# TCS NQT aptitude questions set 1

1. A mother, her little daughter and her just born infant boy together stood on a weighing machine which shows 74kgs. How much does the daughter weighs if the

mother’s weight is 46kg more than the combined weight of daughter and the infant and the infant weighs 60% less than the daughter.

a) 9

b) 10

c) 11

d) None of these

Ans. b

Let daughter’s weight be x.

Also, Infant’s weight is 60% less than daughter i.e 0.4x

Mother’s weight :

(x + 0.4x + 46)

Total weight = x + 0.4x + (x+0.4x+46) = 74

2.8x = 28

x = 10

2. Consider two tumblers, the first containing one litre of water. Suppose you take one spoon of water out of the first tumbler and pour it into the second tumbler and after which you take one spoon of the mixture from the second tumbler and pour it back into the first tumbler. Which one of the following statements holds true ?

a) There is less coffee in the first tumbler than water in the second tumbler.

b) There is more coffee in the first tumbler than water in the second tumbler.

c) There is as much coffee in the first tumbler as there is water in the second tumbler.

d) None of the statements holds true.

Ans. c

Let us assume that spoon can contain 5 drops.

and tumbler can contain 100 drops.

Tumbler 1 –> Tumbler 2

(spoon contains 5w drops)

Tumbler 1: 95w

Tumbler 2: 100c + 5w

Tumbler 2 –> Tumbler 1

(spoon contains 4c+1w drops)

Tumbler 1 : 96w

Tumbler 2 : 96c

There is as much coffee in the first tumbler as there is water in the second tumbler.

3. 100 students appeared for two different examinations 60 passed the first,50 the second and 30 both the examinations. Find the probability that a student selected at random failed in both the examination ?

a) 5/6

b) 1/5

c) 1/7

d) 5/7

Ans. b

Probability that a student selected failed in both exams :

100 – (60 + 50 – 30)/100

100 – 80/100

20/100

1/5

4. How many positive integers less than 4300 of digits 0 – 4.

a) 560

b) 573

c) 574

d) None of these

Ans. c

5. It was the semester exam day, Vidhya caught the college bus. She enjoyed travelling by bus. Moving at 6 mph, the bus took Vidhya to college at the right time. She finished her exam and had a chit chat with her friends and suddenly she realized that it was 6 pm and she had missed the college bus. She decided to walk back home at 4 mph. What is her average speed for the day ?

a) 4 mph

b) 5 mph

c) 2.4 mph

d) 4.8 mph

Ans. (d)

Since distance is constant,

Average speed is given by 2xy/x+y

So,

(2*6*4)/(6+4) = 48/10 = 4.8mph.

6. There are 5 letters and 5 addressed envelopes. If the letters are put at random in the envelops, the probability that only 2 letters are in the correct envelopes is :

a) 3/8

b) 1/12

c) 1/6

d) 4/9

Ans. (c)

Ways of putting 5 letters into 5 envelopes = 5! = 120

Only 2 letters are in the correct envelopes

Let ABCDE be the letters.

A and B alone are put in the correct envelopes.

No. of ways:

AB ECD

AB DEC

2 ways.

No. of ways of selecting 2 letters from 5 = 5C2 = 10

No. of ways in which 2 letters are put in correct envelopes = 10*2 = 20

So, Probability that only 2 letters are in the correct envelopes is :

20/120 = 1/6

7. Find the greatest number that will divide 148 246 and 623 leaving remainders 4, 6 and 11 respectively.

a) 20

b) 12

c) 6

d) 48

Ans. b

Greatest Such number :

HCF{(148-4), (246-6), (623-11))} = 12

8. There are 10 points on a straight line AB and 8 on another straight line AC none of them being point A. how many triangles can be formed with these points as vertices?

a) 680

b) 720

c) 816

d) 640

Ans. **(d)**

To form a triangle we need 3 points

Select 2 points from the 10 points of line AB & 1 from the 8 on AC

(_{10}C^{2})*(_{8}C^{1})

Select 2 points from the 8 points of line AC & 1 from the 10 on AB

(_{8}C^{2})*(_{10}C^{1})

Total number of triangles = s1 + s2 = 640

9. A triangle is made from a rope. The sides of the triangle are 25 cm, 11 cm and 31 cm. What will be the area of the square made from the same rope?

a) 280.8565

b) 280.5625

c) 281.5646

d) 282.5624

Ans. d

Length of the rope = 25+11+31 = 67cm

Side of the square = 67/4 = 16.75cm

Area of the square = (side of the square)^{2} = 16.75^{2}

280.5625 cm^{2}

10. A lady has fine gloves and hats of different colors in her closet 18 blue, 32 red and 25 yellow. The lights are out and it is totally dark. In spite of the darkness, she can make out the difference between a hat and a glove. She takes an item out of the closet only if she is sure that it is a glove. How many gloves must she take out to make sure that she has a pair of each color ?

a) 6

b) 8

c) 60

d) 59

Ans. d

If we consider that all the items are gloves.

Then, 32+25+2 = 59