Data Sufficiency

AAPL wrote:GMAT Prep

If \(n\) and \(m\) are positive integers, what is the remainder when \(3^{(4n+2)}+m\) is divided by \(10\)?

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

OA B

If you divide a number by 10, the remainder you get is just the number's units digit. So the question is just asking "what is the units digit of \(3^{(4n+2)}+m\) ?"

There are other units digit/exponent methods that are more flexible, but I've explained those in other posts, so I'll just use exponent rules here:

3^(4n + 2) = (3^(4n))(3^2) = (3^4)^n (3^2) = (81^n) (9)

and since 81^n will have a units digit of 1 always, the units digit of (81^n)(9) will always be 9, no matter what n is equal to.

So the units digit of 3^(4n + 2) is always 9, and we don't care what n is equal to. When we calculate 3^(4n + 2) + m, we're just adding something ending in 9 to m, and as long as we know the units digit of m, we'll know the units digit of this sum. So Statement 2 is sufficient alone, and the answer is B (and in fact the expression ends in 0, so it is divisible by 10).