6500+ Quantitative Aptitude Questions and Answers With Explanation

Q:

In how many ways can 5 different toys be packed in 3 identical boxes such that no box is empty, if any of the boxes may hold all of the toys ?

A) 36	B) 25
C) 24	D) 72

Answer & Explanation Answer: B) 25

Explanation:

The toys are different; The boxes are identical

If none of the boxes is to remain empty, then we can pack the toys in one of the following ways

a. 2, 2, 1

b. 3, 1, 1

Case a. Number of ways of achieving the first option 2 - 2 - 1

Two toys out of the 5 can be selected in $5 C_{2}$ ways. Another 2 out of the remaining 3 can be selected in $3 C_{2}$ ways and the last toy can be selected in $1 C_{1}$ way.

However, as the boxes are identical, the two different ways of selecting which box holds the first two toys and which one holds the second set of two toys will look the same. Hence, we need to divide the result by 2

Therefore, total number of ways of achieving the 2 - 2 - 1 option is ways $5 C_{2} * 3 C_{2}$ = 15 ways

Case b. Number of ways of achieving the second option 3 - 1 - 1

Three toys out of the 5 can be selected in $5 C_{3}$ ways. As the boxes are identical, the remaining two toys can go into the two identical looking boxes in only one way.

Therefore, total number of ways of getting the 3 - 1 - 1 option is $5 C_{3}$ = 10 = 10 ways.

Total ways in which the 5 toys can be packed in 3 identical boxes

= number of ways of achieving Case a + number of ways of achieving Case b= 15 + 10 = 25 ways.

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Filed Under: Permutations and Combinations

34 25435

Q:

If $s + \frac{1}{s} = 4$ , then the value of $s^{2} + \frac{1}{s^{2}}$

A) 14	B) 16
C) 20	D) 24

Answer & Explanation Answer: A) 14

Explanation:

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Filed Under: Simplification
Exam Prep: Bank Exams

0 25411

Q:

If the letters of the word CHASM are rearranged to form 5 letter words such that none of the word repeat and the results arranged in ascending order as in a dictionary what is the rank of the word CHASM ?

A) 32	B) 24
C) 72	D) 36

Answer & Explanation Answer: A) 32

Explanation:

The 5 letter word can be rearranged in 5!=120 Ways without any of the letters repeating.

The first 24 of these words will start with A.

Then the 25th word will start will CA _ _ _.
The remaining 3 letters can be rearranged in 3!=6 Ways. i.e. 6 words exist that start with CA.

The next word starts with CH and then A, i.e., CHA _ _.
The first of the words will be CHAMS. The next word will be CHASM.

Therefore, the rank of CHASM will be 24+6+2= 32

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Filed Under: Permutations and Combinations

17 25404

Q:

At what time between 3 and 4 o’clock will the minute hand and the hour hand are on the same straight line but facing opposite directions ?

A) 3:15 2/8	B) 3:49
C) 3:49 1/11	D) 3:51

Answer & Explanation Answer: C) 3:49 1/11

Explanation:

On straight line means 180 degree angle.
180 = 11/2 min – 30 hrs
180 = 11/2 m – 30 × 3
180 = 11/2 m – 90
(180 + 90) 2 = 11 m
m = 540/11 = 49 1/11 minutes.

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

30 25394

Q:

The mean temperature of Monday to Wednesday was 37C and of Tuesday to Thursday was 34C . If the temperature on Thursday was (4/5) th that of Monday, the temperature on Thursday was?

Answer

$\inline \fn_jvn M+T+W =(37\times 3)^{0}=111^{0}C$ -----------(1)