Question

A number when divided by 5 leaves a remainder 3. What is the remainder when the square of the same number is divided by 5?

Select one:

2

1

3

4

Answer 1

Correct option is (d) 4

Let the number be N.

N = 5 × Q + 3 

N² = (5Q + 3)²

⇒ 25Q² + 9 + 30Q 

On N² ÷ 5 = 5(5Q² + 30Q) + 5 + 4 

⇒ 5(5Q² + 30Q + 1) + 4 

∴ The required remainder is 4.