What is the highest possible sum of (m +
n) if the number '9m813n2' is divisible by 12?

ATQ,

A number is divisible by 12 if it is divisible by both 3 and 4.

A number is divisible by 4 when the last two digits of the number are divisible by 4.

'n2' is divisible by 4 when 'n' = 0, 2, 4, 6, or 8.

Since we have to find the maximum value, so 'n' = 8.

A number is divisible by 3 when the sum of its digits is divisible by 3.

So, (9 + m + 8 + 1 + 3 + 8 + 2) = (31 + m) must be divisible by 3.

So, 'm' = 2, 5, or 8.

Since we have to find the maximum value, so 'm' = 8.

Therefore, required value = 8 + 8 = 16 .