Find the maximum value of (a +
b) if '7a253b2' is divisible by 12.

A number is divisible by 12 if it divisible by both 3 and 4. A number is divisible by 4 when last two digits of the number is divisible by 4. 'b2' is divisible by 4 when 'b' = 1, 3, 5, 7 or 9. Since, we have to find maximum value, so 'b' = 9. A number is divisible by 3 when sum of its digit is divisible by 3. So, (7 + a + 2 + 5 + 3 + 9 + 2) = (28 + a) must be divisible by 3. So, 'a' = 2, 5 or 8. Since, we have to find maximum value, so 'a' = 8. Therefore, required value = 8 + 9 = 17