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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 [#permalink] New post 18 Sep 2010, 11:48
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 29 Mar 2013, 01:41, edited 2 times in total.
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Re: Divisor of 3,176,793 [#permalink] New post 18 Sep 2010, 12:00
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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"
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Re: Divisor of 3,176,793 [#permalink] New post 18 Sep 2010, 12:06
Precisely, for this reason, I have posted this question here.
I am unclear is 0 should be considered as divisor.
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Re: Divisor of 3,176,793 [#permalink] New post 18 Sep 2010, 12:10
Orange08 wrote:
Precisely, for this reason, I have posted this question here.
I am unclear is 0 should be considered as divisor.


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
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Last edited by shrouded1 on 18 Sep 2010, 15:50, edited 1 time in total.
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Re: Divisor of 3,176,793 [#permalink] New post 18 Sep 2010, 19:11
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Orange08 wrote:
If n is a non-negative integer such that 12n 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


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.
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Exponents [#permalink] New post 25 Feb 2011, 07:25
Can someone help me with this?

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n ?
a) - 11
b) - 1
c) 0
d) 1
e) 11
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Re: Exponents [#permalink] New post 25 Feb 2011, 07:56
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Merging similar topics.

rosgmat wrote:
Can someone help me with this?

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n ?
a) - 11
b) - 1
c) 0
d) 1
e) 11


rosgmat, please format the questions properly.
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Re: Divisor of 3,176,793 [#permalink] New post 25 Feb 2011, 08:56
Nice question!

Bunuel's approach is very good.

Thanks!
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Re: Divisor of 3,176,793 [#permalink] New post 25 Feb 2011, 21:22
Thanks Bunnel's for this in depth explanation!!
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Re: Exponents [#permalink] New post 27 Feb 2011, 12:42
sorry for that, I didn;t notice it. And thanks for your help!

Bunuel wrote:
Merging similar topics.

rosgmat wrote:
Can someone help me with this?

If n is a non-negative integer such that 12n is a divisor of 3,176,793, what is the value of n12 – 12n ?
a) - 11
b) - 1
c) 0
d) 1
e) 11


rosgmat, please format the questions properly.
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new [#permalink] New post 15 Feb 2012, 21:00
-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.
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Re: If n is a non-negative integer such that 12n is a divisor of [#permalink] New post 28 Mar 2013, 21:12
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nave81 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


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.
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Re: If n is a non-negative integer such that 12n is a divisor of [#permalink] New post 28 Mar 2013, 23:24
nave81 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



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
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Re: Divisor of 3,176,793 [#permalink] New post 05 Jul 2013, 08:08
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?
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Re: Divisor of 3,176,793 [#permalink] New post 05 Jul 2013, 08:17
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fozzzy wrote:
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?


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
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Re: If n is a non-negative integer such that 12^n is a divisor [#permalink] New post 05 Jul 2014, 16:43
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Re: If n is a non-negative integer such that 12^n is a divisor   [#permalink] 05 Jul 2014, 16:43
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