Question

Given that the number $\overline{35a64}$ is divisible by 3, where a is a digit, what are the possible volues of a?

Answer 1

$\therefore$ The number $\overline{35a64}$ is divisible by 3
$\therefore$ The sum of its digits will also be divisible by 3
$\therefore$ 3+5+a+b+4 is divisible by 3
$\Rightarrow$ 18+a is divisible by 3
$\Rightarrow$ a is divisible by 3
$(\therefore 18isdivisibleby3)$
$\therefore$ Values of a can be, 0,3,6,9