If n is a non-negative integer such that 12^n is a divisor

Question

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

Bunuel · Accepted Answer

If the answer is B then I think it should be  12^n  instead of  12n

So the question would be:
 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?

3,176,793 is an odd number. The only way it to be a multiple of  12^n  (even number in integer power) is when  n=0 , in this case  12^n=12^0=1  and 1 is a factor of every integer.

Then  n^{12}-12^n=0^{12}-12^0=-1 .

Answer: B.

Hope it helps.

BrentGMATPrepNow · Answer

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

shrouded1 · Answer

3176793 is odd
12n is even
How can 12n be a divisor ?

The only answer I can think is n=0 which means -1

But I don't think you can count 0 as a "divisor"

Orange08 · Answer

Precisely, for this reason, I have posted this question here.
I am unclear is 0 should be considered as divisor.

shrouded1 · Answer

What's the source of the question ?

I am sure the only possible answer is -1, just not sure about the validity of the question

miguelmick · Answer

Nice question!

Bunuel's approach is very good.

Thanks!

mukgera · Answer

Thanks Bunnel's for this in depth explanation!!

calreg11 · Answer

-12^n will always be an even number because it will be a multiple of 12. however 3,176,793 is odd and there is no case when a positive number of n would be a factor of 3,176,793. Only number that would match is when n is zero.

mau5 · Answer

n is any integer  >=0 . Also,  12^n  is a divisor of the given number.  12^0  = 1 is a divisor of the given number. Replacing n = 0 in the given expression, we have 0^12 - 12^0 = -1.

Note that for any other value of n, there will be a factor of 2 in  12^n . But the given number is odd and thus, has no factor of 2. Therefore, any other power of 12, can not be a divisor of the given number.

B.

Zarrolou · Answer

The only way that  12^n  can be a divisor of 3 is if  n=0, 12^0=1 . So  n=0 
0^(12) - 12^0=0-1=-1

B

fozzzy · Answer

3,176,793 is an odd number. The only way it to be a multiple of  12^n  (even number in integer power) is when  n=0 , in this case  12^n=12^0=1  and 1 is a factor of every integer.

Can you elaborate on this.. The sum of the digits add up to 9 the only example I thought of 12^2 = 144

does sum of the digits have any relation to this question or it isn't related?

Bunuel · Answer

No, the sum of the digits is not relevant for this question. 3,176,793 is an odd number. An odd number cannot be a multiple of any even number, and 12^n is even for any positive integer n. Therefore n cannot be positive which means that n can only be 0. Hope it's clear. Similar question to practice: new-tough-and-tricky-exponents-and-roots-questions-125956-40.html#p1029223

Suryangshu · Answer

0^anything=0

anything^0=1

Therefore the only value for n=0.

Answer : 0-1=-1(B)

EMPOWERgmatRichC · Answer

Hi All,

This question is built around a number of interesting Number Property rules. Here's how you can use those rules to avoid doing a lot of 'math' on this question.

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:

(0^12) - (12^0) = 0 - 1 = -1

Final Answer:  B

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

billionaire999 · Answer

It does help,
But I wonder, it could still be a divisor and have a remainder correct? Hence should be 12^6?
6^12-12^6 
Please help

Posted from my mobile device

EMPOWERgmatRichC · Answer

Hi billionaire999,

By definition, a 'divisor' divides evenly into a larger number (meaning that there is NO remainder).

For example, both 2 and 4 are divisors of 8 (since 8/2 = 4r0 and 8/4 = 2r0) but 5 is not a divisor of 8 (since 8/5 = 1r3). 
 
GMAT assassins aren't born, they're made,
Rich

nivivacious · Answer

Given: n is non negative so it could be 0 and any positive number
12 = 2x2x3
3176793 is not divisible by 2
hence 12^n to be a divisor of 3176793 has to mean n =0
then 0^12-12^0 
0-1 = -1
Hence B

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If n is a non-negative integer such that 12^n is a divisor

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If n is a non-negative integer such that 12^n is a divisor

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