Question

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

Answer 1

Given: A positive integer n is divided by 9 gives 7 as the remainder.
Let a be quotient
$n=9a+7$
Now, $3n-1=3(9a+7)-1=27a+21-1=27a+20=27a+18+2=9(3a+6)+2$

$\Rightarrow 3n-1=9(3a+6)+2$

So, when $3n-1$ is divided by $9$

Remainder $=2$.

Hence, if $(3n-1)$ is divided by $9$ then the remainder will be $2$