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If n is a non-negative integer such that 6^n is a divisor of

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If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post Updated on: 06 Oct 2009, 14:24
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Difficulty:

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Question Stats:

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If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11
Spoiler: OA

Originally posted by yangsta8 on 06 Oct 2009, 02:46.
Last edited by yangsta8 on 06 Oct 2009, 14:24, edited 2 times in total.
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If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 06 Oct 2009, 14:15
8
6
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


6^n is a divisor of 5,178,791 --> as far as n is non-negative integer (given) the only value of n is 0 (5,178,791 is not even, thus it can not be divided by 6 in any power but 0)

n = 0

0^6 - 6^0 = 0 - 1 = -1

Answer: B.
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 19 Jul 2014, 01:10
1
yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


Let us say that n = 0 then 6^0 = 1 which is a divisor of any number.

Now the question is asking the value of 0^6 - 6^0 = -1
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 14 Dec 2015, 02:47
Dear Bunuel/Others

When its 'non-negative' in the question ; dosent this mean '0' or other positive values?
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 14 Dec 2015, 03:51
seemachandran wrote:
Dear Bunuel/Others

When its 'non-negative' in the question ; dosent this mean '0' or other positive values?


Yes, non-negative numbers include 0 and positive numbers.
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 31 Aug 2017, 09:25
yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


Since 5,178,791 is odd, it is not divisible by 6^n (which is an even number), except when n = 0.

Therefore, 0^6 - 6^0 = 0 - 1 = -1.

Answer: B
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 04 Oct 2017, 19:31
So the most important thing is to determine divisibility by 6.
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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 07 Nov 2018, 23:54
JeffTargetTestPrep wrote:
yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11


Since 5,178,791 is odd, it is not divisible by 6^n (which is an even number), except when n = 0.

Therefore, 0^6 - 6^0 = 0 - 1 = -1.

Answer: B


if this question had asked for the remainder, how would we calculate it?

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Re: If n is a non-negative integer such that 6^n is a divisor of  [#permalink]

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New post 08 Jul 2020, 07:39
yangsta8 wrote:
If n is a non-negative integer such that 6^n is a divisor of 5,178,791, what is the value of n^6 – 6^n?

A. - 11
B. - 1
C. 0
D. 1
E. 11



Hello Bunuel, for this question, shouldn't it say factor instead of divisor ?

When you say divisor, does it not mean evenly divisible / divisible with a remainder ? I assumed since it said divisor, it probably leaves a remainder and hence finding a value of n with this process takes way too long.

Question is easy if it just meant 6^n is a factor of the number provided. Could you confirm if my above statement is correct ?
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Re: If n is a non-negative integer such that 6^n is a divisor of   [#permalink] 08 Jul 2020, 07:39
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