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

It is given that $\overline{67y19}$ is divisible by $9$, and if a number is divisible by $9$ then sum of digits must be a multiple of $9$.
i.e., $6+7+y+1+9$ is multiple of $9$
$\Rightarrow y+23=0,9,18,27,.....$
Here $y$ is a digit, where, $y$ can have between $0$ and $9$
Thus, $y+23=27$
$\Rightarrow y=27-23$
$\therefore y=4$