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

True

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False

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Solution

The correct option is A
True

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

Squaring both sides,

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

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