Number System - Aptitude MCQ Questions and Solutions with Explanations

21

Let x = 224 and y = 322. If the highest common factor of 23x and a × y is divisible by x and y, then what can be the possible value of a?

A) 4 B) 12 C) 8 D) 16

Discuss

Answer & Solution

Answer: Option D

Solution:

x = 224, y = 322
⇒ 23x = 23 × 224 = 23 × 16 × 14
⇒ ay = 322a = a × 23 × 14
⇒ If HCF of 23x and ay is divisible by x and y then,
23 × 16 × 14 = a × 23 × 14
a = 16

22

The number 334 × 545 × 7p is divisible by 3340 then what is the minimum value of P?

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

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & \frac{{334 \times 545 \times 7p}}{{3340}} \cr & \Rightarrow \frac{{334 \times 545 \times 7p}}{{334 \times 10}} \cr & \Rightarrow \frac{{109 \times 7p}}{2} \cr & {\text{Go through by options take 2}} \cr & \Rightarrow \frac{{109 \times 72}}{2} \cr & {\text{So, answer is 2}} \cr} $$

23

The smallest five digit number which is divisible by 12, 18 and 21 is:

A) 10080 B) 30256 C) 10224 D) 50321

Discuss

Answer & Solution

Answer: Option A

Solution:

We know, smallest five digit number is = 10000
LCM of 12, 18, 21 = 252
Number System mcq question image

Difference = 252 - 172 = 80
Then number is = 10000 + 80 = 10080

24

Let, p, q, r and s be positive natural numbers having three exact factors including 1 and the number itself. If q > p and both are two-digit numbers, and r > s and both are one-digit numbers, then the value of the expression $$\frac{{p - q - 1}}{{r - s}}$$ is:

A) 1 - s B) s + 1 C) -s - 1 D) s - 1

Discuss

Answer & Solution

Answer: Option C

Solution:

q > p and r > s
q > p > r > s
All number have three prime factor
One digit → s, r
s → 2 2² = 4
r → 3 3² = 9
Two digit → p, q
p → 5 5² = 25
q → 7 7² = 49
$$\eqalign{ & \frac{{p - q - 1}}{{r - s}} = \frac{{25 - 49 - 1}}{{9 - 4}} = \frac{{ - 25}}{5} = - 5 \cr & - 5 = - 4 - 1 = - s - 1 \cr} $$

25

What decimal of a week is an hour?

A) .0059 B) .0062 C) .062 D) .059

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\frac{1}{{24 \times 7}} = 0.0059$$

26

The sum of three consecutive natural numbers each divisible by 5, is 225. The largest among them is?

A) 85 B) 75 C) 70 D) 80

Discuss

Answer & Solution

Answer: Option D

Solution:

Let numbers are x, x + 5, x + 10
So, x + x + 5 + x + 10 = 225
3x + 15 = 225
3x = 210
x = 70
Largest number = 70 + 10 = 80

27

A six-digit number is divisible by 198. If the digits are rearranged, even then the number will be divisible by:

A) 3 B) 6 C) 2 D) 66

Discuss

Answer & Solution

Answer: Option A

Solution:

Let, 6 digit number after rearranging the digit divisible by 198 is = 0000891
This number is divisible by 3

28

If A = $$\frac{{\sqrt {0.0004} \times \root 3 \of {0.000008} }}{{\root 4 \of {16000} \times \root 3 \of {125000} \times \root 4 \of {810} }}$$ and B = $$\frac{{\root 3 \of {0.729} \times \root 4 \of {0.0016} }}{{\sqrt {0.16} }},$$ what is A × B?

A) $$6 \times {10^{ - 8}}$$ B) $$\left( {\frac{7}{4}} \right) \times {10^{ - 8}}$$ C) $$\left( {\frac{7}{3}} \right) \times {10^{ - 7}}$$ D) $$7 \times {10^{ - 7}}$$

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{A}} = \frac{{\sqrt {0.0004} \times \root 3 \of {0.000008} }}{{\root 4 \of {16000} \times \root 3 \of {125000} \times \root 4 \of {810} }} \cr & = \frac{{0.02 \times 0.02}}{{\root 4 \of {16000 \times 810} \times \root 3 \of {125000} }} \cr & = \frac{{0.02 \times 0.02}}{{20 \times 3 \times 50}} \cr & = \frac{1}{{75 \times {{10}^5}}} \cr & {\text{B}} = \frac{{\root 3 \of {0.729} \times \root 4 \of {0.0016} }}{{\sqrt {0.16} }} \cr & = \frac{{0.9 \times 0.2}}{{0.4}} \cr & = \frac{9}{{20}} \cr & \therefore A \times B = \frac{1}{{75 \times {{10}^5}}} \times \frac{9}{{20}} \cr & = \frac{3}{{25 \times 2}} \times \frac{1}{{{{10}^6}}} \cr & = \frac{3}{5} \times \frac{1}{{{{10}^7}}} \cr & = \frac{3}{5} \times {10^{ - 7}} \cr & = 6 \times {10^{ - 8}} \cr} $$

29

A boy added all natural numbers from 1 to 10, however he added one number twice due to which the sum becomes 58. What is the number which he added twice?

A) 3 B) 4 C) 7 D) 8

Discuss

Answer & Solution

Answer: Option A

Solution:

Sum of natural number from 1 to 10
$$\eqalign{ & = \frac{{\left( n \right)\left( {n + 1} \right)}}{2}\,\,\,\,\,\,\,\left( {{\text{where }}n = 10} \right) \cr & = \frac{{10 \times 11}}{2} \cr & = 55 \cr} $$
Clearly, we can see the number which is added twice = 58 - 55 = 3

30

What is the least value of x such that 517x324 is divisible by 12?

A) 3 B) 1 C) 0 D) 2

Discuss

Answer & Solution

Answer: Option D

Solution:

Divisibility rule of 3 : The sum of all digit should be divide by 3
Number System mcq question image