6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

What is the total no of ways of selecting atleast one item from each of the two sets containing 6 different items each?

A) 2856	B) 3969
C) 480	D) None of these

Answer & Explanation Answer: B) 3969

Explanation:

We can select atleast one item from 6 different items = $2^{6} - 1$

Similarly we can select atleast one item from other set of 6 different items in $2^{6} - 1$ ways.

Required number of ways = $(2^{6} - 1) (2^{6} - 1) = {(2^{6} - 1)}^{2}$ = 3969

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Filed Under: Permutations and Combinations
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1 7574

Q:

A bag contains 3 red balls, 5 yellow balls and 7 pink balls. If one ball is drawn at random from the bag, what is the probability that it is either pink or red?

A) 2/3	B) 1/8
C) 3/8	D) 3/4

Answer & Explanation Answer: A) 2/3

Explanation:

Given number of balls = 3 + 5 + 7 = 15

One ball is drawn randomly = 15C1

probability that it is either pink or red = $\frac{7 C_{1} + 3 C_{1}}{15 C_{1}} = \frac{7 + 3}{15} = \frac{10}{15} = \frac{2}{3}$

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Filed Under: Probability
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22 7573

Q:

April 19th, 1986 falls on which day?

A) Saturday	B) Wednesday
C) Thursday	D) Friday

Answer & Explanation Answer: A) Saturday

Explanation:

19th April, 1986 = (1985 years + Period from 1.1.1986 to 19.4.1986)

Odd days in 1600 years = 0

Odd days in 300 years = 1

85 years has 21 leap years + 64 ordinary years.

Number of odd days in 85 years =( 21 x 2 + 64) = 1 odd day.

Jan. Feb. March April

(31 + 28 + 31 + 19) = 109 days

109 days = 15 weeks + 4 days= 4 odd day.

Total number of odd days = (1 + 0 + 1 + 4) = 6.

Given day is Saturday.

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Filed Under: Calendar

5 7564

Q:

For $x \in N, x > 1$ , and $p = \log_{x} (x + 1)$ , $q = \log_{x + 1} (x + 2)$ then which one of the following is correct?

A) p < q	B) p = q
C) p > q	D) can't be determined

Answer & Explanation Answer: C) p > q

Explanation:

$\frac{k}{l} > \frac{k + 1}{l + 1}$ for (k,l) > 0 and k > l

Let k = x+1 and l = x

Therefore, $\frac{x + 1}{x} > \frac{(x + 1) + 1}{(x) + 1}$

(x + 1) > x

Therefore, $\frac{\log (x + 1)}{\log (x)} > \frac{\log (x + 2)}{\log (x + 1)}$

$\Rightarrow \log_{x} (x + 1) > \log_{x + 1} (x + 2)$

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Filed Under: Logarithms
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33 7554

Q:

A rectangular lawn of dimensions 80 m x 60 m has two roads each 10 m wide running in the middle of the lawn, one parallel to the length and the other parallel to the breadth. What is the cost of traveling the two roads at Rs.3 per sq m ?

A) Rs. 3600	B) Rs. 3800
C) Rs. 3900	D) Rs. 3700

Answer & Explanation Answer: C) Rs. 3900

Explanation:

Area = (l + b – d) d

= (80 + 60 – 10)10

=> 1300 sq.mts

=> 1300 x 3 = Rs.3900

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Filed Under: Area
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Q:

In the following question, four number pairs are given. The number on left side of (–) is related to the number on the right side of (–) with some Logic/Rule/Relation. Three are similar on basis of same Logic/Rule/Relation. Select the odd one out from the given alternatives.

A) 7 – 49	B) 9 – 81
C) 11 – 121	D) 15 – 215

Answer & Explanation Answer: D) 15 – 215

Explanation:

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Filed Under: Odd Man Out

5 7550

Q:

The sides of a right-angled triangle are 12 cm, 16 cm, 20 cm respectively. A new right angle Δ is made by joining the midpoints of all the sides. This process continues for infinite then calculate the sum of the areas of all the triangles so made.

A) 312 sq.cm	B) 128 sq.cm
C) 412 sq.cm	D) 246 sq.cm

Answer & Explanation Answer: B) 128 sq.cm

Explanation:

Area = = 96

Sum of Area =

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Q:

16 women can do a piece of work in 10 days while 15 men can do the same work in 12 days. All men and all women work alternately starting with all men, then find the time taken by them to complete the whole work?

A) 10 5/2 days	B) 11 days
C) 11 2/5 days	D) 12 1/2 days

Answer & Explanation Answer: A) 10 5/2 days

Explanation:

Let efficiency of every man and every woman be 'm' unit/day and 'w' unit/day respectively

15×12×m = 10×16×w

⇒ m/w = 8/9

Total work = 15 × 12 × 9 = 1620 units

In 2 days, total work done = 15 x 9 + 16 x 8 = 263 units

So, in 10 days work done will be = 263 × 5 = 1315 units

Remaining work will be done in = (1620-1315)/(15×8) = 5/2 days

Total days = 10 5/2 days.

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Filed Under: Time and Work
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