Question

Given that the number $35a64$ is divisible by $3$, where $a$ is a digit, what are the possible values of $a$?

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

Answer 1

Answer: (D)

All of these

The sum of digits of a number divisible by $3$ is a multiple of $3$

$3+5+a+6+4=3n$

$18+a=3n$

If $n=6\Rightarrow 18+a=18\Rightarrow a=0$

If $n=7,\Rightarrow 18+a=21\Rightarrow a=3$

If $n=8\Rightarrow 18+a=24\Rightarrow a=6$

$\therefore a=0,3,6$