GATE-2013 Solutions (General Aptitude)(CS-IT/ME/PI)

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

(A)36   (B)30   (C)24   (D)18

Sol:

This is a simple formula based one.

Average speed = total distance/ total time

Let the total distance be ‘x’

=>  x/2 covered at 60 km/h, x/4 covered at 30 km/h and x/4 covered at 10 km/h

=> the respective times taken are (x/2)/60, (x/4)/30, (x/4)/10

=> total time taken = x/120 + x/120 + x/40 = 5x/120= x/24

Average speed = x/(x/24) = 24 km/h

Ans: C

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

(A)16,500        (B)15,180        (C)11,000        (D)10,120

Sol:

The cost is nothing but the product of labour wages per day and the number of working days.

Cost is directly proportional to (labour wages per day)*(no. of working days)

labour wages per day is increased by 1/5 of the current wages => new wages/day changes by  =( 1 + 1/5) proportion

= 6/5 proportion

working hours decreased by 1/24 => new working hours changes by = 1- 1/24 = 23/24 proportion

=> new total cost changes by = (6/5)*(23/24) proportion = 23/20 proportion

=> new total cost = (23/20)*(old total cost) = (23/20)*(13200) = 23*660

We need not do complete multiplication here. We can observe that, the answer ends with '80’ and the only option is 15180

Ans: B

3. Which one of the following is closest in meaning to the word given below?

Nadir

(A) Highest      (B) Lowest       (C) Medium     (D) Integration

Sol:

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.

Ans: B

4. Complete the sentence:

Universalism is to Particularism         as Diffuseness is to ______

(A) specificity  (B)neutrality    (C) generality  (D) adaptation

Sol:

Universalism is almost an opposite word of Particularism. So we need to find the opposite word (antonym) of Diffuseness.

Diffuseness is nature of spreading.  Specificity may be the nearest answer

 Ans: A

5. What will be the maximum sum of 44,42,40,…?

 (A) 502           (B) 504            (C) 506            (D) 500

Sol:

44,42,40,…

This is a decreasing AP. If you leave it like that, it will go in to negative terms -2,-4,….

But to make the sum maximum, we need to stop at ‘0’. Otherwise the –ve terms make the sum decrease.

So the series is 44,42,40,…..0.

44+42+40+…+0 = 2(22+21+20+…0) = 2(sum of first 22 integers) = 2(n*(n+1)/2), where n =22

=> Sum = 2*(22*23/2) = 22*23 = 506

Ans: C

6. Find the sum of the expression:

1/√1+√2 + 1/√2+√3 + 1/√3+√4 + ….1/√80+√81

(A) 7    (B)8     (C) 9    (D) 10

Sol:

The simplification involves just rationalization…

1/√1+√2 + 1/√2+√3 + 1/√3+√4 + ….1/√80+√81

= (√2-√1)/(√1+√2) (√2-√1) + (√3-√2)/(√2+√3) (√3-√2) +……+(√81-√80)/(√80+√81) (√81-√80)

= (√2-√1) + (√3-√2) +……+(√81-√80)

= -√1+√81 = -1+9 = 8

Ans: B

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?

(A) 13/90         (B) 12/90         (C) 78/90         (D) 77/90

Sol:

The two digit numbers between 1 and 100 are 10,11,….99 => there are 90 in all.

The two-digit multiples of 7 are 14,21,….98 => 2*7 to 14*7 => 13 in all

So the numbers not divisible by 7 are 90-13 = 77 in all

So the answer is 77/90

Ans: D

8. Were you a bird, you ____ in the sky.

(A) would fly    (B) shall fly      (C) should fly   (D) shall have flown

Ans: A

9. Choose the grammatically INCORRECT sentence:

(A) He is of Asian origin

(B) They belonged to Africa

(C) She is an European

(D) They migrated from India to Australia

Sol:

It might be – ‘a Europian’ and not 'an European'
Though European starts with vowel 'E', as it starts with a sound 'Yu', it should be preceded with 'a' but not 'an'.

Ans: C

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.

Which one of the following assertions is best supported by the above information?(A) Failure is the pillar of success

(B) Honesty is the best policy

(C) Life begins and ends with adventures

(D) No adversity justifies giving up hope

Ans: D