Number System - Aptitude MCQ Questions and Solutions with Explanations

41

Which of the following is a prime number ?

A) 33 B) 81 C) 93 D) 97

Discuss

Answer & Solution

Answer: Option D

Solution:

Clearly, 97 is a prime number.

42

What is the unit digit in {(6374)¹⁷⁹³ x (625)³¹⁷ x (341⁴⁹¹)}?

A) 0 B) 2 C) 3 D) 5

Discuss

Answer & Solution

Answer: Option A

Solution:

Unit digit in (6374)¹⁷⁹³
= Unit digit in (4)¹⁷⁹³
= Unit digit in [(4²)⁸⁹⁶ x 4]
= Unit digit in (6 x 4) = 4

Unit digit in (625)³¹⁷
= Unit digit in (5)³¹⁷
= 5

Unit digit in (341)⁴⁹¹
= Unit digit in (1)⁴⁹¹
= 1

Required digit
= Unit digit in (4 x 5 x 1)
= 0

43

5358 × 51 = ?

A) 273258 B) 273268 C) 273348 D) 273358 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

5358 × 51
= 5358 × (50 + 1)
= 5358 × 50 + 5358 × 1
= 267900 + 5358
= 273258

44

The sum of first five prime numbers is:

A) 11 B) 18 C) 26 D) 28 E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Required sum = (2 + 3 + 5 + 7 + 11) = 28
Note: 1 is not a prime number
Definition : A prime number (or a prime) is a natural number that has exactly two distinct natural number divisors: 1 and itself.

45

The difference of two numbers is 1365. On dividing the larger number by the smaller, we get 6 as quotient and the 15 as remainder. What is the smaller number ?

A) 240 B) 270 C) 295 D) 360 E) None of these

Discuss

Answer & Solution

Answer: Option B

Solution:

Let the smaller number be x
Then larger number = (x + 1365)
∴ x + 1365 = 6x + 15
⇒ 5x = 1350
⇒ x = 270
∴ Smaller number = 270

46

(12)³ × 6⁴ × 432^-1 = ?

A) 5184 B) 5060 C) 5148 D) 5084 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

$$\eqalign{ & {\text{Given}}\,{\text{Exp}}{\text{.}} \cr & = \frac{{{{\left( {12} \right)}^3} \times {6^4}}}{{432}} \cr & = \frac{{{{\left( {12} \right)}^3} \times {6^4}}}{{12 \times {6^2}}} \cr & = {\left( {12} \right)^2} \times {6^2} \cr & = {\left( {72} \right)^2} \cr & = 5184 \cr} $$

47

72519 × 9999 = ?

A) 725117481 B) 674217481 C) 685126481 D) 696217481 E) None of these

Discuss

Answer & Solution

Answer: Option A

Solution:

72519 × 9999
= 72519 × (10000 - 1)
= 72519 × 10000 - 72519 × 1
= 725190000 - 72519
= 725117481

48

Which of the following number is divisible by 24 ?

A) 35718 B) 63810 C) 537804 D) 3125736 E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

24 = 3 × 8, where 3 and 8 co-prime
Clearly, 35718 is not divisible by 8, as 718 is not divisible by 8
Similarly, 63810 is not divisible by 8 and 537804 is not divisible by 8
Consider option (D),
Sum of digits = (3 + 1 + 2 + 5 + 7 + 3 + 6) = 27, which is divisible by 3
Also, 736 is divisible by 8
∴ 3125736 is divisible by (3 × 8), i.e., 24

49

On dividing a number by 5, we get 3 as remainder. What will the remainder when the square of the this number is divided by 5 ?

A) 0 B) 1 C) 2 D) 4 E) None of these

Discuss

Answer & Solution

Answer: Option D

Solution:

Let the number be x and on dividing x by 5, we get k as quotient and 3 as remainder
∴ x = 5k + 3
⇒ x² = (5k + 3)²
⇒ x² = (25k² + 30k + 9)
⇒ x² = 5 (5k² + 6k + 1) + 4
∴ On dividing x² by 5, we get 4 as remainder

50

On dividing a number by 357, we get 39 as remainder. On dividing the same number 17, what will be the remainder ?

A) 0 B) 3 C) 5 D) 11 E) None of these

Discuss

Answer & Solution

Answer: Option C

Solution:

Let x be the number and y be the quotient. Then,
x = 357 × y + 39
= (17 × 21 × y) + (17 × 2) + 5
= 17 × (21y + 2) + 5
∴ Required remainder = 5