Common Admission Test (CAT) Questions and Answers with Explanation

Q:

What is the number of digits in $3^{3^{3}}$ ? Given that log3 = 0.47712?

A) 12	B) 13
C) 14	D) 15

Answer & Explanation Answer: B) 13

Explanation:

Let $L e t x = (3^{3^{3}})$ = ${(3^{3})}^{3}$

Then, $\log (x) = 3^{3} \log (3)$

= 27 x 0.47712 = 12.88224

Since the characteristic in the resultant value of log x is 12

$∴$ The number of digits in x is (12 + 1) = 13

Hence the required number of digits in $3^{3^{3}}$ is 13.

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Filed Under: Logarithms
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Q:

Two passenger trains start at the same hour in the day from two different stations and move towards each other at the rate of 16 kmph and 21 kmph respectively. When they meet, it is found that one train has traveled 60 km more than the other one. The distance between the two stations is ?

A) 387 kms	B) 242 kms
C) 145 kms	D) 444 kms

Answer & Explanation Answer: D) 444 kms

Explanation:

1h ----- 5 kms
? ------ 60 kms

Time = 12 hrs

Relative Speed = 16 + 21 = 37 kmph

T = 12 hrs

D = S x T = 37 x 12 = 444 kms.

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Filed Under: Problems on Trains
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Q:

A quantity of tea is sold at Rs. 5.75 per kilogram. The total gain by selling the tea at this rate is Rs. 60. Find the quantity of tea being sold if a profit of 15% is made on the deal ?

A) 72 kgs	B) 80 kgs
C) 76 kgs	D) 84 kgs

Answer & Explanation Answer: B) 80 kgs

Explanation:

Say total cost price of tea is x.
Then total profit at a rate of 15% is = (15x/100)
According to question,
15x/100 = 60
so x = 400
C.p of the tea is Rs. 400.
so total selling price will be = (400+60) = Rs.460
so the quantity of the tea will be = (460/5.75) = 80kg.

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Filed Under: Profit and Loss
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12 12370

Q:

Find the logarithm of 144 to the base $2 \sqrt{3}$ :

A) 2	B) 4
C) 8	D) None of these

Answer & Explanation Answer: B) 4

Explanation:

$\log_{2 \sqrt{3}} (144) = 4$

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Filed Under: Logarithms
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Q:

Find x if

$l o g_{\frac{1}{\sqrt{2}}} (\frac{1}{\sqrt{8}}) = l o g_{2} (4^{x} + 1) . l o g_{2} (4^{x + 1} + 4)$

A) 0	B) 1
C) 2	D) None of these

Answer & Explanation Answer: A) 0

Explanation:

By trial and error method, when we substitute

x = 0

Both LHS and RHS are equal.

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Filed Under: Logarithms
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Q:

Bold, Italic, Regular are known as

A) Text Effects	B) Font Styles
C) Font Effects	D) Word Art

Answer & Explanation Answer: B) Font Styles

Explanation:

Bold, Italic, Regular are known as Font Styles.

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Filed Under: Computer
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Q:

Find the one which does not belong to that group ?

A) 343	B) 2197
C) 1331	D) 121

Answer & Explanation Answer: D) 121

Explanation:

343 = $7^{3}$ , 1331 = $11^{3}$ , 2197 = $13^{3}$ , 121 = $11^{2}$

343, 1331, 2197 are perfect cubes, but not 121.

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Filed Under: Odd Man Out
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12 12341

Q:

Ice is to water as rock is to

A) Lava	B) Oil
C) Sand	D) Mud

Answer & Explanation Answer: A) Lava

Explanation:

When ice melts it changes its physical state to water. Similarly, when rock melts it changes into lava or magma.

Hence, ice is to water as rock is to lava.

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Filed Under: Analogy
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