Question

When a positive integer k is divided by 6, the remainder is 1. what is the remainder when 5k is divided by 3?

Answer 1

$k\equiv1\mod6\implies k=6n+1$ for some integer $n$.

$5k=5(6n+1)=30n+5$
$\implies5k\equiv30n+5\equiv3(10n)+5\equiv5\equiv2\mod3$