GATE Questions and Answers with Explanation

Q:

The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class ?

A) 1:3	B) 2:3
C) 3:2	D) 3:1

Answer & Explanation Answer: B) 2:3

Explanation:

Let number of boys = x , Let number of girls = y
Total numbers of students = x + y
(x + y) × 15.8 = 16.4x + 15.4y
0.6x = 0.4y
x/y = 0.4/0.6 = 2/3

Ratio of boys and girls in the class is 2:3

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Filed Under: Problems on Ages
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35 22177

Q:

What should come next in the following number series?

9 8 7 6 5 4 3 2 1 8 7 6 5 4 3 2 1 7 6 5 4 3 2 1

A) 9	B) 8
C) 7	D) 6

Answer & Explanation Answer: D) 6

Explanation:

Here the series is:

987654321, 87654321, 7654321, 65...

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Filed Under: Number, Ranking and Time Sequence Test
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27 22169

Q:

In a row, Kumar is at 7th place from the left and Pawan is at 9th place from the right. When they interchange the positions Kumar becomes 11th from left. How many were seated in the row ?

A) 19	B) 20
C) 21	D) 27

Answer & Explanation Answer: A) 19

Explanation:

Initialy from left 7th = kumar
from right 9th = pawan
Interchange kumar = 11th from left, from right kumar = 9th;
11+8 = 19;
8 is 1,2,3,4,5,6,7(pawan),8,9,10,11(kumar),12,13,14,15,16,17,18,19;
simply count the 9th place from right we will get total as 19.

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Filed Under: Number, Ranking and Time Sequence Test
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35 22166

Q:

Which of the Following is an Amorphous solid?

A) Quartz Glass(Sio2)	B) Chrome Alum
C) Silicon Carbide(SiC)	D) Graphite

Answer & Explanation Answer: A) Quartz Glass(Sio2)

Explanation:

An amorphous or non-crystalline solid is a solid that lacks the long-range order that is characteristic of a crystal. In Brief, An amorphous solid is any noncrystalline solid in which the atoms and molecules are not organized in a definite lattice pattern. Such solids include glass, plastic, and gel.

Quartz glass (SiO2) is an amorphous solid due to its short range order of constituent particles. Note Quartz is a crystalline solid while quartz glass is an amorphous solid.

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Filed Under: Chemistry
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52 22068

Q:

A letter is takenout at random from 'ASSISTANT' and another is taken out from 'STATISTICS'. The probability that they are the same letter is :

A) 35/96	B) 19/90
C) 19/96	D) None of these

Answer & Explanation Answer: B) 19/90

Explanation:

$A S S I S T A N T \to A A I N S S S T T$

$S T A T I S T I C S \to A C I I S S S T T T$

Here N and C are not common and same letters can be A, I, S, T. Therefore

Probability of choosing A = $\frac{2_{C_{1}}}{9_{C_{1}}} \times \frac{1_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing I = $\frac{1}{9_{C_{1}}} \times \frac{2_{C_{1}}}{10_{C_{1}}}$ = 1/45

Probability of choosing S = $\frac{3_{C_{1}}}{9_{C_{1}}} \times \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/10

Probability of choosing T = $\frac{2_{C_{1}}}{9_{C_{1}}} \times \frac{3_{C_{1}}}{10_{C_{1}}}$ = 1/15

Hence, Required probability = $\frac{1}{45} + \frac{1}{45} + \frac{1}{10} + \frac{1}{15} = \frac{19}{90}$

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Filed Under: Probability
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97 21954

Q:

At what time, between 3 o’clock and 4 o’clock, both the hour hand and minute hand coincide each other ?

A) 3:16 7/11	B) 3:16 11/4
C) 3:30	D) 3:16 4/11

Answer & Explanation Answer: D) 3:16 4/11

Explanation:

Coincide means 00 angle.

This can be calculated using the formulafor time A to B means [11m/2 - 30 (A)]

Here m gives minutes after A the both hands coincides.

Here A = 3, B = 4

0 =11m/2 –30 × 3
11m = 90 × 2 = 180
m= 180/11 = 16 ⁴/₁₁

So time = 3 : 16 ⁴/₁₁

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Filed Under: Clocks
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33 21947

Q:

A number of cats got together and decided to kill between them 999919 rats. Every cat killed an equal number of rats. Each cat killed more rats than there were cats. How many rats do you think that each cat killed ?

A) 1009	B) 991
C) 2000	D) 1000

Answer & Explanation Answer: A) 1009

Explanation:

Given total number of rats = 999919

999919 = 1000000 - 81 = $(1000^{2} - 9^{2})$ = (1000+9)(1000-9) = 1009 x 991.
Since there were more rats than there were cats, 991 cats killed 1009 rats each.

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Filed Under: Math Puzzles
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53 21938

Q:

Find the next number in the given number series?

8, 11, 19, 23, 32, ?

A) 37	B) 39
C) 47	D) 49

Answer & Explanation Answer: A) 37

Explanation:

The given number series is 8, 11, 19, 23, 32, ?

It follows a pattern that

8 + 11 = 19

11 + 12 = 23

19 + 13 = 32

23 + 14 = 37

32 + 15 = 47

....

Hence, the next number in the given series = 37.

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Filed Under: Number Series
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12 21881

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