Question

A number when divided by 6 leaves a remainder 3. When the square of the number is divided by 6, the remainder is 3.

• A. True
• B. False

Answer 1

The correct option is A

True

Let the number be $x$
Given: $x=6q+3$ where q is a whole number.

Squaring both sides,

$x^2=(6q+3{)}^2$
$\Rightarrow$ $x^2=36q^2+36q+9$
$\Rightarrow$ $x^2=6(6q^2+6q+1)+3$
$\therefore$ When $x^2$ is divided by 6, then the remainder is 3.