Question

A number when divided by 7 leaves a remainder 5. When the square of the number is divided by 7, then the remainder is

• A. 4
• B. 0
• C. 1
• D. 2

Answer 1

The correct option is A 4

Let the number be x.

As, Dividend = Divisor × Quotient + Remainder

x = 7k + 5 (Where k is any natural number)

$x^2={(7k+5)}^2$

$=49k^2+70k+25$

$=7(7k^2+10k+3)+4$

Therefore, when $x^2$ is divided by 7, then remainder is 4.

Hence, the correct answer is option (a).