If n[i] and m are positive integers, what is the remainder when "3^(4n+2) + m" is divided by 10 ?

(1) n = 2
(2) m = 1

The answer is 'B', but I don't get it!!! if m is one, you still don't know what 3^(4n+2) is... right? all we know is it's a power of 3... so it's units digit could be any number between 0-9.... thus, we still don't know what the remainder would be if divided by 10.... please help!!!!

here's the cut&paste of the problem

Rephrase the expression: -
3^(4n+2) +m = (9)*3^(4n) + m

statement (1) n =2 so the expression = (9)*3^8 + m but we do not know what m is - so cannot predict the value of the expression. INSUFFICIENT

statemtn (2) m = 1 which makes the expression:

(9)*3^(4n) + 1 Since we know n is +ve integer, now it gets tricky: -

for n = 1,2,3,4 the exponential component of the expression will be

3^4, 3^8, 3^12 or
9^2, 9^4, 9^6 or

81, 81^2, 81^3 ans so on... the unit digit of all these values will be 1, now this value will be multiplied by 9 and '1' will be added to the result. It will make the unit digit of the result - 0. It means the result will be prefectly divided by 10. So the remainder will be 0

SUFFICIENT, So the answer is (B)

Hope it helps

GMAT 2007

Very nice, GMAT 2007!