Question

if $24x$ is a multiple of $3$, where $x$ is a digit. What is the value if $x$.

Answer 1

Let’s say, $24x$ is a multiple of $3$.
Then, according to the divisibility rule of $3$, the sum of all the digits should be a multiple of $3$.

$2+4+x=6+x$
So, $6+x$ is a multiple of $3$, and $6+x$ is one of these numbers: $0,3,6,9,12,15,18$ and so on.

Since, x is a digit, the value of x will be either $0$ or $3$ or $6$ or $9$, and the sum of the digits can be $6$ or $9$ or $12$ or $15$ respectively.


Thus, $x$ can have any of the four different values: $0$ or $3$ or $6$ or $9$.