Question

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

• A. $0$
• B. $3$
• C. $6$
• D. All of these

Answer 1

Answer: (D)

All of these

Since $24x$ is a multiple of $3$, the sum of its digits $2+4+x=(6+x)$ is a multiple of $3$.
$\therefore (6+x)$ is one of the numbers $0,3,6,9,12,15,18...$
But $x$ is a digit.

Therefore, $(6+x)$ must be equal to $6$ or $9$ or $12$ or $15$.
i.e., $6+x=6$ or $9$ or $12$ or $15$
$\Rightarrow x=0$ or $3$ or $6$ or $9$.
Thus, $x$ can have any of the four different values, namely, $0,3,6$ or $9$.