Question

The number 9a84 is divisible by 12. What are the possible values of `a'?

• A. $0$
• B. $3$
• C. $6$
• D. $9$

Answer 1

Answer: (A), (B), (C), (D)

$9$

Given, $9a84$ is divisible by $12$.
$\therefore$ This number is also divisible by $3$ and $4$ simultaneously, Because For a number to be divisible by $12$ it must be divisible by $3$ and $4$.

Now,
Sum of digits of number will be divisible by $3$.
$\Rightarrow 9+a+8+4=21+a$
Different possible values of $a$ will be,

1. $a=0$, $\Rightarrow 21+a=21+0=21$. Which is divisible by $3$.
2. $a=3$, $\Rightarrow 21+a=21+3=24$. Which is divisible by $3$.
3. $a=6$, $\Rightarrow 21+a=21+6=27$. Which is divisible by $3$.
4. $a=9$, $\Rightarrow 21+a=21+9=30$. Which is divisible by $3$.

$\therefore a$ can be $0,3,6$ and $9$.