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GRE Prep Club Team Member
Joined: 20 Feb 2017
Posts: 2506
Given Kudos: 1055
GPA: 3.39
If n is a non-negative integer such that 12^n is a divisor of 3,176,79
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15 Apr 2021, 00:52
15 Apr 2021, 00:52
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Question Stats:
60% (01:28) correct
40% (03:38) wrong based on 5 sessions
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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
A. -11
B. -1
C. 0
D. 1
E. 11
If n is a non-negative integer such that 12^n is a divisor of 3,176,79
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15 Apr 2021, 02:33
15 Apr 2021, 02:33
1
Quote:
\(12^n\) is a divisor of 3,176,793
Forget about n. Can 12 be a divisor of the given number? If yes, then the number must be divisible of 3 and 4. But since the unit digit is not even an even number, the given number cannot be divisible by 4, let alone 12. So, n can only be 0.
Quote:
what is the value of \(n^{12}-12^n\)?
Plugin n = 0. The answer is -1.
Hence, B is the correct answer.
Retired Moderator
Joined: 10 Apr 2015
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Re: If n is a non-negative integer such that 12^n is a divisor of 3,176,79
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15 Apr 2021, 06:13
15 Apr 2021, 06:13
1
GeminiHeat 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
A. -11
B. -1
C. 0
D. 1
E. 11
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
n^12 - 12^n = 0^12 - 12^0 = 0 - 1
= -1
Answer: B
Cheers,
Brent
