Find the smallest value of the sum of p and q so that the number 6p5q2 is divisible by 3.

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

Here, sum of the known digits of 6p5q2 = 6 + p + 5 + q + 2 = 13 + p + q

Now, the number next to 13, which is divisible by 3 is 15.

Thus, if we replace the p+q by 2, then the sum of digits will become 15 and the number becomes divisible by 3.

Hence, p+q is replaced by 2.