Question

If $31z5$ is a multiple of $9$, where $z$ is a non zero digit, what is the value of $z$?

• A. $9$
• B. $1$
• C. $2$
• D. $5$

Answer 1

The correct option is A $9$

Since the number $31z5$ is a multiple of $9$, the sum of its digits $3+1+z+5=9+z$ is a multiple of $9$.
$\therefore (9+z)$ is either 0 or 9 or 18 or 27...

Since $z$ is a non zero digit, so $(9+z)$ must be equal to $18$.
i.e., $9+z=9\Rightarrow z=0$

OR $9+z=18\Rightarrow z=9$

Hence, option A is correct.