non negative exponent of 12

j_shreyans wrote: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 ?

A)- 11
B)- 1
C)0
D)1
E)11

OAB

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 whether n = 0 works.
Well, 12^0 = 1, and 1 is a divisor of 3,176,793. So n must equal 0.

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

Cheers,
Brent

Hi j_shreyans,

Brent brings up an interesting Number Property rule that applies to this question. Here's another...

12^N implies that we're probably dealing with an EVEN number (unless N = 0, in which 12^0 = 1). But we're told that 12^N is a divisor of 3,176,793, which is a big ODD number. EVEN numbers DO NOT divide evenly into ODD numbers, so N CANNOT be a positive number. Since we're told that N is A NON-NEGATIVE INTEGER, the only other possibility is when N = 0.

Knowing this, the rest of the math is fairly straightforward (as Brent has pointed out).

Final Answer: B

GMAT assassins aren't born, they're made,
Rich