Question

Given that the number $\overline{67y19}$ is divisible by 9, where y is a digit, what are the possible values of y?

Answer 1

$\because$ The number $\overline{67y19}$ is diviseble by 9
$\therefore$ The sum of its digits will also be divisible by 9
$\Rightarrow 6+7+y+1+9$ is divisible by 9
$\Rightarrow$ 23+ y is divisible by9
$\because$ The numbers greater than 23 are 27,36,45,.........
Which are divisible by 9
$\therefore$ y = 9