## Tuesday, 14 February 2012

### GATE-2012 Solutions (General Aptitude)(EC/EE/NI)

Q1) Raju has 14 currency notes in his pocket consisting of only Rs 20 notes and Rs 10 notes. The total money value of the notes is Rs 230. The number of Rs 10 notes that Raju has is:
(A)  5                     (B)    6             (C)   9              (D)   10                         (2 Marks)
Solution:
Let the number of Rs 20 notes be ‘x’ and that of Rs 10 notes be ‘y’.
x+y = 14                     ---(1)
20x+10y = 230          ---(2)
As we need y, let us eliminate x.
(1)   * 20 => 20x+20y = 280             ---(3)
(3)-(2) => 10y = 50 => y = 5
Answer (A)
Q2) The data given in the following table summarizes the monthly budget of an average household.
 Category Amount (Rs) Food 4000 Clothing 1200 Rent 2000 Savings 1500 Other expenses 1800

The approximate percentage of the monthly budget not spent on savings is
(A)  10%          (B)    14%        (C)   81%         (D)   86%                     (2 Marks)
Solution:
Budget not spent on savings = 4000+1200+2000+1800 = 9000
Total Budget = 9000+1500 = 10500
Percentage of the monthly budget not spent on savings
= 9000/10500 *100
≈ 85%
Answer (D)

Q3) One of the legacies of the roman legions was discipline. In the legions, military law prevailed and discipline was brutal. Discipline on the battle field kept units obedient, intact and fighting, even when the odds and conditions were against them.
Which one of the following statement best sums up the meaning of the above passage?
(A)  Thorough regimentation was the main reason for the efficiency of the Roman legions even in adverse circumstances.
(B)    The legions were treated inhumanly as if the men were animals
(C)   Discipline was the enemies’ inheritance from their seniors
(D)  The harsh discipline to which the legions were subjected to led to the odds and conditions being against them                                                                   (2 Marks)
Answer (A)

Q4) Which of the following options is the closest in meaning to the word given below?
Latitude
(A)  Eligibility (B)    Freedom            (C)   Coercion (D)   Meticulousness             (1 Mark)
Answer (B)

Q5) If (1.001)1259 = 3.52 and (1.001)2062 = 7.85, then (1.001)3321 =
(A)  2.23         (B)    4.33        (C)   11.37      (D)   27.64                  (1 Mark)
Solution:
(1.001)1259 * (1.001)2062 = (1.001)1259+2062
(1.001)3321 =3.52*7.85
From the answer options we can straight away select 27.64.
Answer (D)

Q6)Choose the most appropriate word from the options given below to complete the following sentence:
Given the seriousness of the situation that he had to face, his _____ was impressive.
(A)  beggary (B)    nomenclature (C)   jealousy (D)   nonchalance     (1 Mark)
Solution:
'beggary' is 'poverty' and wont suit in the given situation.
'nomenclature' is 'process of naming' is irrelevant.
' jealousy ' is also irrelevant in the given situation.
'nonchalance' is 'casualness' and fits here.
Answer(D)

Q7)One of the parts (A,B,C,D) in the sentence given below contains an ERROR. Which one of the following is INCORRECT?
I requested that he should be given the driving test today instead of tomorrow.
(A)  requested that
(B)  should be given
(C)   the driving test
(D)  instead of tomorrow                                                                 (1 Mark)
Solution:
“Should” – not to be used in a request
Answer(B)

Q8)choose the most appropriate alternative from the options given below to complete the following sentence:
If the tired soldier wanted to lie down, he ____ the mattress out on the balcony.
(A)  should take
(B)  shall take
(C)   should have taken
(D)  will have taken                                                               (1 Mark)
Answer (C)

Q9) There are eight bags of rice looking alike, seven of which have equal weight and one is slightly heavier. The weighing balance is of unlimited capacity. Using this balance, the minimum number of weighings required to identify the heavier bag is
(A)  2               (B)    3             (C)   4              (D)   8              (2 Marks)
Solution:
This is a good one and needs extension of our thought process.
Most general mistake done here is dividing all the eight bags in to 2 lots of four each, weighing them by placing each lot on one of the two sides of the balance. This makes us to identify the lot with heavier bag. Now we came down to 4 bags from 8 bags. Repeat this process for two lots, each lot containing two bags. Then we will come down to two bags and one more iteration of the process gives us the final result of finding the odd bag out. This process involves three stages of weighing which is not the minimum possible one.
Right approach:
Keep two bags aside and consider two lots of three bags each and weigh them.
Case-I
Unequal weighing results in identifying that the odd one is in those six bags. Then we will be left with three bags with in which one is the odd bag. Then keeping one bag aside, and considering two lots of one bag each and weighing them will give us the final answer. So this involves two stages of weighing.
Case-II
Unequal weighing results in identifying that the odd one is in those two bags, which are kept aside. Then we will proceed with weighing of those two bags and be getting final answer. So this involves two stages of weighing only.
Answer(A)

Q10) A and B are friends. They decided to meet between 1 P.M and 2 P.M on a given day. There is a condition that whoever arrives first will not wait for the other for more than 15 minutes. The probability that they will meet on that day is:
(A)  1/4           (B)    1/16       (C)   7/16        (D)   9/16                                (2 Marks)
Solution:
This is a typical uniform distribution problem in probability. As the given waiting interval is 15 minutes, divide the total time of 1 hour in to 45 minutes and 15 minutes respectively.
Case-I: A arrives first
If A arrives in the interval 12:00 to 12:45, then B must arrive within 15 minutes of A’s arrival. The probability of meeting can be found out by considering double definite integral, with limits (0 to 45) and (x to x+15). The probability density for each A and B is 1/60 and 1/60 respectively. By considering these probability densities and finding out the integral under the above-mentioned limits, we get the probability in this part as 3/16.
If A arrives in the interval 12:45 to 13:00, then B must arrive before 13:00. The probability of meeting can be found out by considering double definite integral, with limits (45 to 60) and (x to 60). By considering the probability densities (1/60 and 1/60 for each A and B) and finding out the integral under the above-mentioned limits, we get the probability in this part as 1/32.
Summing up the two parts, the probability in the Case-I =  3/16 + 1/32 = 7/32
Case-II: B arrives first
Going by the same logic as mentioned in the Case-I, we get
Probability in the Case-II = 7/32
Summing up the two cases, the probability = 7/32 + 7/32 = 7/16
Answer(C)

#### 9 comments:

1. in ques 8 why the ans is not should take?

1. "Should" imposes a rule which is not the case here. The work (soldier lying down) was already completed.Here it is only suggested that he should have taken the mattress out.

2. in qustion 7 why the answer is not "instead of tommorow"
because in indirect speech we dont use tommorow,we use "the next day"

1. Dear Anonymous,
In that reasoning there is some ambiguity in the sense that the same reasoning stands for 'today' also.It must be 'that day' in indirect speech.Moreover, today and tomorrow are allowed when the speaker is reporting it on the same day.
Request 'shall' in direct speech changes to 'would' (not to 'should') in indirect speech.So our choice is 'B'.

3. why there's no answer to the probability problem?

that is easily the toughest question of the lot.

1. Dear Anonymous,
You are right, It was missed in that post. Now that problem with solution is added to the lot. Please check it. Thanks for the information.

2. "should take" is incorrect.
its a simple present tense form of the verb.
but as the ques says that if the soldier wanted to lie i.e somwhere in the past,he "should have taken" out the matress;where "should have taken is past perfect form of the verb which is very much correct!

4. In the GATE answer key the answer of q. no.8 is "should take" means option "A"..can you solve again??

5. This indicates a suggestion after the work (soldier lying down) is completed. Here it is presumed that the soldier laid down without making use of the available resource, 'mattress'. And hence it is suggested that he "should have" made use of the mattress.