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
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 integerj_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
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
