Common Admission Test (CAT) Questions and Answers with Explanation

Q:

If a solid sphere of radius 10 cms is moulded into 8 spherical solid balls of equal radius, then surface area of each ball (in sq.cm) is ?

A) 100 π	B) 101/π
C) 99 π/12	D) 54/13π

Answer & Explanation Answer: A) 100 π

Explanation:

4/3 π x 10 x 10 x 10 = 8 x 4/3 π x r x r x r
r = 5
4π x 5 x 5 = 100π

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Filed Under: Volume and Surface Area
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17 11058

Q:

Sonika invested an amount of Rs.5800 for 2 years. At what rate of compound interest will she get an amount of Rs.594.50 at the end of 2 years ?

A) 6.5%	B) 6%
C) 5%	D) 4.5%

Answer & Explanation Answer: C) 5%

Explanation:

C.I = $P [{(1 + \frac{r}{100})}^{t} - 1]$

594.5 = $5800 [{(1 + \frac{r}{100})}^{2} - 1]$

$\frac{594.5}{5800} + 1 = {(1 + \frac{r}{100})}^{2}$

$\frac{r}{100} = 1.05 - 1 = 0.05 = > r = 5$ % .

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Filed Under: Compound Interest
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13 11055

Q:

Pigeon:Peace::White flag:?

A) Surrender	B) War
C) Victory	D) friendship

Answer & Explanation Answer: A) Surrender

Explanation:

Pigeon is a symbol of peace and white flag is a symbol of surrender.

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Filed Under: Analogy
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18 11054

Q:

The absorption of ink by blotting paper involves

A) viscosity of ink	B) diffusion of ink through the blotting
C) capillary action phenomenon	D) siphon action

Answer & Explanation Answer: C) capillary action phenomenon

Explanation:

The absorption of ink by blotting paper involves capillary action phenomenon because the blotting paper is a thin and a smooth paper which allows a little thicker liquids like ink to absorb.

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Filed Under: Physics
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11 11049

Q:

Bread : Yeast :: Curd : ?

A) Fungi	B) Bacteria
C) Germs	D) Virus

Answer & Explanation Answer: B) Bacteria

Explanation:

First is produced by the action of the second.

Hence, Bread : Yeast :: Curd : Bacteria.

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Filed Under: Analogy
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6 11019

Q:

A man could buy a certain number of notebooks for Rs.300. If each notebook cost is Rs.5 more, he could have bought 10 notebooks less for the same amount. Find the price of each notebook ?

A) 15	B) 20
C) 10	D) 8

Answer & Explanation Answer: C) 10

Explanation:

Let the price of each note book be Rs.x.

Let the number of note books which can be brought for Rs.300 each at a price of Rs.x be y.

Hence xy = 300

=> y = 300/x

(x + 5)(y - 10) = 300 => xy + 5y - 10x - 50 = xy

=>5(300/x) - 10x - 50 = 0 => $- 150 + x^{2} + 5 x$

multiplying both sides by -1/10x

=> $x^{2} + 15 x - 10 x - 150 = 0$

=> x(x + 15) - 10(x + 15) = 0

=> x = 10 or -15

As x>0, x = 10.

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Filed Under: Simplification
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9 11008

Q:

In what time would a cistern be filled by three pipes which diameters are 2 cm, 3 cm and 4 cm running together, when the largest alone can fill it is 58 minutes? The amount of water flowing in each pipe is proportional to the square of its diameter.

A) 26 min	B) 32 min
C) 36 min	D) 42 min

Answer & Explanation Answer: B) 32 min

Explanation:

Given that the diameters of the three pipes are 2 cm, 3 cm and 4 cm

From the given data,

Amount of water from three pipes is 4 units, 9 units and 16 units.

Let the capacity of cistern be 'p' units.

∴ p/58 = 16

⇒ p = 928 units.

In 1 minute, quantity to be filled by 3 pipes = 29 units

∴ Total time required = 928/29 = 32 minutes.

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Filed Under: Pipes and Cistern
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11 11007

Q:

A man saves Rs. 200 in each of the first three months of his service. In each of the subsequent months his saving increases by Rs. 40 more than the saving of immediately previous month. His total saving from the start of service will be Rs. 11040 after ?

A) 19 months	B) 21 months
C) 18 months	D) 20 months

Answer & Explanation Answer: B) 21 months

Explanation:

Total savings = 200 + 200 + 200 + 240 + 280 + ... to n months = 11040

= 120 + 80 + 160 + 40 + 200 + 240 + ....n terms
= 40 + 80 + 120 + 160 + 200 + 240 + ...n terms
= n/2[2a + (n-1)d] + 80 + 40 = 11040
= n/2[240 + (n-1)40] = 10920
= n[6+n-1] = 546
= n[n+5] = 546
n = 21

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Filed Under: Odd Man Out
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10 10990

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