Question

On dividing a positive integer $n$ by $9$, we get $7$ as remainder. What will be the remainder when $(3n-1)$ is divided by $9$

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

The correct option is B $2$

Let $n=9q+7\Rightarrow 3n-1=27q+20$

$\Rightarrow 27q+18+2=9(3q+2)+2$

$\therefore 3n-1=9k+2$

$\therefore$ Remainder is $2$ when $3n-1$ is divided by $9$.