Question:
Given that the number $\overline{67 y 19}$ is divisible by 9 , where $y$ is a digit, what are the possible values of $y$ ?
Solution:
It is given that $\overline{67 \mathrm{y} 19}$ is a multiple of 9 .
$\therefore(6+7+\mathrm{y}+1+9)$ is a multiple of 9 .
$\therefore(23+\mathrm{y})$ is a multiple of 9 .
$23+\mathrm{y}=0,9,18,27,36 \ldots$
But $\mathrm{x}$ is a digit. So, $\mathrm{x}$ can take values $0,1,2,3,4 \ldots 9$.
$23+\mathrm{y}=27$
$\Rightarrow y=4$