1. The number $\overline{1 a b 76}$ is divisible by 72 . List down all the possible values of $a+b$.
Answer: 4 and 13 (accept 4 or 13 as well)
Solution: Since $\overline{1 a b 76}$ is divisible by 72 , it is divisible by 8 and 9 . Since it is divisible by $9,1+a+b+7+6$ or $14+a+b$ is divisible by 9 . Therefore, $a+b$ is necessarily 4 or 13 . The only other condition we require is that $\overline{b 76}$ must be divisible by 8 , which is equivalent to $b$ being odd. Therefore $a+b$ being equal to 4 or 13 are both attainable.