Question

If $a679b$ is a five-digit number in base $10$ and is divisible by $72$, then the values of $a$ and $b$ are respectively _________.

• A. $3,2$
• B. $6,2$
• C. $2,3$
• D. $2,6$

Answer 1

The correct option is A $3,2$

Divisibility by $72$ $\Rightarrow$ Divisibility by $8$ and $9$

Divisibility test of $9:$

$\frac{(a+6+7+9+b)}{9}$ gives no remainder.

$\Rightarrow a+b=5$ or $14$

Divisibility test of $8:$

Last $3$ digits should be divisible by $8$

$\Rightarrow 79b$ should be divisibile by $8$

$\therefore b=2$

$\therefore a=3$