5555+ Aptitude and Reasoning Questions, 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 26542

Q:

A man can row 6 kmph in still water. When the river is running at 1.2 kmph, it takes him 1 hour to row to a place and back. What is the total distance traveled by the man ?

A) 4.58 kms	B) 6.35 kms
C) 5.76 kms	D) 5.24 kms

Answer & Explanation Answer: C) 5.76 kms

Explanation:

Speed in still water = 6 kmph

Stream speed = 1.2 kmph

Down stream = 7.2 kmph

Up Stream = 4.8 kmph

x/7.2 + x/4.8 = 1

x = 2.88

Total Distance = 2.88 x 2 = 5.76 kms

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

37 26541

Q:

The following table represents the rainfall (in mm) of five states from June to September in a year.

Consider the information and answer questions based on it.

Which state shows a gradual increase in its rainfall from June to September?

A) HP	B) WB
C) GA	D) TN

Answer & Explanation Answer: C) GA

Explanation:

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Filed Under: Table Charts
Exam Prep: Bank Exams

0 26533

Q:

Is Arun taller than Sachin ?

I. Dinesh is of the same height as Arun and Sachin.

II. Sachin is not shorter than Dinesh.

A) If the data in statement I alone are sufficient to answer the question	B) If the data in statement II alone are sufficient answer the question
C) If the data either in I or II alone are sufficient to answer the question;	D) If the data even in both the statements together are not sufficient to answer the question

Answer & Explanation Answer: A) If the data in statement I alone are sufficient to answer the question

Explanation:

From statement I, we can conclude that Dinesh. Arun and Sachin are of the same height So. Arun is not taller than Sachin. Thus, only statement I is sufficient to answer the question. .

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Filed Under: Data Sufficiency

16 26528

Q:

Find the area of a right-angled triangle whose base is 12 cm and hypotenuse is 13cm.

A) 30	B) 40
C) 50	D) 60

Answer & Explanation Answer: A) 30

Explanation:

Height of the triangle = $\sqrt{(13^{2} - 12^{2})} = \sqrt{25}$ = 5 cm.

Its area = $\frac{1}{2} * b a s e * h e i g h t$ = $\frac{1}{2} * 12 * 5$ = $30 c m^{2}$ .

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Filed Under: Area
Exam Prep: Bank Exams
Job Role: Bank PO

49 26455

Q:

If Deepesh had walked 20 km/h faster he woulh have saved 1 hour in the distance of 60km. what is the usual speed of Deepesh?

A) 100	B) 120
C) 150	D) None of these

Answer & Explanation Answer: A) 100

Explanation:

Let the original speed be x km/h, then

$\frac{600}{x} - \frac{600}{(x + 20)} = 1$

$\Rightarrow 600 (\frac{x + 20 - x}{x (x + 20)}) = 1$

$\Rightarrow x^{2} + 120 x - 12000 = 0$

$\Rightarrow (x - 120) (x - 100) = 0$

Therefore, original speed = 100km/h

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Filed Under: Time and Distance

32 26438

Q:

What will be the total weight of 10 poles each of the same weight ?

I. One-fourth of the weight of a pole is 5 kilograms.

II. The total weight of three poles is 20 kilograms more than the total weight of two poles.

A) If the data in statement I alone are sufficient to answer the question	B) If the data in statement II alone are sufficient answer the question
C) If the data either in I or II alone are sufficient to answer the question;	D) If the data even in both the statements together are not sufficient to answer the question

Answer & Explanation Answer: C) If the data either in I or II alone are sufficient to answer the question;

Explanation:

From I, we find that the weight of one pole is (5 x 4) = 20 kg ,and so the weight of 10 poles is 200 kg.

Thus, I alone is sufficient.

From II. we have : (weight of 3 poles — weight of 2 poles) -= 20 kg or weight of one pole - 20 kg.

So. weight of 10 poles 200 kg.

Thus. II alone is also sufficient

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Filed Under: Data Sufficiency

24 26437

Q:

Which one of the following Venn diagrams best illustrates the three classes.

Rhombus, Quadrilaterals, Polygons

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

Aptitude and Reasoning Questions

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Non Verbal Reasoning

Quantitative Aptitude - Arithmetic Ability

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