Common Admission Test (CAT) Questions and Answers with Explanation

Q:

Find the least number by which 175760 be divided to make it a perfect cube.

A) 6	B) 10
C) 9	D) 30

Answer & Explanation Answer: B) 10

Explanation:

175760 =2³ x 2 x 5 x 13³
= 2³ x 2 x 5 x 13³

To make perfect cube, it must be divided by 2 x 5 = 10

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Filed Under: Arithmetical Reasoning
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20 16097

Q:

Two trains of equal length, running with the speeds of 60 and 40 kmph, take 50 seconds to cross each other while they are running in the same direction. What time will they take to cross each other if they are running in opposite directions ?

A) 10 sec	B) 11 sec
C) 12 sec	D) 8 sec

Answer & Explanation Answer: A) 10 sec

Explanation:

Relative Speed = 60 -40 = 20 x 5/18 = 100/18

Time = 50

Distance = 50 x 100/18 = 2500/9

Relative Speed = 60 + 40 = 100 x 5/18

Time = 2500/9 x 18/500 = 10 sec.

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Filed Under: Problems on Trains
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13 16094

Q:

If the volume of the cube is 729 $c m^{3}$ , then the surface area of the cube will be

A) 486 sq.cm	B) 456 sq.cm
C) 446 sq.cm	D) 476 sq.cm

Answer & Explanation Answer: A) 486 sq.cm

Explanation:

volume = $a^{3}$ = 729;

=> a = 9

surface area= 6 $a^{2}$ = (6 x 9 x 9) = 486 sq.cm

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Filed Under: Volume and Surface Area
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19 16082

Q:

Sanjeev ranks seventh from the top and twenty eighth from the bottom in a class. How many students are there in the class?

A) 33	B) 36
C) 35	D) 34

Answer & Explanation Answer: D) 34

Explanation:

Total number of students in the class = 28 + 6 i.e, from top(7-1)

28 + 6 = 34

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Filed Under: Number, Ranking and Time Sequence Test
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64 16062

Q:

A man lost half of its initial amount in the gambling after playing 3 rounds. The rule of gambling is that if he wins he will receive Rs. 100, but he has to give 50% of the total amount after each round.Luckily he won all the three rounds. The initial amount with which he had started the gambling was :

A) 500/3	B) 700/3
C) 300	D) 600

Answer & Explanation Answer: B) 700/3

Explanation:

Let the initial amount be x (with gambler), then

$[[(x + 100) \frac{1}{2} + 100] \frac{1}{2} + 100] \frac{1}{2} = \frac{x}{2}$

=> x = 700/3

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Filed Under: Percentage
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21 16062

Q:

Length of train is 170 meters and speed of train is 63 km/hour. This train can pass a bridge in 30 seconds, then find the length of the bridge.

A) 355 mts	B) 325 mts
C) 365 mts	D) 312 mts

Answer & Explanation Answer: A) 355 mts

Explanation:

Given speed = 63 km/hr = $63 \times \frac{5}{18} = \frac{35}{2}$ m/s

Let the length of the bridge = x mts

Given time taken to cover the distance of (170 + x)mts is 30 sec.

We know speed = $\frac{d i s \tan c e}{t i m e}$ m/s

$\Rightarrow \frac{35}{2} = \frac{170 + x}{30}$

--> x = 355 mts.

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Filed Under: Problems on Trains
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19 16027

Q:

Whose signature on Indian currency notes?

A) Finance minister	B) RBI Governor
C) Prime minister	D) President

Answer & Explanation Answer: B) RBI Governor

Explanation:

Except a one rupee note, all other denomination currencies have the signature of RBI Governor on it. One rupee note will have the sign of finance secretary of India.

whose_signature_on_indian_currency_notes1553773379.jpg image

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Filed Under: General Awareness
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11 16026

Q:

In a 48 ltr mixture, the ratio of milk and water is 5:3. How much water should be added in the mixture so as the ratio will become 3:5 ?

A) 24 lit	B) 16 lit
C) 32 lit	D) 8 lit

Answer & Explanation Answer: C) 32 lit

Explanation:

Given mixture = 48 lit

Milk in it = 48 x 5/8 = 30 lit

=> Water in it = 48 - 30 = 18 lit

Let 'L' lit of water is added to make the ratio as 3:5

=> 30/(18+L) = 3/5

=> 150 = 54 + 3L

=> L = 32 lit.

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Filed Under: Alligation or Mixture
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36 15911

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