divisor tough questn

[sukh]

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 - 12n
answer choices are 11, 1,0,-1,-11

[Brent@GMATPrepNow]

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 - 12n
answer choices are 11, 1,0,-1,-11

This question is posted incorrectly. As it stands, there is no answer.

Here's why: Notice that since 12 is even, 12n must be even. If 12n is even, it cannot be a divisor of 3,176,793 (since this number is odd).

Aside: 0 is not a divisor of 3,176,793

The question should read:

If n is a non-negative integer such that 12^n is a divisor of 3,176,793, what is the value of n^12 - 12^n.

First notice the big hint right from the start: n is a non-negative integer
Your first reaction should be "Why not just tell us that n is positive?" The reason is that the test-maker wants to include zero as a possible value for n (and zero is neither positive nor negative).

Since the test-maker went to the trouble to keep zero as a possible value for n, let's check to see if n works.
Well, 12^0 = 1, and 1 is a divisor of 3,176,793. So n must equal zero.

Now that we know the value of n, we can evaluate n^12 - 12^n
We get 0^12 - 12^0 = -1, so the answer is D

Cheers,
Brent