Common Admission Test (CAT) Questions and Answers with Explanation

Q:

A driver of auto rickshaw makes a profit of 20% on every trip when he carries 3 passengers and the price of petrol is Rs. 30 a litre. Find the % profit for the same journey if he goes for 4 passengers per trip and the price of petrol reduces to Rs. 24 litres ?

A) 68%	B) 80%
C) 75%	D) 100%

Answer & Explanation Answer: D) 100%

Explanation:

When 3 passengers income was 3x
expense= Rs.30
profit =20% of 30 = Rs.6
That means his earning is Rs.36. so that per passenger fare must be Rs.12.

When 4 passengers
earning = 12x4=Rs.48.
expense =Rs.24.
profit = Rs.24 = 100%

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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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Q:

If $a^{2} + b^{2} = c^{2}$ , then $\frac{1}{l o g_{c + a} (b)} + \frac{1}{l o g_{c - a} (b)} = ?$

A) 1	B) 2
C) 4	D) 8

Answer & Explanation Answer: B) 2

Explanation:

Given $a^{2} + b^{2} = c^{2}$

Now $\frac{1}{\log_{c + a} (b)} + \frac{1}{\log_{c - a} (b)}$

= $\log_{b} (c + a) + \log_{b} (c - a)$

= $\log_{b} (c^{2} - a^{2})$

= $2 \log_{b} (b) = 2$

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31 11681

Q:

What is the Tagline of Bank of Baroda?

A) A tradition of trust	B) India’s International Bank
C) Relationships beyond Banking	D) One Family One Bank

Answer & Explanation Answer: B) India’s International Bank

Explanation:

Bank of Baroda is an Indian International banking and financial services company headquartered in Vadodara in Gujarat, India. The Tagline of Bank of Baroda is India’s International Bank.

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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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55 11680

Q:

What comes once in a year, twice in a week and never in a day?

A) Sunday	B) New moon day
C) E	D) All of the above

Answer & Explanation Answer: C) E

Explanation:

YEAR - 1 E

WEEK - 2 E

DAY - 0 E

Hence, the letter 'E', comes once in a year, twice in a week and never in a day.

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Q:

What is the name of the virus that fool a user into downloading and executing them by pretending to be useful applications ?

A) Trojan horses	B) Keylogger
C) Worm	D) File virus

Answer & Explanation Answer: A) Trojan horses

Explanation:

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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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