IMO C

I assume that this is the expression - [3 ^ (4n + 2)] + M.

(1) and (2) are clearly insufficient alone. Because, the value of m or n can be any no and when divided by 10, you get different possible remainders.

Take n=2, 3 ^ (8+2) + M = 3^10 + M = 59049 + M. M could take any value from 0-9 and when added with the 59049 and divided by 10, different remainder values turn up.

Combined, only then it is sufficient.

papgust wrote:IMO C

I assume that this is the expression - [3 ^ (4n + 2)] + M.

(1) and (2) are clearly insufficient alone. Because, the value of m or n can be any no and when divided by 10, you get different possible remainders.

Take n=2, 3 ^ (8+2) + M = 3^10 + M = 59049 + M. M could take any value from 0-9 and when added with the 59049 and divided by 10, different remainder values turn up.

Combined, only then it is sufficient.

your assumption is correct
Answer is incorrect

Ian Stewart wrote:

hpgmat wrote:if n and m are positive integers , what is the reminder when 3 ^ (4n + 2) + M is divided by 10

n= 2
m=1

Notice that 3^(4n + 2) = (3^4n)(3^2) = (3^4)^n * 9 = 81^n * 9. Since the units digit of 81^n will be 1 no matter what the value of n, the units digit of 81^n * 9 will always be 9. So we don't care what n is. We do need the value of m, however, so the answer is B.

Perfect explanation.
Thank you so much.