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: $0,3,6,9,13,15,18,\dots$.

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.