6500+ Quantitative Aptitude Questions and Answers With Explanation

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 11254

Q:

Two boys and a girl can do a work in 5 days, while a boy and 2 girls can do it in 6 days. If the boy is paid at the rate of 28$ a week, what should be the wages of the girl a week ?

A) 24 $	B) 22 $
C) 16 $	D) 14 $

Answer & Explanation Answer: C) 16 $

Explanation:

Let the 1 day work of a boy=b and a girl=g, then
2b + g = 1/5 ---(i) and
b + 2g = 1/6 ---(ii)
On solving (i) & (ii), b=7/90, g=2/45
As payment of work will be in proportion to capacity of work and a boy is paid $ 28/week,
so a girl will be paid $28 \times \frac{\frac{2}{45}}{\frac{7}{90}}$ = 16 $.

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

5 11233

Q:

The two trains of lengths 400 m, 600 m respectively, running at same directions. The faster train can cross the slower train in 180 sec, the speed of the slower train is 48 kmph. Then find the speed of faster train ?

A) 68 kmph	B) 52 kmph
C) 76 kmph	D) 50 kmph

Answer & Explanation Answer: A) 68 kmph

Explanation:

Let the speed of the faster train be 'X' kmph,
Then their relative speed= X - 48 kmph
To cross slower train by faster train,
Distance need to be cover = (400 + 600)m = 1 km. and
Time required = 180 sec = 180/3600 hr = 1/20 hr.
Time = Distance/Speed
=> 1/20 = 1/(x-48)
X = 68 kmph

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Filed Under: Problems on Trains
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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14 11231

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 11230

Q:

$18800 \div 470 \div 20 = ?$

A) 1	B) 2
C) 3	D) 4

Answer & Explanation Answer: B) 2

Explanation:

Given Expression = $\frac{18800}{470} \div 20$ = $40 \div 20$ = 2

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Filed Under: Simplification

12 11195

Q:

If a - b = 3, $(a^{2} + b^{2}) = 29$ , find the value of ab.

A) 10	B) 12
C) 15	D) 18

Answer & Explanation Answer: A) 10

Explanation:

2ab= $(a^{2} + b^{2}) - (a^{2} - b^{2})$

29-9=20

=>ab=10

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Filed Under: Simplification

8 11194

Q:

In a purse there are 30 coins, twenty one-rupee and remaining 50-paise coins. Eleven coins are picked simultaneously at random and are placed in a box. If a coin is now picked from the box, find the probability of it being a rupee coin?

A) 4/7	B) 2/3
C) 1/2	D) 5/6

Answer & Explanation Answer: B) 2/3

Explanation:

Total coins 30

In that,

1 rupee coins 20

50 paise coins 10

Probability of total 1 rupee coins = 20C11

Probability that 11 coins are picked = 30C11

Required probability of a coin now picked from the box is 1 rupee = 20C11/30C11 = 2/3.

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Filed Under: Probability
Exam Prep: AIEEE , Bank Exams , CAT , GATE
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17 11180

Q:

Three numbers are in the ratio of 3:4:5 and their L.C.M is 3600.Their HCF is:

A) 40	B) 60
C) 100	D) 120

Answer & Explanation Answer: B) 60

Explanation:

Let the numbers be 3x, 4x, 5x.

Then, their L.C.M = 60x.

So, 60x=3600 or x=60.

Therefore, The numbers are (3 x 60), (4 x 60), (5 x 60).

Hence,required H.C.F=60

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Filed Under: HCF and LCM
Exam Prep: CAT
Job Role: Bank PO

14 11167

Quantitative Aptitude - Arithmetic Ability Questions

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