6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

The H.C.F. of two numbers is 23 and the other two factors of their L.C.M. are 13 and 14. The larger of the two numbers is:

A) 276	B) 299
C) 322	D) 345

Answer & Explanation Answer: C) 322

Explanation:

Clearly, the numbers are (23 x 13) and (23 x 14).

Larger number = (23 x 14) = 322.

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Filed Under: Quantitative Aptitude - Arithmetic Ability

12 11667

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
Exam Prep: AIEEE , Bank Exams , CAT
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55 11662

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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Filed Under: Logarithms
Exam Prep: GRE , GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk , Analyst

31 11658

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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Filed Under: Profit and Loss
Exam Prep: GATE , CAT , Bank Exams , AIEEE
Job Role: Bank PO , Bank Clerk

19 11654

Q:

Shawn invested one half of his savings in a bond that paid simple interest for 2 years and received Rs.550 as interest. He invested the remaining in a bond that paid compound interest, interest being compounded annually, for the same 2 years at the same rate of interest and received Rs.605 as interest. What was the value of his total savings before investing in thesetwo bonds?

A) Rs.2543	B) Rs.2534
C) Rs.2546	D) Rs.2750

Answer & Explanation Answer: D) Rs.2750

Explanation:

Shawn received an extra amount of (Rs.605 – Rs.550) Rs.55 on his compound interest paying bond as the interest that he received in the first year also earned interest in the second year.

The extra interest earned on the compound interest bond = Rs.55

The interest for the first year =550/2 = Rs.275

Therefore, the rate of interest = $\frac{55}{275} * 100$ = 20% p.a.

20% interest means that Shawn received 20% of the amount he invested in the bonds as interest.

If 20% of his investment in one of the bonds = Rs.275, then his total investment in each of the bonds = $\frac{275}{20} * 100$ = 1375.

As he invested equal sums in both the bonds, his total savings before investing = 2 x 1375 =Rs.2750.

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Filed Under: Compound Interest
Exam Prep: Bank Exams
Job Role: Bank PO

12 11641

Q:

The least number which when divided by 5, 6, 7 and 8 leaves a remainder 3, but when divided by 9 leaves no remainder, is

A) 1677	B) 1683
C) 2523	D) 3363

Answer & Explanation Answer: B) 1683

Explanation:

L.C.M of 5, 6, 7, 8 = 840

Therefore, Required Number is of the form 840k+3.

Least value of k for which (840k+3) is divisible by 9 is k = 2

Therefore, Required Number = (840 x 2+3)=1683

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Filed Under: HCF and LCM

38 11624

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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50 11608

Q:

How many alphabets need to be there in a language if one were to make 1 million distinct 3 digit initials using the alphabets of the language?

A) 1000	B) 100
C) 500	D) 999

Answer & Explanation Answer: B) 100

Explanation:

1 million distinct 3 digit initials are needed.

Let the number of required alphabets in the language be ‘n’.

Therefore, using ‘n’ alphabets we can form n * n * n = $n^{3}$ distinct 3 digit initials.

Note distinct initials is different from initials where the digits are different.

For instance, AAA and BBB are acceptable combinations in the case of distinct initials while they are not permitted when the digits of the initials need to be different.

This $n^{3}$ different initials = 1 million

i.e. $n^{3} = 10^{6}$ (1 million = $10^{6}$ )

=> n = $10^{2}$ = 100

Hence, the language needs to have a minimum of 100 alphabets to achieve the objective.

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Filed Under: Permutations and Combinations

7 11603

Quantitative Aptitude - Arithmetic Ability Questions

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