Question

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

• A. $3$
• B. $6$
• C. $9$
• D. All of these

Answer 1

The correct option is D All of these

It is given that $24x$ is a multiple of $3$
$\therefore 2+4+x$ is a multiple of $3$
$\Rightarrow 6+x$ is a multiple of $3$
$\Rightarrow 6+x=0,3,6,9,12,15,......\left(1\right)$
But $x$ is a digit of the number $24x$
$\therefore x$ can take value $0,1,2,....,9$
$\Rightarrow 6+x$ can take values $6,7,8,...,\mathrm{15...}\left(2\right)$
From (1) and (2), we get
$6\times x=6$ or $9$ or $12$ or $15$
$\Rightarrow 6+x=6$ or $6+x=9$, or $6+x=12$ or $6+x=15$
$\Rightarrow x=0$ or $x=3$, or $x=6$ or $x=9$
Hence, $x=0,3,6,9.$