Problems on Numbers Practice Test Questions – Aptitude -- Free Practice

Practice questions on number system problems, including two-digit and three-digit number puzzles, digit reversal, sum and difference of digits, and linear equations based on numbers

Question 1

The sum of two numbers is 75 and their difference is 20. Find the difference of their squares.

1500✓✗

1600✓✗

1550✓✗

None of these✓✗

Explanation

Difference of squares = (sum) × (difference) = 75 × 20 = 1500
(Using the identity a² - b² = (a + b)(a - b))

Question 2

A number consists of two digits. The digit in the tens place is 3 times the digit in the unit's place. If 54 is subtracted, the digits are reversed. The number is:

39✓✗

92✓✗

93✓✗

94✓✗

Explanation

Let the units digit = u, so the tens digit = 3u.
Number = 30u + u = 31u. Reversed number = 10u + 3u = 13u.
31u - 54 = 13u
18u = 54
u = 3
Number = 31 × 3 = 93

Question 3

In a two-digit number, the digit in the ten's place is twice the digit in the unit's place. If 18 is subtracted from the number, the digits are reversed. Find the number.

63✓✗

21✓✗

42✓✗

None of these✓✗

Explanation

Let the unit's digit = u, so the ten's digit = 2u.
Number = 20u + u = 21u. Reversed number = 10u + 2u = 12u.
21u - 18 = 12u
9u = 18
u = 2
Number = 21 × 2 = 42

Question 4

The sum of two numbers is 62 and their product is 960. The sum of their reciprocals is

31480✓✗

29480✓✗

61960✓✗

41960✓✗

Explanation

Sum of reciprocals = 1a + 1b = a + bab = 62960 = 31480

Question 5

A number consists of two digits. The digit in the ten's place is 3 times the digit in the unit's place. If 54 is subtracted from the number, then the digits are reversed. The number is:

39✓✗

62✓✗

93✓✗

31✓✗

Explanation

Let the unit's digit = u, so the ten's digit = 3u.
Number = 30u + u = 31u. Reversed number = 10u + 3u = 13u.
31u - 54 = 13u
18u = 54
u = 3
Number = 31 × 3 = 93