Question

If $24x$ is a multiple of $3$, where $x$ is a digit, what is the value of $x$?

Answer 1

(Since $24x$ is a multiple of $3$, its sum of digits $6+x$ is a multiple of $3$; so $6+x$ is one of these numbers: $0,3,6,9,12,15,18$ . But since x is a digit, it can only be that $6+x=6$ or $9$ or $12$ or $15$. Therefore, $x=0$ or $3$ or $6$ or $9$. Thus, x can have any of four different values.)