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

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Senior Manager
Joined: 21 Jun 2006
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If n is a non-negative integer such that 12^n is a divisor [#permalink]  16 Jun 2007, 20:00
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 ?
Director
Joined: 26 Feb 2006
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Re: numbers problem [#permalink]  16 Jun 2007, 20:32
ArvGMAT 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 ?

the question is wrong because n is a non-negative integer, 3,176,793 is an odd integer/number and 12^n is an even integer. no matter the value of n, 12^n can not be a divisor of 3,176,793.
Senior Manager
Joined: 21 Jun 2006
Posts: 287
Followers: 1

Kudos [?]: 34 [0], given: 0

ArvGMAT 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 ?

the question is wrong because n is a non-negative integer, 3,176,793 is an odd integer/number and 12^n is an even integer. no matter the value of n, 12^n can not be a divisor of 3,176,793.

First of all, Question is Right

n^12-12^n = -1

only number that satisfies this is n = 0 (which is non-negative integer)

12^0 = 1 which divides the large number
Director
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Re: numbers problem [#permalink]  16 Jun 2007, 20:56
Himalayan wrote:
ArvGMAT 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 ?

the question is wrong because n is a non-negative integer, 3,176,793 is an odd integer/number and 12^n is an even integer. no matter the value of n, 12^n can not be a divisor of 3,176,793.

Nice catch himalayan..
Director
Joined: 26 Feb 2006
Posts: 905
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Kudos [?]: 59 [0], given: 0

ArvGMAT wrote:
ArvGMAT 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 ?

the question is wrong because n is a non-negative integer, 3,176,793 is an odd integer/number and 12^n is an even integer. no matter the value of n, 12^n can not be a divisor of 3,176,793.

First of all, Question is Right

n^12-12^n = -1

only number that satisfies this is n = 0 (which is non-negative integer)

12^0 = 1 which divides the large number

interesting and make sense.

if you include the answer choices, would be much easier.
Senior Manager
Joined: 21 Jun 2006
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Yeah... there was a reason i did not include it. It becomes obvious if it were included.
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