope of the para and all
other options are mentioned.<b><span style="color: #002060;"><o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage-4<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
A
number of empirical studies find that farmers are risk-averse, though only
moderately in many cases. There is also evidence to show that farmers’ risk
aversion results in cropping patterns and input use designed to reduce risk
rather than to maximize income. Farmers adopt a number of strategies to manage
and cope with agricultural risks. These include practices like crop and field
diversification, non-form employment, storage of stocks and strategic migration
of family members. These are also institutions ranging from share tenancy to
kinship, extended family and informal credit agencies. One major obstacle to
risk sharing by farmers is that the same type of risk can affect a large number
of farmers in the region. Empirical studies show that the traditional methods
are not adequate. Hence there is a need for policy interventions, especially
methods that cut across geographical regions.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
Policies
may aim at tackling agricultural risks directly or indirectly. Examples of
risk-specific policies are crop insurance, price stabilization and the
development of varieties resistant to pests and diseases. Policies which affect
risk indirectly are irrigation, subsidized credit and access to information. No
single risk specific policy is sufficient to reduce risk and is without side
effects, where as policies not specific to risk influence the general situation
and affect risks only indirectly. Crop
insurance as a policy measure to tackle agricultural risk directly, deserves
careful consideration in the Indian context and in many other developing
countries – because the majority of farmers depend on rain-fed agriculture and
in many areas yield variability is the predominant cause of their income
instability. <b><span style="color: #002060;"><o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">57</span>. The need for policy intervention to mitigate risks
in agriculture is because </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
farmers are extremely risk averse</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)farmers
do not know how to mitigate risks</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
the methods adopted by farmers and existing risk sharing institutions are not
adequate</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)majority
of farmers depend on rain-fed agriculture</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
This is a
straight forward question. </div>
<div class="MsoNormal" style="line-height: 150%;">
“Empirical
studies show that the traditional methods are not adequate. Hence there is a
need for policy interventions, especially methods that cut across geographical
regions”=> these last two lines of 1<sup>st</sup> para hints at answer
option (c) </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">58</span>. Which of the following observations emerge from
the above passage? </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a)
One can identify a single policy that can reduce risk without any side-effect.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)No
single risk-specific policy is sufficient to reduce agricultural risk.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
Policies which affect risk indirectly can eliminate it.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)Government’s
policy intervention can mitigate agricultural risk completely.</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
It’s again a straight forward one and the
answer can be directly taken from 4<sup>th</sup> line of 2<sup>nd</sup>
paragraph.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div align="center" class="MsoNormal" style="line-height: 150%; text-align: center;">
<b><span style="font-size: 12.0pt; line-height: 150%;">Passage-1<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
The law in many parts of the world
increasingly restricts the discharge of agricultural slurry in to water
courses. The simplest and most economically sound practice returns the material
to the land as semisolid manure or as sprayed slurry. This dilutes its concentration in the
environment to what might have occurred in a more primitive and sustainable
type of agriculture and converts pollutant into fertilizer. Soil microorganisms
decompose the organic components of sewage and slurry and most of the mineral
nutrients become available to be absorbed again by the vegetation.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
The
excess input of the nutrients, both nitrogen and phosphorus – based, from
agricultural runoff (and human sewage) has caused many ‘healthy’ oligotrophic
lakes (low nutrient concentrations, low plant productivity with abundant water
weeds, and clear water) to change to eutrophic condition where high nutrient
lead to high phytoplankton productivity (sometimes dominated by bloom-forming
toxic species). This makes the water turbid, eliminates large plants and, in
the worst situations, leads to anoxia and fish kills; so called cultural
eutrophication. Thus important ecosystem services are lost, including the
provisioning service of wild-caught fish and cultural service associated with
recreation. </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
The
process of cultural eutrophication of lakes has been understood for some time.
But only recently did scientists notice huge ‘dead zones’ in the oceans near
river outlets, particularly those draining large catchment areas such as
Mississippi and North America and the Yangtze in China. The nutrient enriched
water flows through streams, rivers and lakes and eventually to the estuary and
ocean where the ecological impact may be huge, killing virtually all
invertebrates and fish in areas up to 70,000 km<sup>2</sup> in extent. More than 150 sea areas worldwide
are now regularly starved of oxygen as a result of decomposition of algal
blooms, fuelled particularly by nitrogen from agricultural runoff of
fertilizers and sewage from large cities. Oceanic dead zones are typically
associated with industrialized nations and usually lie off countries that
subsidize their agriculture, encouraging farmers to increase productivity and
use more fertilizer. </div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">59</span>. According to the passage, why should the discharge
agricultural slurry into watercourses be restricted?</div>
<div class="MsoNormal" style="line-height: 150%;">
1. Losing nutrients in this way is not a
good practice economically.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
2. Water courses do not contain the microorganisms that
can decompose organic components of agricultural slurry.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
3. The discharge may lead to the eutrophication of water
bodies.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(a) 1 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
2 and 3 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
1 and 3 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
1,2 and 3 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
“The law in many
parts of the world increasingly restricts the discharge of agricultural slurry
in to water courses. The simplest and most economically sound practice returns
the material to the land as semisolid manure or as sprayed slurry”=> These
sentences from 1<sup>st</sup> paragraph hint that loosing the nutrients in this
way is not a good economical practice. So option (1) can be considered.</div>
<div class="MsoNormal" style="line-height: 150%;">
Options (2) and
(3) are evident from 2<sup>nd</sup> paragraph.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">60</span>. The passage refers to the conversion of “pollutant
to fertilizer”. What is the pollutant and what is the fertilizer in this
context?</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: 2.25pt;">
(a) Decomposed organic component of slurry is pollutant and
microorganisms in soil constitute fertilizer.</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
Discharged agricultural slurry is pollutant and decomposed slurry in soil is
fertilizer </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
Sprayed slurry is pollutant and watercourse is fertilizer</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
None of the above expressions is correct in this context <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option (b) is
easy to select. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">61</span>. According to the passage, what are the effects of
indiscriminate use of fertilizer? </div>
<div class="MsoNormal" style="line-height: 150%;">
1. Addition of pollutants to the soil
and water.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
2. Destruction of decomposer microorganisms in soil.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
3. Nutrient enrichment of water bodies.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
4. Creation of algal blooms.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: 2.25pt;">
(a) 1 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
1,3 and 4 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
2 and 4 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
1,2,3 and 4 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Option 2 ie.,
destruction of microorganisms is not mentioned anywhere in the passage whereas
all other options seem to be taken from the passage.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">62</span>. What is/are the characteristics of a water body
with cultural eutrophication? </div>
<div class="MsoNormal" style="line-height: 150%;">
1. Loss of ecosystem services.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
2. Loss of flora and fauna.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in;">
3. Loss of mineral nutrients.</div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: 2.25pt;">
(a) 1 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
1 and 2 only </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
2 and 3 only</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
1,2 and 3 <u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Options 1 and 2 seem
to be the characteristics of ‘cultural eutrophication‘. Option 1 can be taken
from para-2 and option 2 can be implied from para-3. Option 3 seems odd option
in this context.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">63</span>. Consider the following diagrams:</div>
<div class="MsoNormal" style="line-height: 150%;">
x men, working
at constant speed, do a certain job in y days. Which one of these diagrams
shows the relation between x and y?</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-J3EdWXqFTvQ/UbX2OvSbTtI/AAAAAAAAAkM/S5ddKfSbEdQ/s1600/csat2013.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-J3EdWXqFTvQ/UbX2OvSbTtI/AAAAAAAAAkM/S5ddKfSbEdQ/s320/csat2013.jpg" height="281" width="320" /></a></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: 2.25pt;">
(a) diagram I</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(b)
diagram II </div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(c)
diagram III</div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.5in;">
(d)
diagram IV<u><o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Logical
Explanation:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Diagram I:</b> Even if for zero x, there
exists some y. This means, even if there is no men, there exist some working
days, which is wrong.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Diagram II:</b> If x is increased y is also
increased here. This means if no.of men is increased then the no of working
days increased, which is wrong.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Diagram III:</b> This has two parts in it,
a vertical line and a horizontal line. Vertical line suggests infinite working
days for some number of workers, which is wrong. Horizontal line suggests, same
working days even if the no of men is increased/decreased which is also wrong.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Diagram IV: </b>This depicts the correct
relation. When no.of men increases, then no.of days decreases and vice versa.</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Mathematical
Explanation:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Here x and y are
inversely related. If x, the number of men increases, then, y, the number of
days for completing the work decreases => x α (1/y) => xy = constant
=> this is an equation of a rectangular hyperbola. Diagram IV resembles a hyperbola
and hence is the answer. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(d)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">64</span>. A cube has
six numbers marked 1, 2, 3, 4, 5 and 6 on its faces. Three views of the cube
are shown below:<o:p></o:p></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-paU0QQEWPH8/UbX1kjldHmI/AAAAAAAAAkA/4Yu0_Sf39t0/s1600/csat2013_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://3.bp.blogspot.com/-paU0QQEWPH8/UbX1kjldHmI/AAAAAAAAAkA/4Yu0_Sf39t0/s1600/csat2013_2.png" /></a></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #004586;"> </span></b><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 150%; text-indent: -0.25in;">(a)<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;">
</span></span><span style="font-family: Calibri, sans-serif; font-size: 11pt; line-height: 150%; text-indent: -0.25in;">2 and 3 (b) 6 and 1 (c) 1 and 4 (d) 3 and 1</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
If we check the
first two cubes, the common number 1 has numbers 4,6,2 and 3 on its four
adjacent faces. So the remaining number 5 is on the opposite face of 1. <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-symbol-font-family: Wingdings;">à</span>
(1)</div>
<div class="MsoNormal" style="line-height: 150%;">
Check the 4<sup>th</sup>
cube. Here we need to find two adjacent numbers of 5.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u>Method-I<o:p></o:p></u></b></div>
<div class="MsoNormal" style="line-height: 150%;">
From
statement(1), in other way, we can say that, 2,3,4 and 6 are the adjacent numbers
of 5. So out of all, answer option (a) has
correct combination.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u>Method-II<o:p></o:p></u></b></div>
<div class="MsoNormal" style="line-height: 150%;">
From the statement
(1) itself, we can eliminate three answer options. Number 1 should not be an
adjacent number of 5 because it is the opposite number of 5 (from statement
(1)) . So answer options (b),(c) and (d) can be eliminated as each of these
options have 1 as one of its two numbers. </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Direction for the following 5 (five) items:</b></div>
<div class="MsoNormal" style="line-height: 150%;">
Study the two
figures given below and answer the five items that follow:</div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-lNPrp2OGh_s/UbX1TDVbhgI/AAAAAAAAAjw/3Y4fQf7e2qk/s1600/csat2013_3_1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-lNPrp2OGh_s/UbX1TDVbhgI/AAAAAAAAAjw/3Y4fQf7e2qk/s1600/csat2013_3_1.png" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-rEiCAWBMFkI/UbX1ZMNU_JI/AAAAAAAAAj4/XTMA1DD7uIo/s1600/csat2013_3_2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-rEiCAWBMFkI/UbX1ZMNU_JI/AAAAAAAAAj4/XTMA1DD7uIo/s1600/csat2013_3_2.png" /></a></div>
<div class="MsoNormal" style="line-height: 150%;">
<img height="1" src="file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image002.jpg" style="line-height: 150%;" v:shapes="_x0000_i1025" width="1" /></div>
<div class="MsoNormal" style="line-height: 150%;">
<!--[if gte vml 1]><v:shape
id="_x0000_i1026" type="#_x0000_t75" style='width:.75pt;height:.75pt'>
<v:imagedata src="file:///C:\Users\ADMINI~1\AppData\Local\Temp\msohtmlclip1\01\clip_image003.jpg"
o:href="http://www.jagranjosh.com/imported/images/E/Articles/Figure2.JPG"/>
</v:shape><![endif]--><!--[if !vml]--><img height="1" src="file:///C:/Users/ADMINI~1/AppData/Local/Temp/msohtmlclip1/01/clip_image004.jpg" v:shapes="_x0000_i1026" width="1" /><!--[endif]--><o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">65</span>. How many Physics professors belong to the age
group 35 - 44?<br />
(a) 18 (b) 16 (c) 14 (d)
12</div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
From fig-2, we can say that 40% of Physics professors belong to the age
group 35-44. From fig-1, we can find that there are 32 male and 8 female
Physics professors. In total there are 40 Physics professors, out of which 40%
belong to 35-44 age group. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
40% 0f 40 = 16 </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">66</span>. Which one of the following disciplines has
the highest ratio of males to females?<br />
(a) Physics (b) Mathematics (c) Chemistry (d) Economics<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
Check answer options one by one for ratio of
males to females.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Physics:</b> Male:Female = 32:8 = 4:1 </div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Mathematics:</b> Male:Female = 28:8 = 7:2 =
3.5:1</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Chemistry:</b> Male:Female = 16:22 < 1
and hence can be eliminated (as it is asked for highest ratio)</div>
<div class="MsoNormal" style="line-height: 150%;">
<b>Economics:</b> Male:Female = 24:8 = 3:1 </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">67</span>. What percentage of all Psychology professors
are females?<br />
(a) 40% (b) 50% (c) 60% (d)
70%<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
There are 4 male and 6 female Psychology
professors. In total there are 10 Psychology professors.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
There are 6
female professors out of all Psychology professors => 6/10 *100 = 60% </div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(c)</span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">68</span>. If the number of female Physics professors in
the age group 25 - 34 equals 25% of all the Physics professors in that age
group, then what is the number of male Physics professors in the age group 25 -
34?<br />
(a)9 (b) 6 (c) 3 (d) 2<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
From fig-2, we can see that 30% of Physics professors belong to the age
group 25-34. From fig-1, we can find that there are 32 male and 8 female
Physics professors. In total there are 40 Physics professors, out of which 30%
belong to 25-34 age group. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
30% of 40 = 12. So there are 12
Physics professors in the age group 25-34 <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-symbol-font-family: Wingdings;">à</span>
(1)</div>
<div class="MsoNormal" style="line-height: 150%;">
It is given
that, the number of female Physics
professors in the age group 25 - 34 equals 25% of all the Physics professors in
that age group => 25% of 12 = 3 are female professors in that age group <span style="font-family: Wingdings; mso-ascii-font-family: Calibri; mso-char-type: symbol; mso-hansi-font-family: Calibri; mso-symbol-font-family: Wingdings;">à</span> (2)<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
From (1) and
(2), we can say that 12-3=9 male professors belong to 25-34 age group.</div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(a)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red;">69</span>. If the Psychology professors in the
University constitute 2% of all the professors in the University, then what is
the number of professors in the University?<br />
(a) 400 (b) 500 (c) 600 (d)
700<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<u>Solution:<o:p></o:p></u></div>
<div class="MsoNormal" style="line-height: 150%;">
From fig-1, we can find that there are 4+6=10 Psychology professors. It
is given that this constitutes 2% of all professors.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
If 2% is 10, then what is 100% => 100/2 * 10 = 500<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #002060;">Ans: </span><span style="color: #004586;">(b)<o:p></o:p></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com15tag:blogger.com,1999:blog-5567027158491397321.post-52583557659952643232013-05-14T21:00:00.001+05:302013-06-02T16:09:00.653+05:30Numerator/Denominator confusion<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="line-height: 150%;">I observed that a bit of confusion prevails while simplifying fractions.
The confusion is about which number will go to numerator part and which number
will go to denominator part. This post is intended to clear the confusion.</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Consider a fraction in the form (a/b)/(c/d).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Let us call the variables like this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">a – Numerator-numerator<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">b – Numerator-denominator<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">c – Denominator-numerator<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">d – Denominator-denominator<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span><br />
<a name='more'></a></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="line-height: 150%;"><u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The rules:</span></u></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Numerator-numerator remains in the the numerator part of the
result fraction<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Numerator-denominator remains in the the denominator part of the
result fraction<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Denominator-numerator always goes to the denominator part of the
result fraction<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Denominator-denominator always goes to the numerator part of the
result fraction<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="line-height: 150%;"><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The thumb rule</span></b><span style="font-family: Calibri, sans-serif; line-height: 150%;"> here is:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If the number is either of type “Numerator-numerator” or
“Denominator-denominator”, then it will go to numerator part. In other cases,
it will go to denominator part.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;">So applying these rules, the given fraction takes the following
form:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">'a' remains in numerator, 'b' goes to denominator, 'c' remains in
denominator and 'd' comes up to the numerator.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(a/b)/(c/d) = (a*d)/(b*c)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;">It's not like always there exist four parts in such fractions.
Sometimes it is like this: (x/y)/z. This contains only three numbers. Here</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">x is Numerator-numerator,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">y is Numerator-denominator,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">and z is Denominator-numerator.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Applying the thumb rule, x remains in numerator while y and z
settle in denominator.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">=> (x/y)/z = x/(y*z)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;">If we take the other form p/(q/r), it changes like this: (p*r)/q</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-family: Calibri, sans-serif; line-height: 150%;">Try out the following examples:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Question set:</span></u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(3/4)/(7/8)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">3/(4/5)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(3/4)/5<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(2/3)/4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(8/9)/(2/3)<u><o:p></o:p></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Solution set:</span></u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(3/4)/(7/8) =
(3*8)/(4*7) = 6/7<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">2.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">3/(4/5) =
(3*5)/4 = 15/4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">3.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(3/4)/5 =
3/(4*5) = 3/20<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">4.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(2/3)/4 =
2/(3*4) = 1/6<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">5.<span style="font-family: 'Times New Roman'; font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">(8/9)/(2/3) =
(8*3)/(9*2) = 4/3<o:p></o:p></span></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-665429546793157382013-05-01T18:39:00.000+05:302013-06-02T16:09:38.546+05:30Stuff for school kids (standard 5 to 10)<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">I thought of
providing some stuff for students studying in the range 5<sup>th</sup> to 10<sup>th</sup>
standard. This stuff is a combination of two sets. One is Math&Logic based
and the other is Knowledge based. This stuff is a mix of some questions that
are based on math fundamental concepts and remaining questions that are based
on commonsensical and out-of-box thinking. These do not look like standard
questions that are given in school-level exams but mostly resemble or can act
as base for the math and logic aptitude sort of questions that are asked in
various entrance exams. My primary intention is to inculcate in kids an
interest and liking on maths. I strongly opine that math solving skills are
very much needed to excel in diverse fields of studies ranging from Science, Engineering
to Economics, Management studies etc. </span>
<br />
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">To be frank
on my part, I am starting this post with small number of questions at hand but
I will try to enrich this bit bank by updating it from time to time.</span><br />
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span><br />
<a name='more'></a><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Math and
Logic Based Set:</span></u></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">A number when
used in denominator results in an 'undefined' value. What's that number?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">X is a
number. If you add X to any other number you get the other number. If you
subtract X from any other number, even then you get the other number. What is
the number X?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Y is a number.
If you multiply Y with any other number you get the other number. If you divide
any other number with Y, even then you get the other number. What is the number
Y?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">It's a
geometric figure and there is one point 'X' with in that figure. All points on
that figure are equidistant from X. What is that geometric figure?What is the
point X called?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The one and
only number which is even and prime is_____</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Which of the
English alphabets are symmetric in shape when written in upper case? (If
bisected vertically)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Which of the
English alphabets are symmetric in shape when written in upper case? (If
bisected horizontally)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">How many two
digit numbers having both identical digits are there?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">9.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Consider a
two digit number such that if you add it's two digits, you should get a sum of
9. How many such two digit numbers are possible?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">10.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">How many
three digit numbers can be formed by using all the digits 0,1,2. Here
repetition<span style="mso-spacerun: yes;"> </span>of a digit in a number is not
allowed. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">11.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">What are all
the years in twenty first century that use all the four digits 0,1,2,3? </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">12.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">What are all
the years in twenty first century that are palindromes?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">13.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Is 2013 a
prime number?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">14.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">For a right
triangle, if 24 and 25 are two sides then what is the other side?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">15.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">What is the
square of 995?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">16.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Ram walked 6
m Eastwards and turned 90 degrees to his left and continued to walk for 8m and
stopped there. At what distance and direction is the final point positioned
with respect to the initial point if we join the two points by a straight line?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">17.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Amar can do a
work in 60 days and Akbar in 90 days. In how many days both of them can jointly
do that work?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">18.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Anthony
started a journey by car to his home town which is 100 km away. He travels
first 40 km at a speed of 40 kmph, next 40 km at a speed of 80 kmph and the
remaining distance at a speed of 40 kmph. What is the average speed with which
he travelled to reach the destination?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">19.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Given the
radius of a circle is 5 cm, what is the distance between two points on the
circle which are located exactly opposite to each other?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">20.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“The radius
of a circular path is 7 m. If I start at a point on the path and travel 88 m
along the path, then I will reach the same point at which I have started”. Is
this statement True/False?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">21.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The statement
“X/X = 1” does not work when X=____<span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">22.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“Square root
of 16 is 4”- is this sentence perfectly correct?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">23.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“Square of 4
is 16”- is this sentence perfectly correct?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">24.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If I say “A/B
= C/D”, does it mean A=C and B=D?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">25.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If I say “A*B
= C*D”, does it mean either A=C or A=D?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">26.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If X<sup>Y</sup>
= 0, then X must be___, irrespective of the value of Y.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">27.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If X<sup>Y</sup>
= 1, then Y must be___, irrespective of the value of X.</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Knowledge
Based Set:</span></u></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">That's an
English word, which is an acronym representing all the four sides. What's it?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">We all
remember him for his magic square. Who is that great Indian mathematician?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The great
Indian lady mathematician famously known for her quick calculations on large
numbers (recently she has passed away)________</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">The great
Indian mathematician who invented Pujyam ('0') is ____ </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“For a right
angle triangle if 'a' is hypotenuse and 'b' and 'c' are sides then, a<sup>2</sup>=b<sup>2</sup>+c<sup>2</sup>”
- whose theorem is this?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“Any three
points which are not collinear can form a triangle”. Is this statement
True/False?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“For any two
points on a plane, if we join them by a straight line, it gives the shortest
path”. Is this statement True/False?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“In a right
angle triangle, hypotenuse is the largest side”. Is this statement True/False? </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">9.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">“In a right
angle triangle, length of hypotenuse is the greater than sum of the lengths of
other two sides”. Is this statement True/False?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l2 level1 lfo3; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">10.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">If the length
and breadth of a rectangle are made equal, then it becomes a _____</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Answers (Math
& Logic Based Set):</span></u></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">0</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">0</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>Clue:</span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> X+0=0+X=X</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>Clue:</span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> Y*1=1*Y=Y</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Circle,
Centre of the circle</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">2</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">A,H,I,M,O,T,U,V,W,X
(clue: If we bisect each of these letters vertically, the left and right
portions appear as mirror images)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">D,E,H,I,K,O,X
(clue: If we bisect each of these letters horizontally, the upper and lower
portions appear as mirror images)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">9 (they are-
11,22,33,44,55,66,77,88,99)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">9.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">9 (they are-
18,81,27,72,36,63,45,54,90)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">10.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">4 (they are-
102,120,201,210)</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">11.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">2013 and 2031</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">12.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">only one -
2002. </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>Notes:</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>Palindrome is a word or number with
a unique property that when it is reversed, it yields the <span style="mso-tab-count: 1;"> </span>same word or number </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>Clue:</span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> As it should
belong to twenty first century we start with taking 20 as the first two digits.
<span style="mso-tab-count: 1;"> </span>To fulfill the condition of
palindrome, the next two digits must be 0 and 2 respectively. Thus <span style="mso-tab-count: 1;"> </span>2002 is the only palindrome in the
twenty first century. Likewise, 2112 is the only palindrome <span style="mso-tab-count: 1;"> </span>in the 22<sup>nd</sup> century. </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">13.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">No </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>Notes:</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> Try to
factorize the number. 2013=11*183</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">14.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">7 </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>Notes:</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> Let us try
to use Pythagoras theorem. First let us find the squares of the given two <span style="mso-tab-count: 1;"> </span>numbers. 25^2 = 625 and 24^2=576. Then
let us check whether sum or difference of these two <span style="mso-tab-count: 1;"> </span>squares is a perfect square.625+576 = 1201. We are not sure
whether this is a perfect square or <span style="mso-tab-count: 1;"> </span>not.
So let us consider difference. 625-576=49=> this is square of 7 and hence 7
is the other <span style="mso-tab-count: 1;"> </span>side. Here 25, which is
biggest of the three sides is called hypotenuse.</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">15.<span style="font: 7.0pt "Times New Roman";"> </span></span></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">990025<span style="mso-tab-count: 1;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>short cut: </u></span></b></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>step-1</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>consider the part of the number
excepting the unit's digit 5 => 99</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>step-2:</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>multiply this with it's next number
=> 99*(99+1)=99*100=9900 </span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span><u>step-3:</u></span></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-tab-count: 1;"> </span>append 25 to the right side of 9900
=> we get 990025</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">16.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">10 m NE </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">17.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">36</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">18.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">50 kmph</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">19.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">10 cm</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">20.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">True</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">21.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">0</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">22.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">No. Square root
of 16 is either +4 or -4</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">23.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Yes</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">24.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">No</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">25.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">No</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">26.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">0</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l4 level1 lfo5; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">27.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">0</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><u><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Answers
(Knowledge Based Set):</span></u></b><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">1.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">NEWS –
North,East,West,South</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">2.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Srinivasa
Ramanujam</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">3.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Shakuntala
Devi</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">4.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Aryabhatta</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">5.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Pythagoras'</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">6.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">True</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">7.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">True</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">8.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">True</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">9.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">False</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l3 level1 lfo4; tab-stops: list .5in; text-align: justify; text-indent: -.25in;">
<span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">10.<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-family: "Calibri","sans-serif"; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Square</span></div>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-5351515533847300552013-02-11T19:44:00.001+05:302013-02-12T06:53:26.476+05:30A land mark on GATE exam day<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
<i><span style="font-family: "Arial","sans-serif";"> </span><span style="font-family: "Arial","sans-serif";">Yesterday
(10<sup>th</sup> Feb'13) GATE exam was conducted. It's an all India exam
conducted by IITs annually for entry to M.Tech courses. Some PSUs also consider
the GATE scores for offering jobs. </span><span style="font-family: "Arial","sans-serif";">In GATE, there are a total of 65 questions carrying a total of
100 marks, out of which 10 questions carrying total of 15 marks are in General
Aptitude (GA). The remaining 85% of the total marks is devoted to the
Engineering syllabus.</span><span style="font-family: "Arial","sans-serif";"> From last year (GATE-2012), </span></i><br />
<a name='more'></a><i><span style="font-family: "Arial","sans-serif";">General Aptitude section has been
introduced in the exam along with the traditional Engineering stuff. This
section contains Quantitative,Verbal and Logical ability questions and
contributes to 15% of the total score. (in fact, it's a remarkable portion
given low scores in GATE exam). More or less, this section is in the lines of
MBA entrance exams like CAT,XAT, etc.</span></i></div>
<div class="MsoNormal" style="text-align: justify;">
<i><br /></i></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Arial","sans-serif";"><span style="mso-tab-count: 1;"> </span>Yesterday
was a good day for this blog </span><span style="color: black;"><a href="http://mathbyvemuri.blogspot.in/"><span style="font-family: "Arial","sans-serif"; mso-bidi-font-family: Mangal;">http://mathbyvemuri.blogspot.in</span></a><span style="font-family: "Arial","sans-serif";">. My Math blog was
introduced in Oct'2011 and so far the journey is exciting. Initially the page
hits per day were 10-30 and gradually it is increased to 40-60 and for the last
3-4 months the pace has been maintained at 90-120 page hits/ day. <b>Yesterday
the total page hits were '934', highest figure in my blogging experience thanks
to GATE aspirants</b>.</span></span></i></div>
<div class="MsoNormal" style="text-align: justify;">
<i><br /></i></div>
<div class="MsoNormal" style="text-align: justify;">
<i><span style="font-family: "Arial","sans-serif";"><span style="mso-tab-count: 1;"> </span>The
GATE-2013 exam was conducted in two slots (morning and evening). I started
posting the detailed solutions for the aptitude section of the GATE-2013 by
around 6.30 PM. Within 2 hours of my posting, there were around 250 hits and
the count went on with that pace.</span></i></div>
<div class="MsoNormal" style="text-align: justify;">
<i><br /></i></div>
<div style="text-align: justify;">
<i><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="mso-tab-count: 1;"> </span></span><span style="font-family: "Arial","sans-serif"; font-size: 12.0pt; mso-ansi-language: EN-US; mso-bidi-font-family: Mangal; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">This
type of moments are very special to me and are big stepping stones in building
up and pushing ahead my self with mathbyvemuri...</span></i></div>
<div style="text-align: justify;">
<i><br /></i></div>
<div class="separator" style="clear: both; text-align: justify;">
<i><a href="http://4.bp.blogspot.com/-oZ7GQxd6d9I/URj8kha3m1I/AAAAAAAAAiY/32mWi2lGC1M/s1600/Blog_gate.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="179" src="http://4.bp.blogspot.com/-oZ7GQxd6d9I/URj8kha3m1I/AAAAAAAAAiY/32mWi2lGC1M/s320/Blog_gate.png" width="320" /></a></i></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-74750598697335392822013-02-10T20:22:00.001+05:302013-02-11T22:01:11.953+05:30GATE-2013 Solutions (General Aptitude)(EC/EE/IN)<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1. A car travels 8 km in the first quarter of an hour, 6 km in the
second quarter and 16 km in the third quarter. The average speed of the car in
km per hour over the entire journey is</span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A)30<span style="mso-tab-count: 1;"> </span>(B)36<span style="mso-tab-count: 1;"> </span>(C)40<span style="mso-tab-count: 1;"> </span>(D)24</span></div>
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<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">This is a simple formula based one.</span></div>
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<a name='more'></a><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Average speed = total distance/ total time</span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Total distance = 8+6+16 = 30 km</span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Total time taken = 3 quarters of an hour = ¾ hr</span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Average speed = total distance/ total time = 30/(3/4) = 40 kmph</span></div>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">C</b></span></div>
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<br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">2. Find the sum to n terms of the series 10+84+734+….</span><br />
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+ n<span style="mso-tab-count: 1;"> </span>(D) 9(9<sup>n</sup>-1)/8 + n<sup>2</sup></span></div>
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<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Check from the options by substituting n = 1,2…</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">For n=1, all options are right</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">For n=2, sum must be 10+84=94.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Only option D is correct for this and we can bank on that…</span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">D</b></span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"></span></span></b></span></div>
<br />
3. The set of values of p for which the roots of the equation 3x<sup>2</sup>+2x+p(p-1)=0
are of opposite sign is<br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"></span></span></b></span><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A)(-∞,0)<span style="mso-tab-count: 1;"> </span>(B)(0,1)<span style="mso-tab-count: 1;"> </span>(C)(1,∞)<span style="mso-tab-count: 1;"> </span>(D)(0,∞)</span></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b><span style="font-weight: normal;"><span style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></span></span></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<b><span style="font-weight: normal;">
</span></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">This is a question on quadratic equations funda.</span></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">For ax<sup>2</sup>+bx+c=0,</span></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">if the two roots are of different signs, their product must be –ve
=> c/a < 0</span></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> p(p-1)/3 < 0 => p(p-1) < 0 => 0 < p < 1</span></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b><b style="mso-bidi-font-weight: normal;"></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">B</b></span></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;">
</b></span><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><!--[if gte mso 9]><xml>
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<m:mathFont m:val="Cambria Math"/>
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</b></b></span><br />
<br />
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4. What is the chance that a leap year, selected at random, will
contain 53 Saturdays?</span></span></b></b></span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A)2/7<span style="mso-tab-count: 1;"> </span>(B)3/7<span style="mso-tab-count: 1;"> </span>(C)1/7<span style="mso-tab-count: 1;"> </span>(D)5/7</span></span></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><b><span style="font-weight: normal;"><span style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b>Sol</b>:</span></u></span></span></b></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">A leap year has 366 days => 365/7 weeks = 52 weeks + 2 days</span></span></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> For a leap year to have 53 Saturdays, either one of the
first two days of first week of the year (Jan 1<sup>st</sup> or 2<sup>nd</sup>)
must be a Saturday. So the probability is 2 out of 7</span></span></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
<span style="font-weight: normal;">
</span></b></b><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"></b></b></span><br />
<div class="MsoNormal">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">A</b></span></b></b></span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;"><br /></b></b></span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><b style="mso-bidi-font-weight: normal;">
</b></b></span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5. In the summer of 2012, in New<u><span style="font-family: "Calibri","sans-serif";"><span style="color: purple;"><b> </b></span></span></u>Delhi, the mean temperature of
Monday to Wednesday was 41<sup>0</sup>C and of Tuesday to Thursday was 43<sup>0</sup>C.
If the temperature on Thursday was 15% higher than that of Monday, then the
temperature in <sup>o</sup>C on Thursday was</span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A)40<span style="mso-tab-count: 1;"> </span>(B)43<span style="mso-tab-count: 1;"> </span>(C)46<span style="mso-tab-count: 1;"> </span>(D)49</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><span style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
<b>
</b></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Let the temperatures on Monday,Tuesday,Wednesday and Thursday is
M,T,W and Th respectively.</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The mean temperature of Monday to Wednesday was 41<sup>0</sup>C
=> (M+T+W)/3 = 41</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> M+T+W = 123 <span style="mso-tab-count: 1;"> </span>---(1)</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The mean temperature of Tuesday to Thursday was 43<sup>0</sup>C=>
(T+W+Th)/3 = 43</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> T+W+Th = 129<span style="mso-tab-count: 1;"> </span>---(2)</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(2)-(1) => Th-M = 6<span style="mso-tab-count: 1;"> </span>---(3)</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">temperature on Thursday was 15% higher than that of Monday =>
Th = 1.15*M<span style="mso-tab-count: 1;"> </span>---(4)</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">From 93) and (4), 0.15M = 6 => M = 6/0.15 => Th =
1.15*6/0.15 = 46</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">Ans: <b><span style="mso-bidi-font-weight: normal;">C</span></b></span></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--></span></span><br />
</div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6. They were requested not to quarrel with others.</span></span></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;">
</span></span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Which one of the following is the closest in meaning to the word
quarrel?</span></span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">make out<span style="mso-tab-count: 1;"> </span>(B)
call out<span style="mso-tab-count: 1;"> </span>(C) dig out<span style="mso-tab-count: 1;"> </span>(D) fall out</span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;">
</span></span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b>D</b></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]--></b></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">7. Statement<span style="mso-tab-count: 1;"> </span>You can always
give me a ring whenever you need</span></span></b></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b>
<span style="font-weight: normal;">
</span></b></span></span></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Which one of the following is the inference from the above
statement?</span></span></b></span></span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">(<span style="font-weight: normal;">A</span>)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Because I have a nice caller tune</span></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">(<span style="font-weight: normal;">B</span>)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Because I have a better telephone facility</span></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">(<span style="font-weight: normal;">C</span>)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Because a friend in need is a friend in deed</span></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-list: Ignore;">(<span style="font-weight: normal;">D</span>)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Because
you need not pay towards the telephone bills when you give me a ring</span></span></span></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b>
</b><b>
</b></span></span></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Explanation:</span></u></b></span></span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b>
</b></span></span></span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">All the other options except (C) can be easily eliminated as they
are illogical</span></span></span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">Ans</span><b><span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">: C</span> </b></span></span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-bidi-font-weight: normal;">
</span></span>
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><!--[if gte mso 9]><xml>
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</div>
<div class="MsoNormal">
<br /><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="color: black;">8</span>. <span style="color: black;"><b>Statement </b>There were different streams of freedom movements in
colonial India carried out by the moderates, liberals, radicals, socialists and
so on.</span></span></span></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;">
<span style="font-weight: normal;">
</span></span></b></span><br />
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<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">Which one of the following is the best inference from the above
statement?</span></span></span></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;">
<span style="font-weight: normal;">
</span></span></b></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">(A)The emergence of colonial India led to our independence</span></span></span></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;">
<span style="font-weight: normal;">
</span></span></b></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">(B)Nationalism in India is emerged in the context of colonialism</span></span></span></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;">
<span style="color: black;"><span style="font-weight: normal;">
</span></span></span></b></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">(C)Nationalism in India is homogeneous</span></span></span></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b style="mso-bidi-font-weight: normal;"><span style="color: purple;">
<span style="color: black;"><span style="font-weight: normal;">
</span></span><div class="MsoNormal">
<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">(D)Nationalism in India is heterogeneous</span></span></span></div>
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<br /></div>
<span style="font-weight: normal;"><span style="font-weight: normal;">
</span></span><div class="MsoNormal">
<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><b><u>Explanation</u>:</b> As<span style="color: purple;"><span style="color: black;"> the movement is in different forms, we can say that nationalism is heterogeneous</span><b> </b></span> </span></span></span></div>
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<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">Ans: <b>D</b></span></span></span><br />
<br />
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<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><b><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">(A) Two and two add four<span style="mso-tab-count: 1;"> </span>(B)
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<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><b><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="font-weight: normal;"><u><b>Explanation:</b></u> This is a question on English usage and 'make' makes sense here</span></span></b></span></span></span></div>
<span style="color: black;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><b>
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<span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="font-weight: normal;">Ans: <b>D</b></span> </span><br />
<br />
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</span><br />
<span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">10. Complete the sentence:</span></span><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="font-weight: normal;">
</span></span><br />
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<span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">Dare ______ mistakes.</span></span></span></div>
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</span></span><br />
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</span></span></span><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;"><span style="font-weight: normal;">commit</span><span style="mso-tab-count: 1;"> </span>(<span style="font-weight: normal;">B</span>)
<span style="font-weight: normal;">to </span>commit<b><span style="font-weight: normal;"><span style="mso-tab-count: 1;"> </span></span></b>(C) committed<span style="font-weight: normal;"><span style="mso-tab-count: 1;"> </span></span>(D) committing</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">
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<span style="font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-bidi-font-family: Calibri;">Ans: <b>A</b></span></span></div>
</span></div>
</b></span></span></span></div>
</span></b><b style="mso-bidi-font-weight: normal;"><span style="color: purple;"><span style="color: black;">
</span></span></b></span></div>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com6tag:blogger.com,1999:blog-5567027158491397321.post-69547499544776281752013-02-10T18:39:00.001+05:302013-02-11T20:01:32.469+05:30GATE-2013 Solutions (General Aptitude)(CS-IT/ME/PI)<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1. A tourist covers half of his journey by train at 60 km/h, half
of the remainder by bus at 30 km/h and the rest by cycle at 10 km/h. The
average speed of the tourist during his entire journey is</span><br />
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<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
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<a name='more'></a><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Let the total distance be ‘x’</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> <span style="mso-spacerun: yes;"> </span>x/2 covered at 60
km/h, x/4 covered at 30 km/h and x/4 covered at 10 km/h</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> the respective times taken are (x/2)/60, (x/4)/30, (x/4)/10</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> total time taken = x/120 + x/120 + x/40 = 5x/120= x/24</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Average speed = x/(x/24) = 24 km/h</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">C</b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">2. The current erection cost of a structure is Rs 13,200. If the
labour wages per day increase by 1/5 of the current wages and the working hours
decreased by 1/24 of the current period, then the new cost of erection in Rs. Is</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A)16,500<span style="mso-tab-count: 1;"> </span>(B)15,180<span style="mso-tab-count: 1;"> </span>(C)11,000<span style="mso-tab-count: 1;"> </span>(D)10,120</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The cost is nothing but the product of labour wages per day and
the number of working days.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Cost is directly proportional to (labour wages per day)*(no. of
working days)</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">labour wages per day is increased by 1/5 of the current wages
=> new wages/day changes by <span style="mso-spacerun: yes;"> </span>=( 1 +
1/5) proportion </span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">= 6/5 proportion</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">working hours decreased by 1/24 => new working hours changes by
= 1- 1/24 = 23/24 proportion</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> new total cost changes by = (6/5)*(23/24) proportion = 23/20
proportion</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> new total cost = (23/20)*(old total cost) = (23/20)*(13200)
= 23*660</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">We need not do complete multiplication here. We can observe that,
the answer ends with '80’ and the only option is 15180</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">B</b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">3. Which one of the following is closest in meaning to the word
given below?</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Nadir</span></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) Highest<span style="mso-tab-count: 1;"> </span>(B) Lowest<span style="mso-tab-count: 1;"> </span>(C) Medium<span style="mso-tab-count: 1;"> </span>(D) Integration</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">This is the traditional word given in competitive exams. Nadir and
Zenith represent two extreme points, Zenith being the highest and Nadir being
the Lowest one.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">B</b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4. Complete the sentence:</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Universalism is to Particularism<span style="mso-tab-count: 1;"> </span>as
Diffuseness is to ______</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) specificity<span style="mso-tab-count: 1;"> </span>(B)neutrality<span style="mso-tab-count: 1;"> </span>(C) generality<span style="mso-tab-count: 1;"> </span>(D) adaptation</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Universalism is almost an opposite word of Particularism. So we
need to find the opposite word (antonym) of Diffuseness.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Diffuseness is nature of spreading.<span style="mso-spacerun: yes;"> </span>Specificity may be the nearest answer</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-spacerun: yes;"> </span>Ans: <b style="mso-bidi-font-weight: normal;">A</b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5. What will be the maximum sum of 44,42,40,…?</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-spacerun: yes;"> </span>(A) 502<span style="mso-tab-count: 1;"> </span>(B) 504<span style="mso-tab-count: 1;"> </span>(C) 506<span style="mso-tab-count: 1;"> </span>(D)
500</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">44,42,40,…</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">This is a decreasing AP. If you leave it like that, it will go in
to negative terms -2,-4,….</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">But to make the sum maximum, we need to stop at ‘0’. Otherwise the
–ve terms make the sum decrease.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">So the series is 44,42,40,…..0.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">44+42+40+…+0 = 2(22+21+20+…0) = 2(sum of first 22 integers) = 2(n*(n+1)/2),
where n =22</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> Sum = 2*(22*23/2) = 22*23 = 506</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">C</b></span></div>
<div class="MsoNormal">
<br /></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6. Find the sum of the expression:</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1/√1+√2 + 1/√2+√3 + 1/√3+√4 + ….1/√80+√81</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) 7<span style="mso-tab-count: 1;"> </span>(B)8<span style="mso-tab-count: 1;"> </span>(C) 9<span style="mso-tab-count: 1;"> </span>(D)
10</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The simplification involves just rationalization…</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1/√1+√2 + 1/√2+√3 + 1/√3+√4 + ….1/√80+√81</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">= (√2-√1)/(√1+√2) (√2-√1) + (√3-√2)/(√2+√3) (√3-√2) +……+(√81-√80)/(√80+√81)
(√81-√80) </span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">= (√2-√1) + (√3-√2) +……+(√81-√80)</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">= -√1+√81 = -1+9 = 8</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b>B</b></span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><!--[if gte mso 9]><xml>
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<w:LidThemeOther>EN-US</w:LidThemeOther>
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</b></span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">7. Out of all the two-digit integers between 1 and 100, a
two-digit number has to be selected at random. What is the probability that the
selected number is not divisible by 7?</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span><br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) 13/90<span style="mso-tab-count: 1;"> </span>(B) 12/90<span style="mso-tab-count: 1;"> </span>(C) 78/90<span style="mso-tab-count: 1;"> </span>(D) 77/90</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><b><span style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></span></b></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The two digit numbers between 1 and 100 are 10,11,….99 => there
are 90 in all.</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The two-digit multiples of 7 are 14,21,….98 => 2*7 to 14*7
=> 13 in all</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
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<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">So the numbers <span style="mso-bidi-font-weight: normal;"><u>not
divisible</u></span> by 7 are 90-13 = 77 in all</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
</span>
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">So the answer is 77/90</span></span></div>
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">Ans: <b><span style="mso-bidi-font-weight: normal;">D</span></b></span> </span></div>
<div class="MsoNormal">
<b><br /></b></div>
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]-->
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">8. Were you a bird, you ____ in the sky.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) would fly<span style="mso-tab-count: 1;"> </span>(B) shall
fly<span style="mso-tab-count: 1;"> </span>(C) should fly<span style="mso-tab-count: 1;"> </span>(D) shall have flown</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b style="mso-bidi-font-weight: normal;">A</b></span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><br /></span></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9. Choose the grammatically <b style="mso-bidi-font-weight: normal;">INCORRECT</b>
sentence:</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) He is of Asian origin</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(B) They belonged to Africa</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(C) She is an European</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(D) They migrated from India to Australia</span></div>
<div class="MsoNormal">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Sol:</span></u></b></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">It might be – ‘a Europian’ and not 'an European'</span><br />
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Though European starts with vowel 'E', as it starts with a sound 'Yu', it should be preceded with 'a' but not 'an'.</span></div>
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Ans: <b>C</b><b style="mso-bidi-font-weight: normal;"></b></span></div>
<div class="MsoNormal">
<br /></div>
<!--[if gte mso 9]><xml>
<w:WordDocument>
<w:View>Normal</w:View>
<w:Zoom>0</w:Zoom>
<w:TrackMoves/>
<w:TrackFormatting/>
<w:PunctuationKerning/>
<w:ValidateAgainstSchemas/>
<w:SaveIfXMLInvalid>false</w:SaveIfXMLInvalid>
<w:IgnoreMixedContent>false</w:IgnoreMixedContent>
<w:AlwaysShowPlaceholderText>false</w:AlwaysShowPlaceholderText>
<w:DoNotPromoteQF/>
<w:LidThemeOther>EN-US</w:LidThemeOther>
<w:LidThemeAsian>X-NONE</w:LidThemeAsian>
<w:LidThemeComplexScript>X-NONE</w:LidThemeComplexScript>
<w:Compatibility>
<w:BreakWrappedTables/>
<w:SnapToGridInCell/>
<w:WrapTextWithPunct/>
<w:UseAsianBreakRules/>
<w:DontGrowAutofit/>
<w:SplitPgBreakAndParaMark/>
<w:DontVertAlignCellWithSp/>
<w:DontBreakConstrainedForcedTables/>
<w:DontVertAlignInTxbx/>
<w:Word11KerningPairs/>
<w:CachedColBalance/>
</w:Compatibility>
<w:BrowserLevel>MicrosoftInternetExplorer4</w:BrowserLevel>
<m:mathPr>
<m:mathFont m:val="Cambria Math"/>
<m:brkBin m:val="before"/>
<m:brkBinSub m:val="--"/>
<m:smallFrac m:val="off"/>
<m:dispDef/>
<m:lMargin m:val="0"/>
<m:rMargin m:val="0"/>
<m:defJc m:val="centerGroup"/>
<m:wrapIndent m:val="1440"/>
<m:intLim m:val="subSup"/>
<m:naryLim m:val="undOvr"/>
</m:mathPr></w:WordDocument>
</xml><![endif]-->
<br />
<div class="MsoNormal">
<span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">10. After several defeats in war, Robert Bruce went in exile and
wanted to commit suicide. Just before committing suicide, he came across a
spider attempting tirelessly to have its nest. Time and again the spider failed
but that did not deter it to refrain from making attempts. Such attempts by the
spider made Bruce curious. Thus Bruce started observing the near-impossible
goal of the spider to have net. Ultimately the spider succeeded in having its
net despite several failures. Such act of the spider encouraged Bruce not to
commit suicide. And then Bruce went back again and won many a battle, and the
rest is history.</span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-US; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">Which one of the following assertions is best
supported by the above information?</span><!--[if gte mso 9]><xml>
<w:LatentStyles DefLockedState="false" DefUnhideWhenUsed="true"
DefSemiHidden="true" DefQFormat="false" DefPriority="99"
LatentStyleCount="267">
<w:LsdException Locked="false" Priority="0" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Normal"/>
<w:LsdException Locked="false" Priority="9" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="heading 1"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 2"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 3"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 4"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 5"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 6"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 7"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 8"/>
<w:LsdException Locked="false" Priority="9" QFormat="true" Name="heading 9"/>
<w:LsdException Locked="false" Priority="39" Name="toc 1"/>
<w:LsdException Locked="false" Priority="39" Name="toc 2"/>
<w:LsdException Locked="false" Priority="39" Name="toc 3"/>
<w:LsdException Locked="false" Priority="39" Name="toc 4"/>
<w:LsdException Locked="false" Priority="39" Name="toc 5"/>
<w:LsdException Locked="false" Priority="39" Name="toc 6"/>
<w:LsdException Locked="false" Priority="39" Name="toc 7"/>
<w:LsdException Locked="false" Priority="39" Name="toc 8"/>
<w:LsdException Locked="false" Priority="39" Name="toc 9"/>
<w:LsdException Locked="false" Priority="35" QFormat="true" Name="caption"/>
<w:LsdException Locked="false" Priority="10" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Title"/>
<w:LsdException Locked="false" Priority="1" Name="Default Paragraph Font"/>
<w:LsdException Locked="false" Priority="11" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Subtitle"/>
<w:LsdException Locked="false" Priority="22" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Strong"/>
<w:LsdException Locked="false" Priority="20" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Emphasis"/>
<w:LsdException Locked="false" Priority="59" SemiHidden="false"
UnhideWhenUsed="false" Name="Table Grid"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Placeholder Text"/>
<w:LsdException Locked="false" Priority="1" SemiHidden="false"
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<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
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<w:LsdException Locked="false" Priority="64" SemiHidden="false"
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<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 1"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 1"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 1"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 1"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 1"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 1"/>
<w:LsdException Locked="false" UnhideWhenUsed="false" Name="Revision"/>
<w:LsdException Locked="false" Priority="34" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="List Paragraph"/>
<w:LsdException Locked="false" Priority="29" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Quote"/>
<w:LsdException Locked="false" Priority="30" SemiHidden="false"
UnhideWhenUsed="false" QFormat="true" Name="Intense Quote"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 1"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 1"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 1"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 1"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 1"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 1"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 1"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 1"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 2"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 2"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 2"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 2"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 2"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 2"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 2"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 2"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 2"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 2"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 2"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 2"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 2"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 2"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 3"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 3"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 3"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 3"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 3"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 3"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 3"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 3"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 3"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 3"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 3"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 3"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 3"/>
<w:LsdException Locked="false" Priority="73" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Grid Accent 3"/>
<w:LsdException Locked="false" Priority="60" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Shading Accent 4"/>
<w:LsdException Locked="false" Priority="61" SemiHidden="false"
UnhideWhenUsed="false" Name="Light List Accent 4"/>
<w:LsdException Locked="false" Priority="62" SemiHidden="false"
UnhideWhenUsed="false" Name="Light Grid Accent 4"/>
<w:LsdException Locked="false" Priority="63" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 1 Accent 4"/>
<w:LsdException Locked="false" Priority="64" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Shading 2 Accent 4"/>
<w:LsdException Locked="false" Priority="65" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 1 Accent 4"/>
<w:LsdException Locked="false" Priority="66" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium List 2 Accent 4"/>
<w:LsdException Locked="false" Priority="67" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 1 Accent 4"/>
<w:LsdException Locked="false" Priority="68" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 2 Accent 4"/>
<w:LsdException Locked="false" Priority="69" SemiHidden="false"
UnhideWhenUsed="false" Name="Medium Grid 3 Accent 4"/>
<w:LsdException Locked="false" Priority="70" SemiHidden="false"
UnhideWhenUsed="false" Name="Dark List Accent 4"/>
<w:LsdException Locked="false" Priority="71" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful Shading Accent 4"/>
<w:LsdException Locked="false" Priority="72" SemiHidden="false"
UnhideWhenUsed="false" Name="Colorful List Accent 4"/>
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<![endif]--><span style="font-size: 12.0pt; line-height: 115%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(A) Failure is the pillar of success</span><br />
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</style>
<![endif]--></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com8tag:blogger.com,1999:blog-5567027158491397321.post-29605350604494997322013-01-29T21:04:00.000+05:302013-01-29T21:21:59.507+05:30My experiences with CAT and learning points<div dir="ltr" style="text-align: left;" trbidi="on">
Attempting exams like CAT is always a tense experience. To keep our nerves under control is the mantra here. I have attempted CAT two times, first time in 2008 and next time in 2012. First one is traditional paper-based type and next one is computer-based test. See my learning points from this experience...<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-wDjoOAp3hJY/UQftsitfUHI/AAAAAAAAAgk/T4pbXyJ_kK8/s1600/CAT_exp.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="544" src="http://4.bp.blogspot.com/-wDjoOAp3hJY/UQftsitfUHI/AAAAAAAAAgk/T4pbXyJ_kK8/s640/CAT_exp.png" width="640" /></a></div>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-14884244103878851142013-01-12T11:59:00.000+05:302013-01-20T10:54:39.164+05:30Puzzle-35 (XAT-2013)<div dir="ltr" style="text-align: left;" trbidi="on">
<div style="text-align: justify;">
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Sara has just joined Facebook. She has 5
friends. Each of her five friends has twenty five friends. It is found that at least
two of Sara’s friends are connected with each other. On her birthday, Sara
decides to invite her friends and the friends of her friends. How many people
did she invite for her birthday party?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; text-indent: -.25in;">
<div style="text-align: justify;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">(A)<span style="font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥
105</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (B) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≤ 123</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (C) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">< 125</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (D)
</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥ 100 and ≤ 125</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥ 105 and ≤ 123</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"></span></i></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="color: red;"><span style="color: blue;"><i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="color: red;"><span style="color: blue;">For solution c</span></span></span></i>lick on 'Read more' below..</span></span></span></i><br />
<a name='more'></a></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="color: red;">Solution:</span></span></i></span></i><br />
<i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="color: red;"> </span></span></i>The key point</span></i><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">:<o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">“Each of Sara’s 5 friends has twenty </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">five </span>friends” => <i><span style="color: #c00000;">Sara is one among
these 25 friends</span></i>. <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">I call this as ‘Facebook Logic’. If A is in friend-contacts
of B, then B is also in the friend-contacts of A. <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">So, in normal case, Sara has to invite 24 contacts of each
of her 5 friends along with those 5 friends (ie., 5 + 5*24 = 125). But this is
not end of story. It is also given that,<o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 360.75pt;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">“<i>At least two of Sara’s friends are connected with each other</i>”: <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">Here ‘at least two’ is another point to note. If two
of 5 friends of Sara are connected with each other, then each one of this pair has
23 contacts (excepting Sara and the other friend in the pair). Each of the remaining
3 of Sara’s friends has got 24 contacts (excepting Sara). So if Sara invites
all, there are 5 + 2*23 + 3*24 = <b><i><span style="color: #c00000;">123</span></i></b>
invitees in all.<o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">“<i><span style="color: #c00000;">At least two</span></i>” hints us that -at maximum, all
the 5 friends of Sara has the other four friends in their contacts. Then each
of these 5 friends has 20 contacts (excepting Sara and the other 4). So if Sara
invites all, there are 5 + 5*20 = <b><i><span style="color: #c00000;">105</span></i></b>
invitees in all.<o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">Finally we arrived at the answer: The count of invitees
ranges from <i><u><span style="color: #c00000;">105
to 123</span></u></i>. <o:p></o:p></span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div style="text-align: justify;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">Ans: <span style="color: red;">E</span></span><br />
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="color: red;"><span style="color: black;">For easy understanding I depict these images:</span></span></span><br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-pg9q5ZpvVvI/UPES_6c2vGI/AAAAAAAAAb8/7PKccWOsFWI/s1600/sara+-+Copy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="http://4.bp.blogspot.com/-pg9q5ZpvVvI/UPES_6c2vGI/AAAAAAAAAb8/7PKccWOsFWI/s320/sara+-+Copy.jpg" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-Bn9uzV93v5A/UPETGNhBipI/AAAAAAAAAcE/ZLIs1n0eNUs/s1600/sara-2+-+Copy.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="http://1.bp.blogspot.com/-Bn9uzV93v5A/UPETGNhBipI/AAAAAAAAAcE/ZLIs1n0eNUs/s320/sara-2+-+Copy.jpg" width="320" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-kaZulDhN6zE/UPETev_YndI/AAAAAAAAAcM/00qZWLQ-eo0/s1600/sara-3.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="284" src="http://4.bp.blogspot.com/-kaZulDhN6zE/UPETev_YndI/AAAAAAAAAcM/00qZWLQ-eo0/s320/sara-3.jpg" width="320" /></a></div>
</div>
</div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com2tag:blogger.com,1999:blog-5567027158491397321.post-41600715453741727802013-01-09T19:44:00.002+05:302013-02-07T06:56:16.501+05:30XAT-2013 Detailed Solutions (Quantitative Ability)<div dir="ltr" style="text-align: left;" trbidi="on">
Along with solutions, here I would like to give '<span style="color: red;">Notes</span>' especially on some problems where I went in a wrong way or spent a little more time than usual while actually solving in the exam. And also for some problems, I summarized crucial clues and tagged those clues under '<span style="color: purple;">Points</span>'. I thought this approach is quite useful to solve the problems and get to know about the nitty-gritties. <br />
<br />
<a name='more'></a><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q1)Prof.
Mandal walks to the market and comes back in an auto. It takes him 90 min to
make the round trip. If he takes an auto both ways it takes him 30 minutes. On a
Sunday he decides to walk both ways. How long would it take him?</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo2; tab-stops: list 0in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">(A)</span><!--[endif]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">100
minutes (B) 120 minutes (C) 140 minutes (D) 150 minutes <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(E)None
of the above<span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">one-way walk + one-way
auto = 90 min ---(1)<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">two-way auto = 30 min<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> one-way auto =
15 min ---(2)<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">From (1) and (2),
one-way walk = 90-15 = 75<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> two-way walk = 2*75 = 150 min<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> D</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q2)At
the centre </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="color: #073763;">of a city’s municipal park</span><span style="color: #0070c0;"> there
is a large circular pool. A fish is release in the water at the edge of the
pool. The fish swims north for 300 feet before it hits the edge of the pool. It
then turns east and swims for 400 feet before hitting the edge again. What is
the area of the pool? </span><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">(A)</span><!--[endif]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">62500π (B) 125000π (C) 250000π (D) 500000π<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> (E)Cannot be answered from the given data <span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">“Travel of 300 m North
and then 400 m East” creates a right-triangle on the circle<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> Funda here is
“angle in semi circle is right angle”<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> hypt. of the
right-triangle = diameter of the circle<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> diameter of the
circle = √(300<sup>2</sup>+400<sup>2</sup>) = 500 m<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> rad. of the
circle = 250 m<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> Area of the
circle =<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> A<u><o:p></o:p></u></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q3)Mr.Mehra
is planning for higher education expenses of his two sons aged 15 and 12.He
plans to divide Rs 15 lakhs in two equal parts and invest in two different
plans such that his sons may have access to Rs 21 lakhs each when they reach
the age of 21. He is looking for plans that will give him a simple interest per
annum. The rates of interest of the plans for his younger son and his elder son
should be</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: .25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)
5% and 7.5% respectively (B)
8% and 12% respectively <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(C)
10% and 15% respectively (D)
15% and 22.5% respectively <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(E)
20% and 30% respectively <span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<b><u><o:p></o:p></u></b></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: purple; font-size: 13pt; line-height: 150%;">Points</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">15 lakhs is divided in
to two equal parts => 7.5 L each<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Elder son aged 15 and
younger one aged 12 years<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Each one has to get 21
lakhs by the time they attain 21 yrs<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> Elder one after
6 years and younger one after 9 yrs<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> one sum of 7.5 L
should grow to 21 L after 6 yrs<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">and other sum of 7.5 L
should grow to 21 L after 9 yrs<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>Interest per
annum for elder one = (21-7.5)*100/(7.5*6)<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">= 13.5*100/(7.5*6) =
30%<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Interest per annum for
younger one = (21-7.5)*100/(7.5*9)<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">= 13.5*100/(7.5*9) =
20%<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> E</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q4)Albela,
Bob and Chulbul have to read a document of seventy eight pages and make a
presentation next day. They realize that the article is difficult to understand
and they would require team work to finish the assignment. Albela can read a page in two minutes, Bob in 3 minutes and
Chulbul in 4 minutes. If they divide the article in to 3 parts so that all
three of them spend the equal amount of time on the article, the number of
pages that Bob should read is</span><br />
<div style="text-indent: 0px;">
<span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="color: #0070c0; font-size: 13pt; line-height: 150%; text-indent: -0.25in;">(A) </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;">24 (B)
25 (C) 26 (D) 27 (E) 28</span></div>
</div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<b><u><o:p></o:p></u></b></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: purple; font-size: 13pt; line-height: 150%;">Points</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Pages in the doc = 78<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">A reads a page in 2
min, B in 3 min and C in 4 min<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> in 1 min, A can
read 1/2 of a page, B can read 1/3 of a page and C can read ¼ of a page<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">They have to divide
the work such that all should spend equal amount of time. Let that be 't' min.<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">In 't' min, A can read
t/2 , B can read t/3 and C can read t/4 pages<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">In total they read
t/2+t/3+t/4 pages<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> t/2 + t/3 + t/4
= 78 => t = 72 min<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">So in his assignment B
reads t/3 ie., 72/3 = 24 pages<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> A</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q5)The
taxis plying in Wasseypur have the following fare structure: Rs 20 for the first
two kilometers, Rs 5 for every km in excess of 2 km and up to 10 km, and Rs 8 for every km in
excess of 10 km. Bullock carts on the other hand charge Rs 2 per km. Sardar
Khan takes a taxi from the Wasseypur Railway station to his home. On the way,
at a distance of 14 km from the railway station, he meets Faizal Khan, and gets
down from the taxi to talk to him. Later he takes a bullock cart to reach his
home. He spends a total of Rs 102 to reach his home from the railway station. How
far is his home from the railway station? <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)17 (B) 18 (C)
19 (D) 20 (E) 21 <span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<b><u><o:p></o:p></u></b></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13pt; line-height: 150%;"><span style="color: purple;">Points</span><b style="text-decoration: underline;">:</b></span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Taxi:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Rs 20 for first 2 km.
Note here that it's not for each km, it is 20 for total 2 km<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Rs 5 for every km from
3 up to 10 km<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Rs 8 for every km for
above 10 km range<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<br /></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Bullock:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">It's a simple rate. Rs
2 per each km<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<br /></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">First, Sardar travels
14 km on Taxi<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us divide this in
to three parts 2+8+4<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>Fare for taxi
= 20 for first 2km + 8*5 for next 8 km
+ 4*8 for next 4 km<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">= 20+40+32 = 92<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Afterwards he went by
bullock. He spent a total amount of 102 for entire journey<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> He spent 102-92
= 10 for Bullock<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> He travels 10/2
= 5km on Bullock<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Total distance of
journey = 14km on Taxi + 5km on Bullock = 19 km<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> C<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note</span></span><b><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">: </span></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">While solving it in
the exam, initially, I considered Rs 20 per each km of first 2km of taxi ride, and
solved like this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Fare of taxi = 2*20+8*5+4*8 = 112. As this figure is exceeding
the total payment of Rs 102, I thought I made a mistake and rechecked. It took
a little more time than usual.</span><br />
<br />
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q6)Consider
the expression: (a<sup>2</sup>+a+1)(b<sup>2</sup>+b+1)(c<sup>2</sup>+c+1)(d<sup>2</sup>+d+1)(e<sup>2</sup>+e+1)/abcde.
The minimum value of the expression is:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)3 (B) 1 (C)
10 (D) 100 (E) 243 <span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(a<sup>2</sup>+a+1)(b<sup>2</sup>+b+1)(c<sup>2</sup>+c+1)(d<sup>2</sup>+d+1)(e<sup>2</sup>+e+1)/abcde<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Take
related terms first and simplify:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(a<sup>2</sup>+a+1)/a
= a+1/a+1 <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">we
know that, minimum value of a+1/a is 2<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>
minimum value of (a+1/a+1) = 2+1 =3<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%; tab-stops: 384.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> minimum value of (a+1/a+1)(b+1/b+1)(c+1/c+1)(d+1/d+1)(e+1/e+1)
= 3<sup>5</sup>=243<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> E</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q7) The
mean of six positive integers is 15. The median is 18, and the only mode of the
integers is less than 18. The maximum possible value of the largest of the six
integers is</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)26 (B) 28 (C)
30 (D) 32 (E) 34 <span style="color: #0070c0;"><o:p></o:p></span></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">If arranged in
ascending order let the numbers be a,b,c,d,e,f. We want the largest number ie.
'f'.<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Mean = 15 =>
(a+b+c+d+e+f)/6 = 15 => a+b+c+d+e+f =
90<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">median = 18 =>
(c+d)/2 = 18 => c+d = 36 => a+b+e+f = 90-36 = 54<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">The only mode is less
than 18:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Mode is a number in
the sequence which is repeated maximum number of times. To make the largest
number maximum, the mode shall be minimum. The minimum possible mode is 1. so
the cases may be <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Case-I<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">a=b=1 <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Case-II:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">a=b=c=1 : This case is
ruled out. Follow the reason here:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">if c=1, d=35 and <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">a+b+e+f = 2+e+f = 54
=> e+f = 52.<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'d' being 35, a value
52 is not possible for e+f because e and f shall be greater than 'd' <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Case-III:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">a=b=c=d=1: This case
is ruled out as c+d shall be 36 <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">So, there is only one
case possible, ie., a=b=1 <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>e+f = 52<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">so the sequence is
1,1,c,d,e,f<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">we have c+d=36. In the sequence, to make f maximum, d
shall be minimum. The least possible vale of 18 is not possible for d because
in that case c is also equal to 18 in which case, there exists another mode
which is not true as per the given condition. So we will go to the next
possible minimum of 'd' ie., 19. So in this case c=17 and the sequence looks
like this:<o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">1,1,17,19,e,f. <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">And we have, e+f = 52.
To make 'f' maximum, 'e' also should be as minmium as possible. Here the as the
value of d is 19, the next minimum possible value for 'e' is 20 and in which
case, <o:p></o:p></span></div>
<div class="Standard" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">f= 52-20 = 32<u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> D</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: purple;">Note</span>:</span><span style="color: #0070c0; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"> </span><span style="font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">It took comparatively more time to solve in the exam.</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> </span><br />
<br />
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q8)Ramesh
bought a total of 6 fruits (apples and oranges) from the market. He found that
he required one orange less to extract the same quantity of juice as extracted from
apples. If Ramesh had used the same number of apples and oranges o make the
blend, then which of the following correctly represents the percentage of apple
juice in the blend? </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)25% (B) 33.3% (C)
60% (D) 66.6% (E) None of the above <u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:<o:p></o:p></span></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">He has used same
number of apples and oranges => A =3 and O =3<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">He found that he
required one orange less to extract the same quantity of juice as extracted from
apples <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> Had he used 2
Oranges and 3 Apples, it would have contributed equal sharing of juice<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> 2 Oranges and 3
Apples would have contributed equal volume of juice. Let that be ‘x’ each. I
mean, 2 Oranges contribute ‘x’ volume of juice and 3 Apples also contribute ‘x’
volume of juice, making a total of ‘2x’ volume<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">But instead, he used 3
Oranges => Oranges contribute x+0.5x = 1.5x volume (x for 2-oranges and 0.5x
for the extra orange) <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> Now the total
volume of juice = 1.5x+x = 2.5x <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(1.5x from Oranges and
x from Apples)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> The percentage
of contribution of Apples = (x/2.5x)*100 = 40% <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <b>E</b> </span><br />
<br />
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q9) p
and q are positive numbers such that p<sup>q</sup> = q<sup>p</sup>, and q=9p.
The value of p is</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)√9 (B) 9<sup>1/6</sup> (C) 9<sup>1/9</sup> (D)
9<sup>1/8</sup> (E) 9<sup>1/3</sup> <u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:<o:p></o:p></span></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us try to solve
the two equations:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p<sup>9p</sup> = (9p)<sup>p</sup>
=> p<sup>9p</sup> = 9<sup>p </sup>* p<sup>p</sup> => p<sup>9p-p</sup> = 9<sup>p</sup>
=> p<sup>8p</sup> = 9<sup>p</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us check answer
options one by one by substitution method.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A) p = √9,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p<sup>8p</sup> = (9<sup>1/2</sup>)<sup>8√9</sup>=
9<sup>4√9</sup><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">9<sup>p</sup> = 9<sup>√9</sup>
<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">As the bases are same
(ie., 9), just compare the powers.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Both are not equal and
hence option A is out.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(B) p = 9<sup>1/6</sup>,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p<sup>8p</sup> = (9<sup>1/6</sup>)^(8*9<sup>1/6</sup>)=
9^( 9<sup>1/6</sup>*4/3)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">9<sup>p</sup> = 9^(9<sup>1/6</sup>)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Both are not equal and
hence option B is out.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(C) p = 9<sup>1/9</sup>,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p<sup>8p</sup> = (9<sup>1/9</sup>)^(8*9<sup>1/9</sup>)=
9^( 9<sup>1/9</sup>*8/9)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">9<sup>p</sup> = 9^(9<sup>1/9</sup>)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Both are not equal and
hence option C is out.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(D) p = 9<sup>1/8</sup>,<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p<sup>8p</sup> = (9<sup>1/8</sup>)^(8*9<sup>1/8</sup>)=
9^( 9<sup>1/8</sup>*8/8) = 9^(9<sup>1/8</sup>)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">9<sup>p</sup> = 9^(9<sup>1/8</sup>)<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Both are equal and
hence option D is <span style="color: #00b050;">correct</span>.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">And of course, we need
not check option E.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> D</span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note</span></span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:
In the examination, first I have directly tried the substitution method without
initially solving the two equations. It was a mess and then I have tried this
way. It killed some time. <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br />
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q10) Sara
has just joined Facebook. She has 5 friends. Each of her five friends has
twenty five friends. It is found that at least two of Sara’s friends are
connected with each other. On her birthday, Sara decides to invite her friends
and the friends of her friends. How many people did she invite for her birthday
party?</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: .5in; margin-right: 0in; margin-top: 0in; mso-hyphenate: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; mso-vertical-align-alt: auto; text-indent: -.25in;">
<!--[if !supportLists]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";">(A)</span><!--[endif]--><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥ 105</span><span style="font-size: 13.0pt; line-height: 150%;"> (B)
</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≤ 123</span><span style="font-size: 13.0pt; line-height: 150%;"> (C) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">< 125</span><span style="font-size: 13.0pt; line-height: 150%;"> (D)
</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥ 100 and ≤ 125</span><span style="font-size: 13.0pt; line-height: 150%;">
(E) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">≥ 105 and ≤ 123</span><span style="font-size: 13.0pt; line-height: 150%;">
<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:<o:p></o:p></span></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">This is a good problem
and it troubled me a lot in exam.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><a href="http://mathbyvemuri.blogspot.in/2013/01/puzzle-35-xat-2013.html">Check
out the solution here</a><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note</span></span><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">: </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">In exam, I made a mistake by not
considering the ‘key point’ mentioned in the above solution. Then I got the
range as ‘110 to 128’, which is not there in the answer options. I cross checked
my way of approach several times but could not get the right one. Result is -it
killed some valuable time.</span><br />
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q11) 70% of the students who joined XLRI last
year play football, 75% play cricket, 80% play basketball and 85% play carrom.
The minimum percentage of people who play all games is:</span></span></div>
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</span><br />
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">(A)</span></span><span style="font-size: 13.0pt; line-height: 150%;"> </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">5%</span><span style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(B) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">10%</span><span style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(C)
</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">15%</span><span style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(D) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">20%</span><span style="font-size: 13.0pt; line-height: 150%;"> (E) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">None of the above</span><span style="font-size: 13.0pt; line-height: 150%;"> </span></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%;">Sol:</span></u></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%;">70% play football => % not playing football = 30%</span></span></div>
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</span>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%;">75% play cricket => % not playing cricket = 25%</span></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%;">Similarly, % not playing cricket = 20%, % not playing carrom
= 15%</span></span></div>
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</span>
<br />
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%;">Max % of people not playing at least one game = 30+25+20+15 =
90%</span></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="font-size: 13.0pt; line-height: 150%;">A max of 90% do not play at least one game. This means, the
remaining 10% play all the four games.</span></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%;">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%;"> <span style="mso-bidi-font-weight: normal;">B</span></span></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><br /></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q12) The central park is 40 meters long and 30
meters wide. The mayor wants to construct two roads of equal width in the park
such that the roads intersect each other at right angles and the diagonals of
the park are also the diagonals of the small rectangle formed at the
intersection of the two roads. Further the mayor wants that the area of the two
roads to be equal to the remaining area of the park. What should be the width
of the roads?</span></span></div>
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<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: 39.75pt; margin-right: 0in; margin-top: 0in; mso-hyphenate: auto; mso-list: l0 level1 lfo2; mso-pagination: widow-orphan; mso-vertical-align-alt: auto; text-indent: -21.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman"; mso-fareast-font-family: "Times New Roman";"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span style="font-size: 13.0pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span></span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">10 meters</span><span style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(B)
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</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">15 meters</span><span style="font-size: 13.0pt; line-height: 150%;"> (E) </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">16
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<span style="color: #c00000; font-size: 13.0pt; line-height: 150%;">Sol:</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-xx1EfKL6_VY/UPSye-45VxI/AAAAAAAAAcg/eBjqdmijCGc/s1600/xat2013_12.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="165" src="http://4.bp.blogspot.com/-xx1EfKL6_VY/UPSye-45VxI/AAAAAAAAAcg/eBjqdmijCGc/s320/xat2013_12.png" width="320" /></a></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%;">x(40-x)+ x(30-x)+x<sup>2</sup> = 40*30-[ x(40-x)+ x(30-x)+x<sup>2</sup>]</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%;">=> 2[x(40-x)+ x(30-x)+x<sup>2</sup>] = 1200</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%;">=> 70x-x<sup>2</sup> = 600 => x<sup>2</sup>-70x+600 = 0
=> (x-10) (x-60) = 0</span></div>
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<span style="font-size: 13.0pt; line-height: 150%;">=> x = 10 or 60</span></div>
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<span style="font-size: 13.0pt; line-height: 150%;">As x must be less than 30, x = 10</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%;">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%;"> <span style="mso-bidi-font-weight: normal;">A</span></span><span style="mso-bidi-font-weight: normal;"></span></div>
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<div class="MsoNormal" style="line-height: 150%;">
<br />
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q13)How
many whole numbers between 100 and 800 contain the digit 2?</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)200<span style="mso-tab-count: 1;"> </span>(B) 214 <span style="mso-tab-count: 1;"> </span>(C)
220 <span style="mso-tab-count: 1;"> </span>(D) 240<span style="mso-tab-count: 1;"> </span>(E) 248 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Here point is the
number to be considered is of 3-digit. So, digit '2' can be in any of the three
places- unit's ten's or hundred's position.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'2' in unit's
position:</span></u></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">102,112,122,.....792=>
by observing the first two digits (10 to 79), we can say that these are <b>70</b>
in number.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'2' in ten's position:</span></u></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">120,121,122,...to 129
(122 should be excluded as it is already considered in the above list) </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">220,221,222,...to 229
(222 should be excluded as it is already considered in the above list) </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">….. such lists up to
729</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> 9*7 = <b>63</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'2' in hundred's
position:</span></u></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">200,202.......299:
(100 numbers)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Out of all these, 220
to 229 shall be excluded. (10 numbers)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Out of all these,
202,212,222,232,... to 292 shall be excluded. (10-1 = 9 numbers)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">100-10-9 = <b>81</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Finally, the number of
whole numbers meeting the criteria = 70+63+81 = <b>214</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> B</span><span style="color: red; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note</span><b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:</span></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">
My mistake in exam: For the case of '2' in ten's position, I had considered 9*8
instead of 9*7. I was contemplating that as the values range from 100 to 800
and so there are 8 such cases each of 9 numbers. But here the range stops at
800 and the numbers such as 820,821,...829 must not be considered. My answer
was not matching with any of the given answer options. It killed some time.<span style="color: #0070c0;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q14) A
number is interesting if on adding the sum of the digits of the number, and the
product of the digits of the number, the result is equal to the number. What
fraction of numbers between 10 and 100 (both 10 and 100 included) is interesting?</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)0.1<span style="mso-tab-count: 1;"> </span>(B) 0.11 <span style="mso-tab-count: 1;"> </span>(C)
0.16<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>(D)
0.22<span style="mso-tab-count: 1;"> </span>(E) None of the above<span style="mso-spacerun: yes;"> </span><span style="color: #c00000;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">As
the number to be considered is in between 10 and 100, we can suppose it to be a
two digit one 'xy'. The number 100 con be neglected as it does not meet the
criteria, as </span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">1+0+0+(1*0*0)
= 1 <span style="color: #222222;">≠</span> 100.</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">For
a number 'xy', on adding the sum of digits of the number, and the product of
the digits of the number yields: x+y+x*y</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">And
if it is to meet the criteria, this sum shall be equal to the number 'xy',
which is nothing but 10x+y.</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-spacerun: yes;"> </span>x+y+x*y =<span style="mso-spacerun: yes;">
</span>10x+y => x*y=9x => x(y-9) = 0 => x=0 or y=9</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">For
the number to be two digit, x must be a non-zero number and hence, x must not
be zero</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>
y = 9.</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">All
the two-digit numbers with y=9, ie., with 9 as unit digit are:</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">19,29,39,49,59,69,79,89,99</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">These
are 9 in number. So, 9 numbers between 10 and 100 (both 10 and 100 included)
are interesting</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 399.75pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>
9 out of 91 are interesting => fraction = 9/91 = 0.099 <span style="color: #222222;">≃</span> <span style="mso-spacerun: yes;"> </span>0.1<u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <span style="mso-bidi-font-weight: normal;">A</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q15)Consider
the expression: (xxx)<sub>b</sub> = x<sup>3</sup>,where b is the base, and x is
any digit of base b. Find the value of b:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)5<span style="mso-tab-count: 1;"> </span>(B) 6 <span style="mso-tab-count: 1;"> </span>(C)
7 <span style="mso-tab-count: 1;"> </span>(D) 8<span style="mso-tab-count: 1;"> </span>(E)
None of the above <span style="color: #94006b;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #94006b; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">It's all about the
base system. For example, '234' in decimal system (base 10) can actually be
written as 2*10<sup>2</sup>+3*10<sup>1</sup>+4*10<sup>0.</sup> </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now I directly plunge
in to the given equation:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(xxx)<sub>b</sub> = x<sup>3</sup></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> x*b<sup>2</sup>+x*b<sup>1</sup>+x*b<sup>0</sup>
= x<sup>3</sup></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> x(b<sup>2</sup>+b+1-x<sup>2</sup>)=
0</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> b<sup>2</sup>+b+1=
x<sup>2</sup></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=><span style="mso-spacerun: yes;"> </span>b<sup>2</sup>+b+1 must be a perfect square</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now check the answer
options one-by-one.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A) b=5 =><span style="mso-spacerun: yes;"> </span>b<sup>2</sup>+b+1 = 25+5+1 = 31 <span style="color: #222222;">≠ a perfect square => option is </span><span style="color: red;">out</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(B) b=6 =><span style="mso-spacerun: yes;"> </span>b<sup>2</sup>+b+1 = 36+6+1 = 43 <span style="color: #222222;">≠ a perfect square => option is </span><span style="color: red;">out</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(C) b=7 =><span style="mso-spacerun: yes;"> </span>b<sup>2</sup>+b+1 = 49+7+1 = 57 <span style="color: #222222;">≠ a perfect square => option is </span><span style="color: red;">out</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(D) b=8 =><span style="mso-spacerun: yes;"> </span>b<sup>2</sup>+b+1 = 64+8+1 = 73 <span style="color: #222222;">≠ a perfect square => option is </span><span style="color: red;">out</span><span style="color: #222222;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #222222; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">So the
only option left out is (E)</span><u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <span style="mso-bidi-font-weight: normal;">E</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q16)
Consider a function f(x) = x<sup>4</sup>+x<sup>3</sup>+x<sup>2</sup>+x+1, where
x is a positive integer greater than 1. What will be the remainder if f(x<sup>5</sup>)
is divided by f(x)?</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)1<span style="mso-tab-count: 1;"> </span>(B) 4<span style="mso-tab-count: 2;"> </span>(C)
5 <span style="mso-tab-count: 1;"> </span>(D) a monomial in x<span style="mso-tab-count: 1;"> </span> (E) a polynomial in x <u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let x = 2.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">f(x) = x<sup>4</sup>+x<sup>3</sup>+x<sup>2</sup>+x+1
</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">f(x<sup>5</sup>) = x<sup>20</sup>+x<sup>15</sup>+x<sup>10</sup>+x<sup>5</sup>+1
=<span style="mso-spacerun: yes;"> </span>x<sup>20</sup>-1+1+x<sup>15</sup>-1+1+x<sup>10</sup>-1+1+x<sup>5</sup>-1+1+1</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=(x<sup>20</sup>-1)+(x<sup>15</sup>-1)+(x<sup>10</sup>-1)+(x<sup>5</sup>-1)+5</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now if we divide f(x<sup>5</sup>)
with f(x), then we need to find the remainder.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">But, just observe one
thing here: all the terms of f(x<sup>5</sup>) except 5, ie., (x<sup>20</sup>-1),
(x<sup>15</sup>-1), (x<sup>10</sup>-1) and (x<sup>5</sup>-1) are divisible by
(x<sup>5</sup>-1). And (x<sup>5</sup>-1) can be split as (x-1)(x<sup>4</sup>+x<sup>3</sup>+x<sup>2</sup>+x+1).</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> all the terms of
f(x<sup>5</sup>) except 5, ie., (x<sup>20</sup>-1), (x<sup>15</sup>-1), (x<sup>10</sup>-1)
and (x<sup>5</sup>-1)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">are divisible by (x<sup>4</sup>+x<sup>3</sup>+x<sup>2</sup>+x+1)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> When we divide
f(x<sup>5</sup>) with f(x), the only term left undivided is<span style="mso-spacerun: yes;"> </span>'5'</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> remainder = 5<span style="color: #94006b;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #94006b; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">I have tried to get
the remainder by directly dividing (x<sup>20</sup>+x<sup>15</sup>+x<sup>10</sup>+x<sup>5</sup>+1)
with (x<sup>4</sup>+x<sup>3</sup>+x<sup>2</sup>+x+1) and got the answer. But as
this involves a bit calculation oriented,<span style="mso-spacerun: yes;">
</span>a little patience is required here, and there is a high chance of
committing mistakes in this method.<u><span style="color: #c00000;"></span></u></span></div>
<u><span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">Answer:</span></u><span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"> C</span><br />
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
</div>
</div>
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</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q17) p,q
and r are three non-negative integers such that p+q+r=10. The maximum value of
pq+qr+pr+pqr is</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
</span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: black;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)
≥ 40 and ≤
50<span style="mso-tab-count: 1;"> </span>(B) ≥
50 and ≤ 60 <span style="mso-tab-count: 1;"> </span>(C)
≥ 60 and ≤
70 <span style="mso-tab-count: 1;"> </span></span></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
<span style="color: black;">
</span></span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: black;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(D)
≥ 70 and ≤
80<span style="mso-tab-count: 1;"> </span>(E) ≥
80 and ≤ 90 </span></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
<span style="color: black;">
</span></span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="color: black;">Sol</span>:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
</span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: black;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">This is a traditional
type of problem, being touched in all types of competitive exams most frequently.
The funda here is p=q=r.</span></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
<span style="color: black;">
</span></span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;"><span style="color: black;"><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">p+q+r=10
=>3p=3q=3r=10 => p=q=r=10/3</span></span></span></div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">
<span style="color: black;">
</span><div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="color: black;">pq+qr+pr+pqr = 3p<sup>2
</sup>+p<sup>3 </sup>= 3(10/3)<sup>2 </sup>+(10/3)<sup>3<span style="mso-spacerun: yes;"> </span></sup>= 100/3 + 1000/27 = 33.3+37.03 > 70</span><u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> D</span></div>
</span><br />
<div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q18)
Ram, Shyam and Hari went out for a 100 km journey. Ram and Hari started the
journey in Ram’s car at the rate of 25 kmph, while Shyam walked at 5 kmph.
After some time Hari got off and started walking at the rate of 5 kmph and Ram
went back to pick up Shyam. All three reached the destination simultaneously.
The number of hours required for the trip was:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)8 (B) 7 (C)
6 (D) 5 (E)
4 <u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></u></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Key point to solve:</span></u><b><i><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></i></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><i><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">“If you break it in to
pieces of each of the three friends individual journey, the puzzle will be
resolved”</span></i></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us take that 'R'
and 'H' initially travels for distance 'x' km before 'H' gets off and starts
walking and 'R' gets back in the car to pick up 'S'. And let us also consider
'y' km as the distance covered by 'R' before he meets 'S'. Then he pics up 'S'
and both of them travel up to the end.<u><o:p></o:p></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now let us consider
the journeys of the three one-by-one:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'H' travels in car
with a speed of 25 kmph up to 'x' km and then he completes the remaining
journey of '100-x' km by walking at a
speed of 5 kmph <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> the time taken
by 'H' = (x/25) + (100-x/5) = (500-4x)/25<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'R' travels in car
with a speed of 25 kmph up to 'x' km and then he goes back in car a distance of
'y' km and pics up 'S' and again travels back 'y' km distance to reach the
point of 'x' km and continues further to complete the remaining '100-x' km
journey. So through out the journey, 'R' travels in the car a distance of
x+y+y+(100-x) = 100+2y<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> the time taken
by 'R' = (100+2y)/25 <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'S' walks at a speed
of 5 kmph for a distance of (x-y) km, where he meets 'R' and continues the
remaining journey of '100-(x-y)' km in the car at a speed of 25 kmph<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> the time taken
by 'S' = (x-y)/5 + (100-(x-y))/25 = {100+4(x-y)}/25<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now the point is : '<span style="color: #0070c0;">All three reached the destination simultaneously ' </span><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> all three took
same time<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> (500-4x)/25 =
(100+2y)/25 = {100+4(x-y)}/25<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> on solving we
get y = 50 and x = 75<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">If we substitute these
values in one of the times taken by R or S or H, we get the answer of <b><span style="color: red;">8</span></b> hrs <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <u><span style="color: #c00000;">Answer:</span></u><span style="color: #c00000;"> <b>A</b></span><span style="color: #0070c0;"> </span></span><o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q19) In
a square PQRS, A and B are two points on PS and SR such that PA = 2AS and
RB=2BS. If PQ=6, the area of the triangle ABQ is (is it a repeat)</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)6 (B) 8 (C)
10 (D) 12 (E) 14 <u><span style="color: #c00000;"><o:p></o:p></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'<span style="color: blue;">The mantra</span>' => “<b><i>Draw a figure and get the
idea</i></b>”<o:p></o:p></span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-w48-fTlspzE/UQ3CgiUxm6I/AAAAAAAAAg8/xOjV-_OisRM/s1600/XAT2013_18.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://4.bp.blogspot.com/-w48-fTlspzE/UQ3CgiUxm6I/AAAAAAAAAg8/xOjV-_OisRM/s1600/XAT2013_18.png" /></a></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13pt; line-height: 150%;">We
can trace out 4 triangles from the figure:</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">ABS,
APQ, QRB and ABQ. <span style="color: blue;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="color: blue; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">The point</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> is - “<b><i>summing up areas of these
4 triangles give us area of the square PQRS</i></b>”. <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">And
here, except ABQ all other are right-triangles and we also know the bases and
heights of these right-triangles such that we can find their areas by using the
formula 1/2*b*h.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Area
of triangle ABS = ½ * 2 * 2 = 2<o:p></o:p></span></div>
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of triangle APQ = ½ * 6 * 4 = 12<o:p></o:p></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Area
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Area
of the square PQRS = 6 * 6 = 36<o:p></o:p></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Area
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Area of the square PQRS - (Area of triangle ABS + Area of triangle APQ + Area
of triangle QRB)<o:p></o:p></span></div>
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<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=
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<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <b>C</b></span></div>
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<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q20) In
the country of Four there are four cities, A,B,C and D. B is to the East of A,
C is to the South of B, D is to the West of C, and A is to the North of D. The
Government of Four is planning to connect these four cities by road such that
it is possible for a person to go from a city to any of the other three cities.
At the same time, the Government wants to ensure that the total road length is
minimum. The distances between A to B, B to C, C to D and D to A are all equal
to 10 km. What should be the total length of the road?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)26.64<span style="mso-tab-count: 1;"> </span>(B) 27.32<span style="mso-tab-count: 1;"> </span>(C)
28.30 <span style="mso-tab-count: 1;"> </span>(D) 30<span style="mso-tab-count: 1;"> </span>(E) 36 <u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">'<span style="color: blue;">The mantra</span>' => “<b><i>Draw a figure and get the
idea</i></b>”</span></div>
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-tlbvl9Y-3tI/URENsjUh34I/AAAAAAAAAhc/xZPVxFGd_dE/s1600/XAT2013_20.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="195" src="http://3.bp.blogspot.com/-tlbvl9Y-3tI/URENsjUh34I/AAAAAAAAAhc/xZPVxFGd_dE/s320/XAT2013_20.png" width="320" /></a></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">The
points A,B,C and D are consecutive vertices of a square. A road with minimum
length which connects each city with the remaining three cities can be built if
the four cities are connected diagonally. There are two diagonals with each
diagonal having a length of 10√2.</span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 408.0pt 411.0pt;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">The
total length of the road = 2 * 10√2 = 28.28<span style="mso-spacerun: yes;">
</span><u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <b style="mso-bidi-font-weight: normal;">C</b></span><br />
<br />
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<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q21)Please
read the following sentences carefully:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">I – 103
and 7 are the only prime factors of 1000027</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">II
-<span style="mso-spacerun: yes;"> </span><sup>6</sup>√6! > <sup>7</sup>√7!</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">III – If
I travel one half of my journey at an average speed of x km/h, it will be
impossible for me to attain an average speed of 2x km/h for the entire journey.
</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)All
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<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(C)
Only statement III is correct <span style="mso-tab-count: 1;"> </span>(D)
Both statements I and II are correct</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(E)
Both statements I and III are correct <u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us try to split
1000027:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">1000027 = 7*142861 =
7*103*1387</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now we have to check
for any factor of 1387:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">First it is odd and
hence 2 or any one of even numbers is not a factor. </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sum of digits =
1+3+8+7 = 19, not a multiple of 3 and hence 3 and 9 are not factors.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Unit digit is neither
0 nor 5 =><span style="mso-spacerun: yes;"> </span>5 or any one of numbers
ending in 5 is not a factor</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">If we check, 7 is not
a factor</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sum of alternate
digits = 1+8 <span style="color: #222222;">≠</span> 3+7 => 11 is not a factor</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">If we check, 13 and 17
are not factors<span style="color: red;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: red; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">but, 19 is a
factor</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">1000027 = 7*103*1387
=<span style="mso-spacerun: yes;"> </span>7*103*19*73</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">So statement I is
wrong => Answer options A,D and E can be eliminated. And the only left out
answer options are B and C => only one of the options II and III is correct<u><span style="color: #c00000;">.</span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Statement III looks a
simpler bet</span></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">One half of the
journey is completed x km/h. Let the other half is completed at an average
speed y km/h. If the total distance is taken as 'd', then the overall average
speed </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">= tot. distance / tot.
time</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">= d/(d/2x + d/2y) =
4xy/(2x+2y) = 2xy/(x+y) </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now let us check
whether this could be be equal to 2x:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">2xy/(x+y) = 2x => y
= x+y => x=0 which is wrong</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> it will be
impossible to attain an average speed of 2x</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> statement III is
correct</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">From the answer
options, as we already know that only one of the statements II or III is
correct, we can count on statement III and we need not check statement II. <u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <b style="mso-bidi-font-weight: normal;">C</b></span><b><u><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></u></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Note:</span></u></b><b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Let us check option
II:</span></b><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Here a little manipulation
is required.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">6! = 6*5! =
(6^6)(1/6^5)(5!)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> <sup>6</sup>√6!
= <b>(6) * <sup>6</sup>√(5!/6^5)<span style="mso-tab-count: 1;"> </span>---(1)</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">7! = 6*7*5! =
(6^7)(1/6^6)(7*5!)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> <sup>7</sup>√7!
= (6) * <sup>7</sup>√(7*5!/6^6) = <b>(6)* <sup>7</sup>√(5!/6^5) * <sup>7</sup>√(7/6)<span style="mso-tab-count: 1;"> </span>---(2)</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Now note the following
two points:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">5!/6^5 < 1 => <sup>7</sup>√(5!/6^5)
> <sup>6</sup>√(5!/6^5) ---(<b>3</b>)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">7/6 > 1 => <sup>7</sup>√(7/6)
> 1<span style="mso-tab-count: 1;"> </span>---(<b>4</b>)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">From (3) and (4), we
can say that,</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(6) * <sup>7</sup>√(5!/6^5)
* <sup>7</sup>√(7/6) >(6) * <sup>6</sup>√(5!/6^5)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> <sup>7</sup>√7!
> <sup>6</sup>√6! </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=> <b>statement-II
is wrong</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Q22)Six
playing cards are lying face down on a table, two of them are kings. Two cards
are drawn at random. Let 'a' denote the probability that at least one of the
cards drawn is a king, and 'b' denote the probability of not drawing a king.
The ratio a/b is </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;"></span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 51.0pt; margin-right: 0in; margin-top: 0in; mso-list: l0 level1 lfo1; tab-stops: list 0in; text-indent: -33.0pt;">
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN; mso-fareast-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";">
</span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">≥ 0.25 and < 0.5 (B) ≥ 0.5 and
< 0.75<span style="mso-tab-count: 1;"> </span>(C) ≥ 0.75 and < 1.0 </span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; margin-left: 18.75pt; margin-right: 0in; margin-top: 0in; tab-stops: 32.25pt; text-indent: -23.25pt;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">(D)
≥ 1.0 and < 1.25 (E) ≥ 1.25<u><span style="color: #c00000;"></span></u></span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<u><span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Sol:</span></u><b><u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;"></span></u></b></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">There
are three scenarios:</span></u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;"></span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Either two
are kings, only one card is king, none of the two is king</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">In all, the
number of combinations of taking 2 cards out of 6 = 6C2 = 15</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Split
of this is like this:</span></u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;"></span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">The number of
combinations of the two cards being kings = 2C2 = 1</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">The number of
combinations of only one card being a king = 2C1 * 4C1 = 2*4 = 8</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">The number of
combinations of neither card being a king =<span style="mso-spacerun: yes;">
</span>4C2 = 6</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Now, a =
P(at least one king) = P(one king)+P(two kings) = (8+1)/15 = 3/5 </span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">b = P(no
king) = 6/15 = 2/5</span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">=> a/b =
3/2 = 1.5 <u><span style="color: #c00000;"></span></u></span></div>
<div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<u><span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-ansi-language: EN-IN;">Answer:<b>E</b></span></u><b style="mso-bidi-font-weight: normal;"><span style="color: red; font-size: 13.0pt; line-height: 150%;"></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Q23)
Arun has to go to the country of Ten to work on a series of tasks for which he
must get a permit from the Government of Ten. Once the permit is issued, Arun
can enter the country within ten days of the date of issue of the permit. Once
Arun enters Ten, he can stay for a maximum of ten days. Each of the tasks has a
priority and takes certain number of days to complete. Arun can not work on
more than one task at a time. The following table gives the details of the priority
and the number of days required for each task.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://1.bp.blogspot.com/-oN2w6ju-KjY/URMCoAnnQHI/AAAAAAAAAh0/LduR7CMi_fg/s1600/XAT2013_23.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="http://1.bp.blogspot.com/-oN2w6ju-KjY/URMCoAnnQHI/AAAAAAAAAh0/LduR7CMi_fg/s1600/XAT2013_23.png" /></a></div>
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Arun's first priority is to complete as many tasks as possible,
and then try to complete the higher priority tasks. His last priority is to go
back as soon as possible. The tasks that Arun should try to complete are:</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(A)T1
and T2<span style="mso-tab-count: 1;"> </span>(B) T1,T2 and T5 <span style="mso-tab-count: 1;"> </span>(C) T1,T4 and T5<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(D)
T1,T2 and T4<span style="mso-tab-count: 1;"> </span>(E) T1,T3 and
T4<span style="mso-spacerun: yes;"> </span><u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Sol:</span></u><span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">“Arun's
first priority is to complete as many tasks as possible”</span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">=>At the most, 3
tasks can be completed with in 10 days and all the combinations possible are:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>T1,T2 and T5 => 3+5+2=10 days</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>T1,T3 and T4 => 3+3+4=10 days</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>T1,T4 and T5 => 3+4+2= 9 days</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>T2,T3 and T5 => 5+3+2=10 days</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"><span style="mso-tab-count: 1;"> </span>T3,T4 and T5 => 3+4+2= 9 days</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">To filter out further,
let us see the second & third priorities:<span style="color: #0070c0;"></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">“try to
complete the higher priority tasks” </span><span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">and<span style="color: #0070c0;"> “to go back as soon as possible”</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">(T1,T2,T5) combination
looks more suitable as it involves top two priorities. <u><span style="color: #c00000;"></span></u></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";">Answer:</span></u><span style="color: #c00000; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: "Times New Roman";"> <b style="mso-bidi-font-weight: normal;">B</b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
</div>
</div>
<span style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; mso-ansi-language: EN-US; mso-bidi-language: HI; mso-fareast-font-family: "Lucida Sans Unicode"; mso-fareast-language: HI; mso-font-kerning: .5pt;">More Problems in line.....</span></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com5tag:blogger.com,1999:blog-5567027158491397321.post-28979636267859112742013-01-08T20:12:00.000+05:302013-01-23T22:38:43.195+05:30Indian Economy, a CR point<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">I
was reading through a write-up on Indian Economy-2012. I wanted to relate one
point from here to the critical reasoning stuff.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">The
following are the facts found in a recent survey:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Fact-1</span><span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">: Indian economy may be
broadly divided in to three sectors- Industry, Agriculture and Services. The
contributions of these sectors to the GDP are as follows: <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Agriculture-15%,
Industry-28%, Services-57%<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Fact-2</span><span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">: For over a
considerable period, there is exodus observed in a significant extent. People
are moving from rural to urban areas. Most of the people who are moving out of
rural areas are not finding agriculture as a lucrative sector and trying to
find jobs in industries in urban areas.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;"></span><br />
<a name='more'></a><span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Surprise Element</span><span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">: <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">India,
being known for a primarily agriculture-based country, has got only 15% of GDP
from that sector. Now the point is why is it so?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">From
the facts-1 & 2 mentioned above, the most general conclusion may be like
this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Most
of the people are not interested to work in Agriculture sector and over a
period, most of the people have moved to urban areas to work in industry and
services sectors. This is the reason why the Services and Industry sectors are
at upper hand in contributing to GDP when compared to the Agriculture sector.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">But
in reality, if we see the third fact, we surprise once again:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Fact-3</span><span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">: Figures of 'labour-force
by occupation' are like this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Agriculture-52%,
Industry-14%, Services-34%<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Even
though more than half of the labour-force works in Agriculture sector, the
contribution from that sector is not to that extent. The point here is - "exodus" may not be the main reason (or it may not be a reason at
all) for this and there must be other factors.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<b><span lang="EN-IN" style="color: #c00000; font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Bottom
line</span></b><span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">Don't
jump for a quick conclusion. Go through all answer options carefully and
evaluate one by one critically.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-family: "Times New Roman","serif"; font-size: 13.0pt; line-height: 150%;">By
name itself, it's a "Critical" Reasoning section, right?</span></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-21202057332984632592013-01-07T22:48:00.000+05:302013-01-23T22:43:15.630+05:30XAT-2013 :My Experience<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="color: #c00000; line-height: 150%;">D'day</span><span style="line-height: 150%;"> - 6th Jan'2013</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Centre</span>: St.Patricks High School, Sebastian Road, Sec'bad<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">Parts</span></b>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Two parts. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">Part-I</span>: 140 min. VA,DM and QA sections <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">Part-II</span>: 40 min. General Awareness and Essay. Surprise this time is
introduction of GA section here.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">Part-I</span></u></b>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
A total of 91 Q's. All are multiple choice Q's having 5
options each.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
This part is divided like this:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Sec-A</span>: Verbal Ability<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Total Q's: 30<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Sec-B</span>: Decision Making<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Total Q's: 25<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Sec-C</span>: Quantitative Ability<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Total Q's: 36<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">-ve Marking</span>: <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
It's a surprise this time. It's a straight forward formula. One
fourth for each wrong Q.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #1f497d; mso-bidi-font-family: "Times New Roman";">Differential Marking</span>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
It's again a surprise this time.No differential marking. All
Q's carry equal marks.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><span style="color: #c00000; mso-bidi-font-family: "Times New Roman";"></span></b><br />
<a name='more'></a><b><span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">My
strategy</span></b>: Spending
35 min each on the three sections in the first round. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Depending on the experiences of first round, dividing the
remaining 35 min - some time on weaker section to fill the gaps and rest on
stronger one to increase the total score. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">First Round of Attempts</span>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; mso-bidi-font-family: "Times New Roman";">Step-I<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
I started with QA and spent 35 min on it and could read
around 15-18 Q's but could answer 10 Q's.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Totally spent on math part of QA and left DI part. I
committed a mistake while rounding answer for one Q. I had rounded it for the
next Q. I came to know this while attempting to mark the answer for the next Q
and unfortunately, the answer choices for the two Q's are different. To avoid
negative marking I had to mark two choices for that one. I lost one mark here
and I prepared to leave that at that point and proceeded further.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; mso-bidi-font-family: "Times New Roman";">Step-II<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
Moved to VA (my weak area) and spent another 35 min. I could
hardly read around 12 Q's and could answer 7.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Spent on Grammar and Para jumbles. Left LR and RC parts.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; mso-bidi-font-family: "Times New Roman";">Step-III<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
Moved to DM and spent another 35 min. Generally, I am
comfortable in this zone but I am slow at reading.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I could read 10 Q's and attempted all 10.This covered 3 sets
in this section.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
Excepting a little disappointment with my speed, first round
is reasonably good. I maintained my time schedules.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Second Round of Attempts</span>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I left with some 25-30 min. My attempts in the 1st round are:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
VA : 7/30, DM: 10/25 and QA: 10/36.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I am a bit content with my attempts in DM section and I
thought of spending the remaining time first on VA and then on QA.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Spent around 15 min on QA and could read around 3-4 Q's and
could attempted 2 Q's. I have spent on LR and left RC totally unattempted.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Last 15 min, I have spent on QA and could see 4-5 Q's and
could attempt 2 Q's. This time I touched a set from DI part also.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
Throughout the second round of 30 min, I was not stable.
There was some underlying tension, don't know why.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
That completed the First part of the exam. My overall
attempts were: VA:9/30, DM:10/25, QA:12/36<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span style="color: #0070c0; mso-bidi-font-family: "Times New Roman";">Part-II</span></u></b>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">GA</span>: 30 Q's. All Q's carry equal marks<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">-ve marking</span>: same as that of Part-I. one-fouth-of allotted mark.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Essay</span>: "Corruption is the root cause of economic slowdown in
Indi "<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I have spent first 12-15 min on GA and could read around
22-25 Q's and could attempt 12 Q's. Then I moved to the essay.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I was very comfortable in writing it. Spent for 3-4 min on
thinking on how to develop it. Spent next 5-8 min for completing the essay
writing. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
In the last 2-3 min time, I attempted 3 more Q's of GA
section. overall attempts in GA: 15/30.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
My accuracy in GA section is around 50%.<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #c00000; mso-bidi-font-family: "Times New Roman";">Final Say</span>:<o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
I am happy with my "above 80%" accuracy in VA, DM
and QA sections. I am ok with my strategy as well. But my worry is my speed. <o:p></o:p></div>
<div class="MsoNormal" style="line-height: 150%;">
That may be mainly due to lack of practice.<o:p></o:p></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-10185700756470745032013-01-06T15:12:00.003+05:302013-01-15T07:08:09.332+05:30XAT-2013 Answer key<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="line-height: 150%;"><span style="color: purple; font-family: "Calibri","sans-serif"; font-size: large;">Quantitative Ability:</span> </span><br />
<span lang="EN-IN" style="line-height: 150%;"><span style="font-family: "Calibri","sans-serif";"><span style="font-size: 13pt;"> </span><a href="http://mathbyvemuri.blogspot.com/2013/01/xat-2013-detailed-solutions.html" target="_blank"><span style="font-size: x-large;">click here for detailed solutions</span></a></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q1)Prof. Mandal walks....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 22.5pt; mso-list: l3 level1 lfo1; text-indent: -4.5pt;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">100 minutes<span style="mso-tab-count: 1;"> </span>(B) 120 minutes <span style="mso-tab-count: 1;"> </span>(C) 140 minutes <span style="mso-tab-count: 1;"> </span>(D)
150 minutes (E)None of the above</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<u><span lang="EN-IN" style="color: purple; font-size: 13.0pt; line-height: 150%;">Answer</span><span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;">:</span></u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> <span style="color: purple;">D</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q2)At the centre</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> of a city’s municipal park<span style="color: #0070c0;"> ....</span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .25in; mso-list: l2 level1 lfo2; text-indent: 0in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">62500</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">π</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(B) 125000</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">π</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> <span style="mso-tab-count: 1;"> </span>(C)
250000</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">π</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> <span style="mso-tab-count: 1;"> </span>(D) 500000</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">π</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (E)Cannot be answered
from the given data </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> A</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q3)Mr.Mehra is planning for higher
education ....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l0 level1 lfo3; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">5% and 7.5% respectively<span style="mso-tab-count: 1;"> </span>(B) 8% and 12% respectively <span style="mso-tab-count: 1;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(C) 10% and 15%
respectively <span style="mso-tab-count: 1;"> </span>(D) 15% and 22.5%
respectively </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(E) 20% and 30%
respectively </span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: -7.1pt; text-indent: 7.1pt;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> E</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q4)Albela, Bob and Chulbul ....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; mso-list: l1 level1 lfo4; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">24<span style="mso-tab-count: 1;"> </span>(B) 25 <span style="mso-tab-count: 1;"> </span>(C) 26 <span style="mso-tab-count: 1;"> </span>(D) 27<span style="mso-tab-count: 1;"> </span>(E)
28 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> A</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q5)The taxis plying in Wasseypur....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)17<span style="mso-tab-count: 1;"> </span>(B) 18 <span style="mso-tab-count: 1;"> </span>(C)
19 <span style="mso-tab-count: 1;"> </span>(D) 20<span style="mso-tab-count: 1;"> </span>(E)
21 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> C</span></span><span lang="EN-IN" style="color: red; font-size: 13.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q6)Consider the expression (a<sup>2</sup>+a+1)....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)3<span style="mso-tab-count: 1;"> </span>(B) 1 <span style="mso-tab-count: 1;"> </span>(C) 10 <span style="mso-tab-count: 1;"> </span>(D) 100<span style="mso-tab-count: 1;"> </span>(E) 243 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> E</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Q7) The mean of six positive integers....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)26<span style="mso-tab-count: 1;"> </span>(B) 28 <span style="mso-tab-count: 1;"> </span>(C)
30 <span style="mso-tab-count: 1;"> </span>(D) 32<span style="mso-tab-count: 1;"> </span>(E)
34 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> D</span></span><span lang="EN-IN" style="color: red; font-size: 13.0pt; line-height: 150%;"></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Q8) Ramesh bought a total of 6 fruits....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)25%<span style="mso-tab-count: 1;"> </span>(B) 33.3% <span style="mso-tab-count: 1;"> </span>(C)
60% <span style="mso-tab-count: 1;"> </span>(D) 66.6%<span style="mso-tab-count: 1;"> </span>(E) None of the above </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> E</span></span><br />
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><b><br /></b></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q9) p and q are positive numbers....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">√</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">9<span style="mso-tab-count: 1;"> </span>(B) (9)<sup>1/6</sup> <span style="mso-tab-count: 1;"> </span>(C)
(9)<sup>1/9</sup> <span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>(D) (9)<sup>1/8</sup><span style="mso-tab-count: 1;"> </span>(E) (9)<sup>1/3</sup> <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> D</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q10)A number is interesting if....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">0.1</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(B) 0.11 <span style="mso-tab-count: 1;"> </span>(C) 0.16
<span style="mso-spacerun: yes;"> </span><span style="mso-tab-count: 1;"> </span>(D)
0.22<span style="mso-tab-count: 1;"> </span>(E) None of the above <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> A</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q11)Consider the expression: (xxx)<sub>b</sub>
= x<sup>3</sup>....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)5<span style="mso-tab-count: 1;"> </span>(B) 6 <span style="mso-tab-count: 1;"> </span>(C) 7 <span style="mso-tab-count: 1;"> </span>(D) 8<span style="mso-tab-count: 1;"> </span>(E) None of the above </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> E</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q12)The figure below show the graph of a
function f(x)....</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)5<span style="mso-tab-count: 1;"> </span>(B) 6 <span style="mso-tab-count: 1;"> </span>(C) 7 <span style="mso-tab-count: 1;"> </span>(D) 8<span style="mso-tab-count: 1;"> </span>(E) None of the above </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> C</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q13)How many whole numbers between 100
and 800 contain the digit 2?</span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)200<span style="mso-tab-count: 1;"> </span>(B) 214 <span style="mso-tab-count: 1;"> </span>(C)
220 <span style="mso-tab-count: 1;"> </span>(D) 240<span style="mso-tab-count: 1;"> </span>(E) 248 </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> B</span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q14)Ram,Shyam and hari..</span><br />
<div style="text-indent: 0px;">
<span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"><span style="color: #0070c0;"> </span>(A)8</span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;">(B) 7</span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;">(C) 6 </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;">(D) 5</span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;"> </span><span style="font-size: 13pt; line-height: 150%; text-indent: -0.25in;">(E) 4</span></div>
</div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> A</span></span><br />
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Q15)Consider a function f(x) = x</span><sup style="color: #0070c0; line-height: 150%;">4</sup><span style="color: #0070c0; font-size: 13pt; line-height: 150%;">+x</span><sup style="color: #0070c0; line-height: 150%;">3</sup><span style="color: #0070c0; font-size: 13pt; line-height: 150%;">+x</span><sup style="color: #0070c0; line-height: 150%;">2</sup><span style="color: #0070c0; font-size: 13pt; line-height: 150%;">+x+1,
where x is a ...</span><br />
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;">
</span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)1 (B) 4 (C) 5 (D) a monomial in x (E) a
polynomial in x <span style="color: #c00000;"><o:p></o:p></span></span></span></div>
<span lang="EN-IN" style="color: purple; font-size: 13.0pt; line-height: 150%;">
<u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;">Answer:</span></u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"> C</span></span><br />
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 25.454544067382813px;"><br /></span>
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 25.454544067382813px;">Q16)Six playing cards are lying ...</span><br />
<div style="color: black; font-family: 'Times New Roman'; font-size: medium; line-height: 24.545454025268555px;">
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 25.454544067382813px;"></span></span></span></div>
<div class="MsoNormal" style="color: black; font-family: 'Times New Roman'; font-size: medium; line-height: 24.545454025268555px; margin-left: 0.5in; text-indent: -0.25in;">
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-size: 13pt;"><span style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;">(A) ≥
0.25 and < 0.5 (B) ≥ 0.5 and < 0.75</span><span style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;"> </span><span style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;">(C) ≥ 0.75 and < 1.0 (D) ≥ 1.0
and < 1.25 </span></span></span></span></span><br />
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-size: 13pt;"><span style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;">(E) </span><u1:p style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;"></u1:p><span style="color: black; font-size: 13pt; line-height: 115%; text-indent: -0.25in;">≥ 1.25</span> <o:p></o:p></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="color: purple; font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">Answer:</span></u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"> C</span></span></span></span><br />
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;">Q17)Please read the following sentences
carefully ...</span><br />
<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="color: #c00000; font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)All the statements are
correct (B) Only statement II is
correct<o:p></o:p></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (C) Only statement III is correct (D) Both statements I and II are
correct<o:p></o:p></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(E) Both statements I and
III are correct <span style="color: #c00000;"><o:p></o:p></span></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="color: purple; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
<u><span lang="EN-IN" style="font-size: 13pt; line-height: 115%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 115%;"> C</span></span></span></span></span></div>
<div class="MsoNormal">
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Q18)In the country of Four ...</span></div>
<div class="MsoNormal">
<div class="MsoNormal" style="line-height: 150%; margin-left: .5in; text-indent: -.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;">(A)26.64 (B) 27.32 (C)
28.30 (D) 30 (E) 36 <o:p></o:p></span></div>
<span style="color: purple;"><u><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 13pt; line-height: 115%;">Answer:</span></u><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 13pt; line-height: 115%;"> C</span></span><br />
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;">Q19)Which is the fastest train between
HHH and NNN?</span><br />
<div style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span><br />
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.5in; text-indent: -0.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)1111 (B) 2222 (C)
4444 (D) 7777 (E) 9999 <span style="color: #c00000;"><o:p></o:p></span></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="color: purple; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> D</span></span></span></span></span><br />
<div style="color: #c00000;">
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;">Q20) Which is the fastest train between AAA
and NNN?</span></div>
</div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)8800 (B) 8888 (C) 6666 (D) 4444 (E)
3333 <span style="color: #c00000;"><o:p></o:p></span></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="color: purple; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> A</span></span></span></span></span><br />
<div style="color: #c00000;">
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 150%;">Q21) If you have to travel from AAA...</span></div>
</div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)1111 and 8800 (B) 1111 and 9900 (C) 8888 and 7777<o:p></o:p></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(D) 8888 and 8800 (E) 8888 and 9900 <span style="color: #c00000;"><o:p></o:p></span></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
</span></span></span></span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;"><u><span lang="EN-IN" style="color: purple; font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span style="color: purple;"> E</span><b style="color: #c00000;"><o:p></o:p></b></span></span></span></span></span></div>
<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"><span lang="EN-IN" style="font-family: 'Times New Roman'; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 19.09090805053711px;">
<span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 115%;">My observation: </span><span lang="EN-IN" style="font-size: 13pt; line-height: 115%;">It appears that 8800 is not stopping at HHH</span></span></span></span></span><br />
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;"><br /></span>
<span style="color: #0070c0; font-size: 13pt; line-height: 150%;">Q22) Considering away matches only,
which of the following team is the second ranking team?</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)AS (B)
CH (C) WG (D) SW (E) WB <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span lang="EN-IN" style="color: purple; font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span style="color: purple;"> D</span><b style="color: #c00000;"><o:p></o:p></b></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q23) Arun has to go the country....?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)T1 and T2 (B) T1,T2 and T5 (C)
T1,T4 and T5 (D) T1,T2 and T4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) T1,T3 and T4 <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> B</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q24) However, Arun’s manager....?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)T1, T2 and T3 (B) T1,T2 and T5 (C) T1,T2 and T4 (D)
T1,T3 and T4<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) T1,T4 and T5 <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> B</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q25) in a square PQRS, A and B are...?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)6 (B)
8 (C) 10 (D) 12 (E) 14 <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> C</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q26) p,q and r are three
non-negative...?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 0.25in; text-indent: 0in;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)<span style="font-size: 7pt; line-height: normal;"> </span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> 40 and < 50 (B) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> 50 and < 60 (C) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> 60 and < 70 (D) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> 70 and < 80 (E) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> 80 and < 90 <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> D</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q27) The central park...?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 39.75pt; text-indent: -21.75pt;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">10
meters</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (B) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">12.5
meters</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (C) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">14
meters</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (D) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">15 meters</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">16
meters</span><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 150%;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> A</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q28) What is the ratio of current
account balance in 2010 to the current account balance in 2005?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 39.75pt; text-indent: -21.75pt;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">0.35</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (B) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">4.56</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (C)
</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">5.01</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (D) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">2.57</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">5.30</span><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 150%;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> E</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q29) Read the statements given below:<o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%; margin-left: 0.5in; text-indent: -0.25in;">
<!--[if !supportLists]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">1.<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Exports were more than imports in 2006<o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%; margin-left: 0.5in; text-indent: -0.25in;">
<!--[if !supportLists]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">2.<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Imports were more than exports in 2009<o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%; margin-left: 0.5in; text-indent: -0.25in;">
<!--[if !supportLists]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">3.<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Exports increased at faster rate than imports
during the period 2005 to 2010<o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%; margin-left: 0.25in;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Which of the above
statements is necessarily true?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 39.75pt; text-indent: -21.75pt;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">1
and 2</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (B) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">1,2, and
3</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (C) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">3 only</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (D) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">2 only</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">1 only</span><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 150%;"> <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="color: purple;"><u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> C</span></span><span lang="EN-IN" style="color: red; font-size: 13pt; font-weight: bold; line-height: 150%;"><o:p></o:p></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q30) What was the approximate number of
unemployed persons in 2006?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)100 million (B) 102 million (C)
98 million<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-indent: 0.25in;">
<span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(D) 105 million (E) 104 million <span style="color: #c00000;"><o:p></o:p></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<u><span lang="EN-IN" style="color: purple; font-size: 13pt; line-height: 150%;">Answer:</span></u><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span style="color: purple;"> A</span><b style="color: #c00000;"><o:p></o:p></b></span></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="color: #c00000; line-height: 150%;">
<span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q31) Sara has just joined Facebook...?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-left: 39.75pt; text-indent: -21.75pt;">
<!--[if !supportLists]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">(A)<span style="font-size: 7pt; line-height: normal;">
</span></span><!--[endif]--><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥
105</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (B) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≤ 123</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (C) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">< 125</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (D)
</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥ 100 and ≤ 125</span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;">≥ 105 and ≤ 123</span><span lang="EN-IN" style="color: #c00000; font-size: 13pt; line-height: 150%;"> <o:p></o:p></span></div>
<span style="color: purple;"><u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;">Answer:</span></u><span lang="EN-IN" style="font-family: Calibri, sans-serif; font-size: 13pt; line-height: 115%;"> E</span></span><br />
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<span style="color: #c00000; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="color: #0070c0; font-size: 13.0pt; line-height: 150%;">Q32) 70% of the students who joined XLRI
last year play football,..?</span></span></div>
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<span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span style="mso-list: Ignore;">(A)<span style="font: 7.0pt "Times New Roman";"> </span></span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-spacerun: yes;"> </span></span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">5%</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(B)
</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">10%</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(C) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">15%</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"><span style="mso-tab-count: 1;"> </span>(D) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">20%</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> (E) </span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">None of
the above</span><span lang="EN-IN" style="font-size: 13.0pt; line-height: 150%;"> </span></div>
<u><span lang="EN-IN" style="color: #c00000; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">Answer:</span></u><span lang="EN-IN" style="color: #c00000; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"> <b style="mso-bidi-font-weight: normal;">B</b></span></span><br />
<span style="color: #c00000; font-family: Calibri, sans-serif; font-size: 13pt; line-height: 25.454544067382813px;"><span lang="EN-IN" style="color: #c00000; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"><b style="mso-bidi-font-weight: normal;"> </b></span> </span><a href="http://mathbyvemuri.blogspot.com/2013/01/xat-2013-detailed-solutions.html" style="font-family: Calibri, sans-serif; line-height: 25.454544067382813px;" target="_blank"><span style="font-size: x-large;">click here for detailed solutions</span></a></div>
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<span lang="EN-IN" style="color: #c00000; font-size: 13.0pt; line-height: 150%;"><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"><span lang="EN-IN" style="font-size: 13pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 13pt; line-height: 115%;">
</span></span></span></span></div>
<div class="MsoNormal">
<b style="line-height: 150%;"><span lang="EN-IN" style="color: red; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">More Questions are in
line.....</span></b></div>
</div>
</div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-69392356908589190412013-01-05T19:27:00.000+05:302013-01-05T19:49:15.325+05:30Patterns observed from Leap year concept<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Consider years from 2001 to 2017. Out of
these 17 years, the following 4 are leap years: 2004, 2008, 2012, 2016</span><br />
<div style="line-height: 150%;">
<br /></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Let us consider a property “Equidistant”
here. If any day of a year is equidistant from the corresponding day of the
previous and next years, then that year is called to exhibit the property
‘Equidistant’. But here, before considering a date, it should be taken care of
two scenarios. One scenario is for the dates from Jan’1<sup>st</sup> to Feb’28<sup>th</sup>
and the other scenario is for the dates from Mar’1<sup>st</sup> to Dec’31<sup>st</sup>.
These two scenarios result in two different patterns. In brief, <b style="mso-bidi-font-weight: normal;">scenario-I</b> set of dates is (<b style="mso-bidi-font-weight: normal;">Jan’1<sup>st</sup> </b>to<b style="mso-bidi-font-weight: normal;"> Feb’28<sup>th</sup></b>) and <b style="mso-bidi-font-weight: normal;">scenario-II</b> set of dates is (<b style="mso-bidi-font-weight: normal;">Mar’1<sup>st</sup> </b>to<b style="mso-bidi-font-weight: normal;"> Dec’31<sup>st</sup></b>).</span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">For example, let us consider a year 2007.
How many days are there from Jan’1<sup>st</sup> of 2006 to Jan’1<sup>st</sup>
of 2007? It is 365. Reason is simple.<span style="mso-spacerun: yes;">
</span>Being a non-leap year, '2006' has 365 days. Similarly, there are 365
days from Jan’1<sup>st</sup> of 2007 to Jan’1<sup>st</sup> of 2008 (here again,
being a non-leap year '2007' consists of 365 days). So here, any day (taken
from <b style="mso-bidi-font-weight: normal;">scenario-I</b> set of dates) of
2007 is equidistant from the corresponding days of 2006 and 2008. And hence, we
can say that year 2007 possesses the property “Equidistant” if scenario-I set
of dates are considered.</span></div>
<div style="line-height: 150%;">
<br /></div>
<div style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Pattern-I</span></u></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Here we consider a date from Jan’1<sup>st</sup>
to Feb’28<sup>th</sup> and the pattern looks like this:</span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">To have some fun, fill out the tables on
your own...</span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">From here onwards, 'E' stands for the
property 'Equidistant' and 'N' for 'Non-Equidistant'.</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: -.25pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2001</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2002</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2003</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2004</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2005</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2006</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2007</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2008</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2009</span></div>
</td>
<td colspan="2" style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2010</span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td colspan="2" style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2011</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2012</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2013</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2014</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2015</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2016</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2017</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
</tbody></table>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">*Years in bold are leap years</span></div>
<div style="line-height: 150%;">
<br /></div>
<div style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><u><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Pattern-II</span></u></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Here we consider a date from scenario-II
set of dates ie., from Mar’1<sup>st</sup> to Dec’31<sup>st</sup> and the
pattern looks like this:</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: -.25pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2001</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2002</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2003</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2004</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2005</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2006</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2007</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2008</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2009</span></div>
</td>
<td colspan="2" style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2010</span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td colspan="2" style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2011</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2012</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2013</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2014</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2015</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2016</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">2017</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
</tbody></table>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">*Years in bold are leap
years</span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<b style="mso-bidi-font-weight: normal;"><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">The
point in common</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"> for the two patterns is, <b>for every four
consecutive years, there exist two E’s and two N’s.</b></span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<br /></div>
<b style="mso-bidi-font-weight: normal;"><u><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Exceptions:</span></u></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span><br />
<br />
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">If it is to be defined
mathematically, <b>Leap year</b> is a number which</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">-must be a multiple of 4 <b>and</b> </span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">-must not be a multiple of 100 <b>but</b> </span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">-can
be a multiple of 400 </span></div>
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Sequence of Leap years is
not in a perfect pattern. For example, If I start writing down the list of leap
years for a period starting from 1895, it goes like this:<span style="mso-spacerun: yes;"> </span><span style="mso-spacerun: yes;"> </span> </span><br />
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1896,1904,1908,1912,1916.....</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">There is an exception for it to be a perfect 'Arithmetic Progression
with a common difference of 4'. The break is between 1896 and 1904. Had 1900
been existing between these two, it would have been so.</span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">As there exist exceptions
in the leap year sequence (I mean, it’s not a perfect Arithmetic Progression.
Every year which is a multiple of 4 is not a leap year. The exception is due to
a year which is being a multiple of 100 (but not a multiple of 400) (and
obviously it’s a multiple of 4) is not a leap year), there exist exceptions too
in our two patterns. There exist breaches in the pattern at any year which is a
multiple of 100 (but not a multiple of 400) and also at one of it’s two
adjacent years. To explain this I take an example set of the years from 1895 to
1911:</span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<br /></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Pattern-I</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">
for this set is:</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: -.25pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1895</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1896</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1897</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1898</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1899</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1900</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1901</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1902</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1903</span></div>
</td>
<td colspan="2" style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1904</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E<b style="mso-bidi-font-weight: normal;"><span style="color: red;"></span></b></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b style="mso-bidi-font-weight: normal;"><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b style="mso-bidi-font-weight: normal;"><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td colspan="2" style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1905</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1906</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1907</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1908</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1909</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1910</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1911</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
</tbody></table>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">*Years in bold are leap
years</span></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<br /></div>
<div style="line-height: 150%; tab-stops: 116.25pt;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">Pattern-II</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">
for this set is:</span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: -.25pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-table-layout-alt: fixed;">
<tbody>
<tr>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1895</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1896</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1897</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1898</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1899</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1900</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1901</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1902</span></div>
</td>
<td style="border-right: none; border: solid black 1.0pt; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1903</span></div>
</td>
<td colspan="2" style="border: solid black 1.0pt; mso-border-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1904</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
</tr>
<tr>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E<b style="mso-bidi-font-weight: normal;"><span style="color: red;"></span></b></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b style="mso-bidi-font-weight: normal;"><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></b></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b style="mso-bidi-font-weight: normal;"><span style="color: red; font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
<td colspan="2" style="border-top: none; border: solid black 1.0pt; mso-border-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.75pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">N</span></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1905</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1906</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1907</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1908</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;"></span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1909</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1910</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">1911</span></div>
</td>
<td style="border-left: solid black 1.0pt; border: none; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.25pt;" valign="top" width="62"><div style="layout-grid-mode: char; line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<br /></div>
</td>
<td style="border: none; mso-cell-special: placeholder; padding: 0in 0in 0in 0in;" width="1"><div class="MsoNormal">
<br /></div>
</td>
</tr>
<tr style="mso-row-margin-right: .5pt; mso-yfti-lastrow: yes;">
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
<td style="border-bottom: solid black 1.0pt; border-left: solid black 1.0pt; border-right: none; border-top: none; mso-border-bottom-alt: solid black .5pt; mso-border-left-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; mso-border-top-alt: solid black .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 46.2pt;" valign="top" width="62"><div style="line-height: 150%; margin-bottom: .0001pt; margin: 0in;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%;">E</span></div>
</td>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-37131333395088360552013-01-01T18:44:00.001+05:302013-01-04T08:43:21.317+05:30"Welcome to New Year - 2013" - a math treat<div dir="ltr" style="text-align: left;" trbidi="on">
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</xml><![endif]--><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Years are coming and fading away in to memories. Yet, every year has got some uniqueness in respect of numbers and this new year '2013' is no different from that trend.... </span><br />
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Say</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span></div>
<div style="line-height: 150%;">
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">goodbye to <b>2</b>+<b>0</b>*<b>1</b>=<b>2</b></span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">welcome to <b>2</b>+<b>0</b>+<b>1</b>=<b>3</b></span></div>
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<br /></div>
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Wish</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">a happy + prosperous new
year</span></div>
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<br /></div>
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Dream:</span></b></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Pleasures = <b>∞</b> </span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Sorrows = <b>0</b></span></div>
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<br /></div>
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">At least Hope</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">pleasures<b>++</b></span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">sorrows<b>--</b></span></div>
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<br /></div>
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Challenge</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span></div>
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<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; line-height: 150%; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">gear up <b>4</b> new challenges</span></div>
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<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Numbers</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">'2013' got all the first four consecutive whole numbers: <b>0</b>,<b>1</b>,<b>2</b>,<b>3</b></span><br />
<br />
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">"Dates in Pattern" </span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">of the Year:</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"><b>11.12.13</b>, 20.12.2013</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">1.7.13, 3.8.13, 5.9.13, 7.10.13, 9.11.13 </span><br />
<br />
<b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Equidistant???</span></b><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">:</span><br />
<span style="font-family: "Calibri","sans-serif";">Is Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2013 equidistant from Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2012 and Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2014?</span><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> </span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Obviously not. 2012 being a leap year, has 366 days where as 2013, a non-leap year has 365 days.</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2012---------------</span><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2013</span><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">---------------</span><span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;">Jan'<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">1<sup>st</sup></span>-2014</span><br />
<span style="font-family: "Calibri","sans-serif"; font-size: 13.0pt; mso-ascii-theme-font: minor-latin; mso-bidi-theme-font: minor-latin; mso-hansi-theme-font: minor-latin;"> 366days 365 days</span><!--[if gte mso 9]><xml>
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MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-4546873908069934552012-12-19T20:30:00.001+05:302012-12-19T21:23:30.496+05:30Photo to Logic to Math<div dir="ltr" style="text-align: left;" trbidi="on">
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<br />
<div class="MsoNormal" style="line-height: 150%;">
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-QFOUF236Xi8/UNFM2nIOR3I/AAAAAAAAAbM/Vsej3Prxt3I/s1600/PHOTO.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="112" src="http://3.bp.blogspot.com/-QFOUF236Xi8/UNFM2nIOR3I/AAAAAAAAAbM/Vsej3Prxt3I/s320/PHOTO.gif" width="320" /></a></div>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">That's a photo of a group
of friends standing</span><span style="font-size: 16px; line-height: 150%;"> </span><span style="font-size: 16px; line-height: 150%;">side by side</span><span style="font-size: 12pt; line-height: 150%;"> in a row.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">It reminds me a logic which
leads to a small math-concept at the end.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Let us consider that some
persons are standing in a row. Some clues are given and we need to find the
number of persons.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></b>
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Problem-1)</span></b><span style="font-size: 16px; line-height: 150%;">Find the number of persons?</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><b>Clue</b>:
"In the row, a person called 'A' is standing second from left and fourth
from right".</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">This clue is enough to
answer the question. If we count from left, </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">A is second from
left=> there are <b>two</b> persons up to A</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">A is fourth from right
=> there are <b>three</b> persons after A (as it is four including A)</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">So total number of persons
= 2+3 = 5</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">It can be shown like
this:</span><br />
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"> *<span style="mso-tab-count: 1;"> </span>A<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Now let us go to a little
complicated problem by introducing some more info.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Problem-2)</span></b><span style="font-size: 16px; line-height: 150%;">Find the number of persons?</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">First Clue</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">: “person 'A' is fourth from
left”</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Second Clue</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">: “person 'B' is fifth from
right”</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Are these clues enough to
get the answer? Obviously not...</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Third Clue</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">: There is one person in between
A and B</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Is it okay now? Can we
solve the puzzle? Let us see...</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">"A is fourth from
left" => there are <b>four</b> persons up to A (including A) from left-end.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">"B is fifth from
right" => there are <b>five</b> (including B) up to the right-end.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">"There is one person
in between A and B" => <b>This guy</b> shall be added to the count</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">So total number of
persons = 4+5+1 = 10</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">It can be shown like
this:</span><br />
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"> *<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>A<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>B<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">But is it okay? </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">No, there is some <b>ambiguity</b>
in the third clue. Ambiguity is about the order that A and B stand in the row. <b>If we count from left</b>, we are not sure whether A comes before B or the other-way-round. In the scenario shown above (let us call it scenario-I), A comes before B. If B comes before A, then another scenario (call it scenario-II) may arise</span><span style="font-size: 12pt; line-height: 150%;"> as
shown below. Can't it satisfy all the three clues?</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"> *<span style="mso-tab-count: 1;"> </span>B<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>A<span style="mso-tab-count: 1;"> </span>*<span style="mso-tab-count: 1;"> </span>*</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Here again, "A is
fourth from left" and "B is fifth from right" and "There is
one person in between A and B".</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">And here there are only
six persons in total.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">My point is</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">: For the second problem, the
given three clues are not enough to answer the question straight away. </span><span style="font-size: 12pt; line-height: 150%;">This type of concept is
useful in "</span><b style="font-size: 12pt; line-height: 150%;">Data Sufficiency</b><span style="font-size: 12pt; line-height: 150%;">"
type of problems given in competitive exams.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span>
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Second problem takes me
to "<b style="mso-bidi-font-weight: normal;">set theory</b>" concept: </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Scenario-I</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"> of second problem leads us to disjoint sets. One set with 4-persons (includes A) and other set with
5-persons (includes B) and there is one person not belonging to these two sets.
We can consider third set for this guy. These three sets are disjoint to one
another. </span><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://4.bp.blogspot.com/-lMI5TY5BH8E/UNFJDCZ001I/AAAAAAAAAaQ/LGVypIU8p3Y/s1600/dis_circles.gif" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="141" src="http://4.bp.blogspot.com/-lMI5TY5BH8E/UNFJDCZ001I/AAAAAAAAAaQ/LGVypIU8p3Y/s320/dis_circles.gif" width="320" /></a></div>
<span style="font-size: 12pt; line-height: 150%;">n(X) = 4</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">n(Y) = 5</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">n(Z) = 1</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12pt; line-height: 18px;">To</span><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12pt; line-height: 18px;">tal number of persons = </span>n(XUYUZ) = n(X)+n(Y)+n(Z)
= 4+5+1 = 10</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b>"<span style="font-size: 16px; line-height: 150%;">n(XUYUZ) = n(X)+n(Y)+n(Z)</span></b><span style="line-height: 150%;"><b>" -this formula holds good for disjoint sets</b>.</span><br />
<span style="line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Scenario-II</span></b><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"> leads us to two intersecting
sets. One set with 4-persons (includes B as well) and </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">other set with 5-persons
(includes A as well) and there is an intersection of these two sets with 3-persons in
common (A, B and the other guy).</span><br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="http://3.bp.blogspot.com/-HvaJMGA0Mp4/UNHiSIqi0MI/AAAAAAAAAbo/XXocQjy2MxM/s1600/int_cir.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="220" src="http://3.bp.blogspot.com/-HvaJMGA0Mp4/UNHiSIqi0MI/AAAAAAAAAbo/XXocQjy2MxM/s320/int_cir.png" width="320" /></a></div>
<br />
<div class="separator" style="clear: both; text-align: center;">
</div>
<span style="font-size: 12pt; line-height: 150%;">n(X) = 4</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">n(Y) = 5</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">n(X</span><span class="subbodytext"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">∩</span></span><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Y)
= 3</span></div>
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">To</span><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">tal number of persons =
n(XUY) = n(X)+n(Y)-n(X<span class="subbodytext">∩</span>Y) = 4+5-3 = 6</span><!--[if gte mso 9]><xml>
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<b><span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-font-family: "Times New Roman"; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">"</span><span style="font-family: Calibri, sans-serif; font-size: 16px; line-height: 18px;">n(XUY) = n(X)+n(Y)-n(X</span><span class="subbodytext" style="font-family: Calibri, sans-serif; font-size: 16px; line-height: 18px;">∩</span><span style="font-family: Calibri, sans-serif; font-size: 16px; line-height: 18px;">Y)</span><span style="font-family: Calibri, sans-serif; font-size: 12pt; line-height: 115%;">" -this formula holds good for intersecting sets.</span></b></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-72357924554254460722012-12-16T17:43:00.001+05:302012-12-17T22:43:44.913+05:30Magic of Numbers-II<div dir="ltr" style="text-align: left;" trbidi="on">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Observe this
table and there after we will find some interesting facts about numbers:</span><br />
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<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">3</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">7</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">8</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.95in;" valign="bottom" width="187"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digits of squares of
1st 10 natural numbers</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 20.85pt;" valign="bottom" width="28"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 16.4pt;" valign="bottom" width="22"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 21.9pt;" valign="bottom" width="29"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.95in;" valign="bottom" width="187"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digits of cubes of 1st
10 natural numbers</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 20.85pt;" valign="bottom" width="28"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 16.4pt;" valign="bottom" width="22"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">8</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 21.9pt;" valign="bottom" width="29"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">7</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">3</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">2</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.95in;" valign="bottom" width="187"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digits of 4th powers of
1st 10 natural numbers</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 20.85pt;" valign="bottom" width="28"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 16.4pt;" valign="bottom" width="22"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 21.9pt;" valign="bottom" width="29"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></b></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<b><span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.95in;" valign="bottom" width="187"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digits of 5th powers of
1st 10 natural numbers</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 20.85pt;" valign="bottom" width="28"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 16.4pt;" valign="bottom" width="22"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">2</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 21.9pt;" valign="bottom" width="29"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">3</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">7</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">8</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 1.95in;" valign="bottom" width="187"><div class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digits of 6th powers of
1st 10 natural numbers</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 20.85pt;" valign="bottom" width="28"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 16.4pt;" valign="bottom" width="22"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 21.9pt;" valign="bottom" width="29"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">5</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">6</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">9</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">4</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">1</span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 24.0pt;" valign="bottom" width="32"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; mso-element-anchor-horizontal: margin; mso-element-anchor-vertical: page; mso-element-frame-hspace: 9.0pt; mso-element-top: 71.3pt; mso-element-wrap: around; mso-element: frame; mso-height-rule: exactly; text-align: center;">
<span style="color: black; font-size: 10.0pt; line-height: 150%; mso-ansi-language: EN-US; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: "Times New Roman"; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">0</span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%;">
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<br /></div>
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<br /></div>
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<br /></div>
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<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal">
<div style="line-height: 150%;">
<br /></div>
<b><span lang="EN-IN"><span style="font-size: small;"><span style="line-height: 150%;">Basing on the above table the following facts can be </span></span><span style="line-height: 24px;">conceptualized</span><span style="font-size: small;"><span style="line-height: 150%;">:</span></span></span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Concept-I</span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The horizontal pattern
repeats for every 4 powers (vertically
downwards) and for every 10 consecutive numbers (Horizontally rightwards) such that we can find
the pattern for any power. </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">For example, the unit-digit
series of 112th<sup></sup> powers is same as that of 4<sup>th</sup> powers,
because 112 (= 4*28) is a multiple of 4 as the series is repeated for
every fourth power.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">We see one more
example to emphasize this concept. We will find the unit digit of 117<sup>123</sup>:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">unit digit of 117<sup>123
</sup>=> unit digit of 7<sup>123</sup> => unit digit of 7<sup>(4*30+3)</sup>
=> unit digit of 7<sup>3</sup> </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> Answer is
“3” <span style="mso-spacerun: yes;"> </span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Concept -II</span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">All the numbers
from 0 to 9 exist in the sequence of unit digits of cubes (and likewise for 7<sup>th</sup>
powers, 11<sup>th</sup> powers etc..) of natural numbers. Each number from 0 to
9 has an occurrence in the series of unit digits of cube roots of first 10
natural numbers. And of course this pattern repeats for the next 10 natural
numbers (ie., from 11 to 20) and so on..</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Here my point is:
n being a natural number, for a set of ‘10n’ consecutive natural numbers, if we
consider unit digits of cubes of all these numbers, the probability of ‘0’ being
the unit digit = probability of ‘1’ being the unit digit = …… = probability of ‘9’ being the unit digit = 1/10</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Concept -III</span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Unit digits of
fourth powers (likewise 8<sup>th</sup> powers, 12<sup>th</sup> powers etc.,) of
natural numbers must be from the set {0,1,5,6}. And in any set of unit-digits of
4<sup>th</sup> powers of 10 consecutive natural numbers, there exist one 0, one
5, four 1’s and four 6’s.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Now I quickly relate to a problem which can be built from this basic concept.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b style="mso-bidi-font-weight: normal;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Find the number of ways of selecting x and y from the set of
natural numbers {1,2,3,4,5,…. up to 10n} such that x<sup>4</sup>-y<sup>4</sup>
is divisible by 5?</span></b></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">For any number to
be divisible by 5, the unit digit must be 0 or 5.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Here as x<sup>4</sup>
and y<sup>4</sup> are fourth powers of natural numbers, their unit digit must
be one of {0,1,5,6}</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">So for x<sup>4</sup>-y<sup>4</sup>
to be divisible by 5, the possible pairs of unit digits of x<sup>4</sup> and y<sup>4</sup>
are: </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(0,0),(1,1),(5,5),(6,6),(0,5),(1,6)
as in all these cases, the unit digit of difference is either 0 or 5.</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">As per the
concept, in each consecutive 10 numbers, there exists one ‘0’ </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> For the
given 10n numbers, there exist ‘n’ number of ‘0’s as the unit digits of fourth
powers</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">As per the
concept, in each consecutive 10 numbers, there exists one ‘5’ </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> For the
given 10n numbers, there exist ‘n’ number of ‘5’s as the unit digits of fourth
powers</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">In each
consecutive 10 numbers, there exist four ‘1’s </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> For the
given 10n numbers, there exist ‘4n’ number of ‘1’s as the unit digits of fourth
powers</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">In each
consecutive 10 numbers, there exist four ‘6’s </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">=> For the
given 10n numbers, there exist ‘4n’ number of ‘6’s as the unit digits of fourth
powers</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Now we will find
the number of ways:</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><span style="mso-spacerun: yes;"> </span>(0,0):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of ways
of having 2 out of n zeros = nC2 = n(n-1)/2</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(1,1):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of
ways of having 2 out of 4n ones = 4nC2 = 4n(4n-1)/2</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(5,5):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of
ways of having 2 out of n fives = nC2 = n(n-1)/2</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(6,6):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of
ways of having 2 out of 4n sixes = 4nC2 = 4n(4n-1)/2</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(0,5):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of
ways of having 1 out of n zeroes and 1 out of n fives = nC1 * nC1 = n<sup>2</sup></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(1,6):</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The number of
ways of having 1 out of 4n ones and 1 out of 4n sixes = 4nC1 * 4nC1 = 16n<sup>2</sup></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Summing up all
the above, the total number of ways = 34n<sup>2</sup>-5n</span><br />
<br />
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Link for the first post in the Magic Series is here: </span><br />
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;"><a href="http://mathbyvemuri.blogspot.in/2011/10/magic-of-numbers-1-unit-digit-patterns.html" target="_blank">http://mathbyvemuri.blogspot.in/2011/10/magic-of-numbers-1-unit-digit-patterns.html </a></span></div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1tag:blogger.com,1999:blog-5567027158491397321.post-51950575601608080642012-11-28T08:00:00.000+05:302012-12-08T08:42:15.065+05:30Bike-riding & Math: My bike’s odometer makes me ‘crazy’<div dir="ltr" style="text-align: left;" trbidi="on">
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<span style="font-size: 12pt; line-height: 150%; text-align: justify;">My bike’s odometer is not
working properly. If all is well, it should get incremented properly to show the
total distance that the bike travelled. It has five digits. Third digit from
left stopped at ‘2’. By that time the first two digits (from left) were showing
4 and 8 respectively. As a result, the first three digits are not moving ahead from
the figure ‘482’ even if the last two digits are working properly (I mean, last
two digits getting incremented properly). This faulty meter is always running
in the range: ‘48200’ to ‘48299’.</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">It reminds me about the
decimal number system. What might be the logic behind the implementation of odometer’s
functionality?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">It has five digits. Each
digit can take numbers from 0 to 9. Each digit gets incremented by one number
starting from ‘0’ up to ‘9’ and returns back to ‘0’ after ‘9’. Each digit
follows a cycle of 10 numbers (‘0’ to ‘9’ and back to ‘0’). When a digit
reaches 9, and in the next instance, when it moves to ‘0’, its adjacent digit (digit
at its immediate left) gets incremented by 1. This logic seems okay for all the
digits except for the left most one as it doesn’t have a digit to its left. For
the extreme left digit, when the turn comes that it moves from 9 to 0, all the
other four digits also change to ‘0’ (by that time all those digits show 9’s),
such that the meter gets reset and all-zeroes figure appears. It can be
explained in a better way like this: When the magic figure 99999 appears on the
meter, the next turn is initiated from the right most digit. The right most digit changes from ‘9’ to ‘0’ and
initiates movement of second-right digit from ‘9’ to ‘0’, which triggers
third-right digit to change to ‘0’, which very action triggers fourth-right
digit to change to ‘0’ and all this cascading effect triggers finally the
fifth-right (or left-most) digit to change to ‘0’. In all, the range of the
meter is from ‘00000’ to ‘99999’. <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">That’s fine. But the odometer
continues to haunt me. It reminds me about the frequency with which each digit
changes. In the meter’s overall journey from 00000 to 99999, how many times does the
left-most digit change? What about the right-most digit?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">The key lies in the very
fact that “when each digit completes its full turn of <b>10</b> levels (0-to-9) and changes from 9 to 0, its immediate-left
digit changes by <b>1</b> level”. Here I stress upon the usage of numbers <b>10</b> and <b>1</b>. I can say it in the other way like this: “By the time a digit
turns up <b>1</b> level, its immediate-right
digit turns by <b>10</b> levels”. So if the
frequency of a digit is ‘f’ then the frequency of its immediate right digit is
‘10f’.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">Now let us start with the
left most digit. By the time meter runs from 00000 to 99999, the left most
digit runs through its full turn (ie, from 0 to 9) by one time. So if we
define ‘frequency’ as ‘number of times a digit changes through’, the frequency of
left most digit can be taken as ‘<b>10’</b>.
From then on we can easily calculate the frequencies of other successive digits
by simply going for successive 10-multiples. The frequency of second-left digit
is 10*10=<b>100</b>, that of third-left
digit is <b>1000</b>, that of fourth-left
digit is <b>10000</b> and that of
fifth-left (or right-most) digit is <b>100000</b>.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">If all is well, by the
time my bike completes ‘99999’ kilometres of journey, the right most digit of odometer
completes ‘<b>100000</b>’ turns.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-bidi-font-family: Calibri;">When you go for next ride
and when you casually look at the odometer, I hope it would not make you think
about all this and that and go crazy. <o:p></o:p></span></div>
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"></span><br />
<div style="text-align: justify;">
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;"><i style="font-size: 12pt; line-height: 115%;">Happy bike riding... </i></span></div>
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-bidi-language: AR-SA; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US;">
</span></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-74475324779836785612012-11-18T11:05:00.001+05:302012-12-08T08:24:03.710+05:30Math @Work: Importance of 'weightage' in finding averages<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-size: 12pt; line-height: 150%;">I have come across the concept of ‘score card’ for
employees in an organization. It is an employee performance-assessment tool.
Each employee’s work is categorized in to some parts and each part is given
some weightage depending on its significance.</span><span style="font-size: 12pt; line-height: 150%;"> </span><span style="font-size: 12pt; line-height: 150%;">The employee is allotted with a score in each part of the work depending
on his performance in that work. Part-wise performance-percentages and overall performance-percentage are calculated and based on these parameters, his salary-hike is decided for the coming fiscal. Can we take the average of all the part-performance
percentages to get the overall-performance figure?</span><br />
<span style="font-size: 12pt; line-height: 150%;"></span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Let us consider
the following scenario:<o:p></o:p></span></span></div>
<span style="font-size: 12pt; line-height: 150%;">
</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">The deciding
parameters are Work Efficiency, Punctuality, Analysation skills and Problem
solving skills each having equal weightage of 25%. And an employee has got the following
scores:<o:p></o:p></span></span></div>
<span style="font-size: 12pt; line-height: 150%;">
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 405px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Parameter<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Weightage<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Employee score<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Part %<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Work efficiency<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">25<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">20<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">80%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Punctuality<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">25<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">25<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">100%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Analyzation skills<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">25<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">15<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">60%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Problem solving skills<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">25<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">20<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">80%<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
</span><br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;">The overall
performance can be calculated straight-away like</span></div>
<span style="font-size: 12pt; line-height: 150%;">
</span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Total score
achieved by employee/ total max. Score = (20+25+15+20)/(25+25+25+25)<o:p></o:p></span></span></div>
<span style="font-size: 12pt; line-height: 150%;">
</span>
<br />
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">= 80%<o:p></o:p></span></span></div>
<span style="font-size: 12pt; line-height: 150%;">
</span>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;"><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">I can also find
it by taking average of part percentages:<o:p></o:p></span></span></div>
<span style="font-size: 12pt; line-height: 150%;">
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">(80+100+60+80)/4
= 320/4 = 80% <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: -13.5pt; margin-right: -21.2pt; margin-top: 0in; text-indent: 13.5pt;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Now I
change the weightages allotted to the parameters like this:<o:p></o:p></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 4.65pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 405px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Parameter<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Weightage<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Employee score<o:p></o:p></span></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<b><span style="font-size: 12pt; line-height: 150%;">Part %<o:p></o:p></span></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Work efficiency<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">50<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">40<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">80%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Punctuality<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">20<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">20<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">100%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Analyzation skills<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">10<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">6<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">60%<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 107.0pt;" width="143"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">Problem solving skills<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 60.15pt;" width="80"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">20<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 88.25pt;" width="118"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">16<o:p></o:p></span></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" width="64"><div align="center" class="MsoNormal" style="line-height: 150%; margin-bottom: .0001pt; margin-bottom: 0in; text-align: center;">
<span style="font-size: 12pt; line-height: 150%;">80%<o:p></o:p></span></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: -13.5pt; margin-right: -21.2pt; margin-top: 0in; text-indent: 13.5pt;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Overall
performance % = (40+20+6+16)/(50+20+10+20) = 82%<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: -.75pt; margin-right: -21.2pt; margin-top: 0in;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">But if I do it by
taking average of individual percentages, I will get (80+100+60+80)/4 = 320/4 =
80%<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-bottom: 10.0pt; margin-left: -13.5pt; margin-right: -21.2pt; margin-top: 0in; text-indent: 12.75pt;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Where
has it gone wrong?<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-right: -21.2pt;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Here
comes <b>the concept of weightages</b>. I need to take care of the weightage of each
part. In the first problem, the weightage given to each part is 25 and hence weightage
fraction for each part is 25/100 = ¼. So when I say that the overall average is
(80+100+60+80)/4, it really meant this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; margin-right: -21.2pt;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">“(1/4)*80
+(1/4)*100 +(1/4)*60 +(1/4)*80” Here I multiply the part-percentages with the
respective weightage.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%; mso-ascii-font-family: Calibri; mso-ascii-theme-font: minor-latin; mso-bidi-font-family: Calibri; mso-bidi-theme-font: minor-latin; mso-hansi-font-family: Calibri; mso-hansi-theme-font: minor-latin;">Coming to the
second problem, the weightage for the first part is 50/100 = ½, weightage for
second part is 20/100 = 1/5, weightage for third part is 10/100 = 1/10 and
weightage for fourth part is 20/100 = 1/5.<o:p></o:p></span></div>
<span lang="EN-IN" style="font-family: "Calibri","sans-serif"; font-size: 12.0pt; line-height: 115%; mso-ansi-language: EN-IN; mso-ascii-theme-font: minor-latin; mso-bidi-language: AR-SA; mso-bidi-theme-font: minor-latin; mso-fareast-font-family: Calibri; mso-fareast-language: EN-US; mso-hansi-theme-font: minor-latin;">So the overall-performance = (1/2)*80 + (1/5)*100
+ (1/10)*60 + (1/5)*80 = 40+20+6+16 = 82%</span></span></div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-43990679056986153772012-11-05T21:34:00.000+05:302012-12-08T08:45:31.887+05:30Programming &Math: Wherever you go, “number theory” follows....<div dir="ltr" style="text-align: left;" trbidi="on">
<span style="font-size: 12pt; line-height: 150%; text-align: justify;">I was in to a perl script
and some part of my code required this logic:</span><br />
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">For a particular mobile
number, if data (customer name, address etc) is available in MySQL table and if
image (scanned application form) is also available in the server, then display data
and image. If data is available and image is not available, then display data.
If data is not available and image is available, then display nothing. Here the
point is more precedence is given for ‘data’.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<b><u><span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Algorithm:<o:p></o:p></span></u></b></div>
<div class="MsoNormal" style="margin-left: 0.5in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>If(data is available)<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>{<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>if(image is available)<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1.5in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>Display ‘data’ and ‘image’<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>Else<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1.5in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>Display ‘data’ <o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 1in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>}<o:p></o:p></i></span></div>
<div class="MsoNormal" style="margin-left: 0.5in; text-indent: 0.5in;">
<span lang="EN-IN" style="font-size: 12.0pt;"><i>Else<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span lang="EN-IN" style="font-size: 12.0pt;"><i> {<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span lang="EN-IN" style="font-size: 12.0pt;"><i> // no action<o:p></o:p></i></span></div>
<div class="MsoNormal">
<span lang="EN-IN" style="font-size: 12.0pt;"><i> }<o:p></o:p></i></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">This is the simple
algorithm for the program.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">I want to relate this to a
mathematical model. Let us assume a simulator which assigns values to two
variables X and Y and adds them up. This assignment depends on the availability
of ‘data’ and ‘image’ respectively. The default value of X and Y is ‘0’.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">If ‘data’ is available,
then X can be assigned ‘2’ and if ‘image’ is available, then Y can be assigned ‘1’.
Here as I have more precedence for ‘data’, I design the simulator to assign a higher
value (ie ‘2’ as against ‘1’ which is assigned to Y if ‘image’ is available).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Now the simulator adds up X
and Y and depending on the Sum, it decides which is to be displayed. If Sum is ‘3’,
then both ‘data’ and ‘image’ are displayed. If the Sum is ‘2’, then only ‘data’
is displayed. If the Sum is ‘1’ or ‘0’, then nothing is displayed.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span style="font-size: 12pt; line-height: 150%;">Now to design a circuit
for this logic, I need to talk in ‘binary’ language (0’s and 1’s):</span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Default value of X and Y is
binary ‘00’. If ‘data’ is available, then X can be assigned ‘10’ and if ‘image’
is available, then Y can be assigned ‘01’. If Sum is ‘11’, then both ‘data’ and
‘image’ are displayed. If the Sum is ‘10’, then only ‘data’ is displayed. If the
Sum is ‘01’ or ‘00’, then nothing is displayed. We can implement the whole
thing with some logic gates (like a ‘Full Adder’ or whatever it may be). I don’t
want to go more in to the circuit designing stuff.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;"><br /></span></div>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Coming back to the
mathematical model, let us extend the logic to three variables with three
different weightages. If we assign weightages 1,2,3 to X,Y,Z then the possible
outcomes are:<o:p></o:p></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 66.75pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>X<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Y<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Z<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Sum<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="color: red; mso-ansi-language: EN-US; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman";">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
5<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<span style="color: red; mso-ansi-language: EN-US; mso-bidi-font-family: Calibri; mso-fareast-font-family: "Times New Roman";">3<o:p></o:p></span></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
3<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
6<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%; text-align: justify;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">But there is an ambiguity here.
Sum is same for two different scenarios (0,0,3) and (1,2,0). So we can’t assume
1,2,3 for X,Y,Z. Then what else...<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Let us try with 1,2,4...<o:p></o:p></span></div>
<table border="0" cellpadding="0" cellspacing="0" class="MsoNormalTable" style="border-collapse: collapse; margin-left: 69.75pt; mso-padding-alt: 0in 5.4pt 0in 5.4pt; mso-yfti-tbllook: 1184; width: 256px;">
<tbody>
<tr style="height: 15.0pt; mso-yfti-firstrow: yes; mso-yfti-irow: 0;">
<td nowrap="" style="border: solid windowtext 1.0pt; height: 15.0pt; mso-border-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>X<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Y<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Z<o:p></o:p></b></div>
</td>
<td nowrap="" style="border-left: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; mso-border-top-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
<b>Sum<o:p></o:p></b></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 1;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 2;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 3;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 4;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
6<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 5;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 6;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
3<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 7;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
0<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
5<o:p></o:p></div>
</td>
</tr>
<tr style="height: 15.0pt; mso-yfti-irow: 8; mso-yfti-lastrow: yes;">
<td nowrap="" style="border-top: none; border: solid windowtext 1.0pt; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-left-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
1<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
2<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
4<o:p></o:p></div>
</td>
<td nowrap="" style="border-bottom: solid windowtext 1.0pt; border-left: none; border-right: solid windowtext 1.0pt; border-top: none; height: 15.0pt; mso-border-bottom-alt: solid windowtext .5pt; mso-border-right-alt: solid windowtext .5pt; padding: 0in 5.4pt 0in 5.4pt; width: 48.0pt;" valign="bottom" width="64"><div align="center" class="MsoNormal" style="margin-bottom: 0.0001pt; text-align: center;">
7<o:p></o:p></div>
</td>
</tr>
</tbody></table>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Yes, here it works.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Now if we have four variables,
then what is the sequence of weightages a circuit designer considers? <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">We can easily guess... <o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">“1,2,4,8” – this gives all
possible 16 combinations (0 to 15).<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%; tab-stops: 86.25pt; text-align: justify;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">I say it again.....<o:p></o:p></span></div>
<div class="MsoNormal" style="text-align: justify;">
<div style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Wherever you go, “number
theory” follows.....</span></div>
<div style="line-height: 150%;">
<br /></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">
My cousin Mr.Aditya, a chip designer commented like this:<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;"><i>"When implemented in
hardware though we do it somewhat differently. When we want to implement a
priority encoder like this, we usually come up with a truth table first and
minimize the terms using a karnaugh map."</i><o:p></o:p></span></div>
<div class="MsoNormal">
<span lang="EN-IN"><span style="font-size: small;"><span style="line-height: 150%;"><br /></span></span></span>
<span lang="EN-IN"><span style="font-size: small;"><span style="line-height: 150%;">A chip designer would not worry about assigning priorities. He
depends on truth table and k-map to arrive at
appropriate Boolean expression. What are these truth table and k-map doing here???<o:p></o:p></span></span></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Truth table </span><span style="font-size: 16px; line-height: 150%;">maps the inputs into either 0-to-3 or 0-to-7 or 0-to-15 etc... possible values and assigns one out put (0 or 1) to each input. </span><span style="font-size: 12pt; line-height: 150%;">K-map
arranges the output values (0's or 1's) of truth table into cells (each cell corresponds to one possible input combination) arranged in a
mesh-form of size 2X2 or 2X4 or 4X4 etc.. So, every time, the total number of
cells in the k-map is either 4 or 8 or 16 etc...</span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span style="font-size: 12pt; line-height: 150%;">My
insistence on importance of "number theory" originates exactly
from here. If I take 1,2,3 as inputs, I can have the following possible sums:
1, 2, 3, 4(1+3), 5(2+3) and 6(1+2+3). For three inputs we have six outputs. </span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">But
if we consider 1,2,4 as inputs, we can have the following possible sums:
1, 2, 3(1+2), 4, 5(1+4), 6(2+4) and 7(1+2+4). For three inputs here we have seven outputs. And this advantage is more clear as the number of inputs increases. If I consider 1,2,4,8 as inputs, I can have all possible values from 1 to 15. Using <b>binary logic</b> in truth-table & k-map concept naturally takes this advantage as 1,2,4,8,16,... are the respective place-values of the binary-system.<o:p></o:p></span></div>
<div class="MsoNormal" style="line-height: 150%;">
<span lang="EN-IN" style="font-size: 12.0pt; line-height: 150%;">Relating
this to our discussion of assigning priorities... Is not the k-map internally
assigning 1,2,4 priorities to X,Y and Z terms respectively???</span></div>
</div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-28064664491908145862012-10-27T08:41:00.000+05:302012-12-14T14:50:42.790+05:30Jogging & Math: "Jogging – Circular path"<div dir="ltr" style="text-align: left;" trbidi="on">
<div class="MsoNormal" style="line-height: 150%;">
</div>
<div class="MsoNormal" style="line-height: 150%;">
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
</div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="color: black;"><span style="font-family: Arial, sans-serif;">One
morning while I was jogging around my apartment complex, I got a
doubt. Let us suppose that I am jogging in a circular path and
another person is also jogging in a parallel circular path (with a
different radius). What is the difference between the distances
travelled by me and the other person? Even if the difference between
the radii is small, the difference between total distances travelled
is more. why so? what is the underlying concept here?</span></span></div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<br />
</div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="color: black;"><span style="font-family: Arial, sans-serif;">Let
us consider that person ‘A’ is jogging in outer circle of radius
‘R’ and ‘B’ is jogging in an inner circle of radius ‘r’.
Obviously R > r. The distance travelled by A in one round is
nothing but the length of circumference of the circular path he
travelled.</span></span></div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<br />
</div>
<div align="LEFT" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="font-family: Arial, sans-serif;">The distance travelled by A = 2πR</span></div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="color: black;"><span style="font-family: Arial, sans-serif;">Similarly,
the distance travelled by B = 2πr</span></span></div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="color: black;"><span style="font-family: Arial, sans-serif;">Difference
of the distances = 2π(R-r).</span></span></div>
<div align="LEFT" style="margin-bottom: 0in;">
<br />
</div>
<div align="LEFT" lang="en-IN" style="line-height: 0.25in; margin-bottom: 0in;">
<span style="color: black;"><span style="font-family: Arial, sans-serif;">The
difference of distances travelled in one round is multiplied by a
factor ‘2π’ to the difference of radii of the two circular
paths. If we consider the approximate value of ‘π’ as 3.14, the
multiplying factor becomes ‘6.28’. This means, if B is jogging at
2 ft lesser radial length to that of A, the total distance travelled
by B in one round is around 12 ft less than that of A. This is only
for one round. If we consider for 10 rounds, the difference becomes
120 ft.</span></span></div>
</div>
</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com0tag:blogger.com,1999:blog-5567027158491397321.post-51462162895320431412012-10-22T05:14:00.000+05:302012-11-01T22:00:47.005+05:30CAT-2012 My Experience<div dir="ltr" style="text-align: left;" trbidi="on">
For the benefit of this blog, to be equipped with the experience of real time testing environment, I have decided to give CAT every year from this time onwards. My last attempt at CAT was in 2008 and that was the last PBT conducted by IIMs. From 2009 onwards, it has been conducted computer based. The very difference between PBT and CBT is that, in PBT we can have our own section-wise timelines. If you are strong in Quant and if you feel that you have already cleared the cut-off in Verbal section, then you can give some extra time to review Quant section and get some points there. But here in CBT, there are clear time lines defined for each section. We have 70 min time for each of QA-DI and VA-LR sections. We can't have 50 min here and 90 min there.<br />
<b><u><br /></u></b>
<b><u>About D'day and Test Centre</u></b><br />
Date 21/10/2012<br />
Time slot 10.00 AM<br />
Candidates shall reach the venue 1.30 hrs before the allotted time slot. I reached by 8.15 AM. Initially finger prints of point-fingers of both hands and live-photo snap (half-size) are taken. Seat number is allotted. 42-systems are arranged in each of the three test-rooms of the Centre. I occupied the allotted seat at around 9.00 AM. Screen appeared with login/password prompt.<br />
Test admin has entered login and password at 10 AM. Two options are provided on screen: Choosing a tutorial of 15 min duration or going straight-away to test. As most do, I opted for tutorial. Even if we know the procedures thoroughly, it is better to go through the tutorial for knowing about any surprise elements if exist.<br />
<br />
<b><u>About the tutorial:</u></b><br />
Tutorial is a comprehensive document on test structure, screens, time duration etc., It explained how to go back and forth of the pages, where to mark for review, how to check the total Q's attempted/mark for review/ left unanswered etc.. It explained the use of scroll bar in browsing through questions of a multiple question-set. It explained about the prompts such as test/section completion prompt, 1-minute pre-completion indication prompt. One point to be noted is: What happens if you answer a question and mark it for review and in hurry it was left like that (forgot to remove "review" tag)? Need not worry, it will be considered while calculating score.<br />
In simple words the summary of the tutorial is: we can go back to any question and answer it or we can change the answer of any attempted question in a section before the closure of the time allotted for that section.<br />
<br />
<b><u>About the test:</u></b><br />
Section-I: Quantitative Ability and Data Interpretation<span class="Apple-tab-span" style="white-space: pre;"> </span>30 Q's<span class="Apple-tab-span" style="white-space: pre;"> </span>70 min<br />
Section-II: Verbal Ability and Logical Reasoning<span class="Apple-tab-span" style="white-space: pre;"> </span>30 Q's<span class="Apple-tab-span" style="white-space: pre;"> </span>70 min<br />
<br />
<u><b>Section-I: </b></u><br />
<br />
<u>Difficulty level: </u><br />
DI medium to tough<br />
QA easy to medium<br />
<b><u><br /></u></b>
<b><u>Section-II: </u></b><br />
<br />
<u>Difficulty level: </u><br />
LR medium to tough<br />
VA easy to medium<br />
<br />
As per the rule, we should not reveal the questions given in the examination and the same commitment is taken online before proceeding to the first screen of the test.<br />
<br />
Given the rules, I could not go beyond this point. This may not be comprehensive but I thought it may be a little bit helpful for the guys taking the exam... All The Best...</div>
MathByVemurihttp://www.blogger.com/profile/02749315381369572618noreply@blogger.com1