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# If k is a non-negative integer, and 6^k is a factor of 345,136 what is

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Joined: 02 Sep 2009
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If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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15 Nov 2016, 02:02
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If k is a non-negative integer, and 6^k is a factor of 345,136 what is 6^k−k?

A. −6
B. −1
C. 0
D. 1
E. 6

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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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15 Nov 2016, 02:06
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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15 Nov 2016, 02:26
We need to find the value for 6^k−k, looking at the options we can try value of 1 and 0 for K and find the only value of K = 0 would suffice for option D.
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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15 Nov 2016, 03:43
Bunuel wrote:
If k is a non-negative integer, and 6^k is a factor of 345,136 what is 6^k−k?

A. −6
B. −1
C. 0
D. 1
E. 6

IMO D

6^k is a factor of 345,136
345,136= 2^4 * 11 * 37 * 53
if 6^k has to be a factor of 345,136, k=0 (no other value of k makes 6^k a factor of 345,136)
6^k-k= 6^0-0 = 1
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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15 Nov 2016, 09:32
2
Bunuel wrote:
If k is a non-negative integer, and 6^k is a factor of 345,136 what is 6^k−k?

A. −6
B. −1
C. 0
D. 1
E. 6

k can be 0/1/2/3...

Given: 6^k is a factor of 345,136.
Note that 6^k is given to be a factor. It doesn't say it is that factor for which k takes the maximum value etc. So k can obviously take value 0 because 6^0 = 1 which is a factor of all integers. This will be the only value of k since it is a PS question.

Put k = 0: 6^k - k = 1 - 0 = 1

If you want to double check your logic, just see that 345,136 is not divisible by 6 at all. It is even but not divisible by 3 (use divisibility rule for 3).
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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28 Feb 2017, 06:24
Any non-negative number substituted for k would always result in 6^0 =1.
ex. 6^(0-0), 6^(1-1), 6^(36-36), 6^(729-729), etc. all = 6^0

Therefore, the number 345,136 can be completely ignored with no algebra or calculations of any sort necessary. This is GMAT's attempt as misdirection.

So the answer can only be D.

Please correct me if I'm wrong!
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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02 Mar 2017, 17:37
Bunuel wrote:
If k is a non-negative integer, and 6^k is a factor of 345,136 what is 6^k−k?

A. −6
B. −1
C. 0
D. 1
E. 6

Since 6^k is a factor of 345,136, 6^k must divide into 345,136. Remember a number is divisible by 6 if it’s divisible by both 3 and 2, and a number is divisible by 3 if the sum of the digits of that number is a multiple of 3. Let’s add up the digits of 345,136.

3 + 4 + 5 + 1 + 3 + 6 = 22, which IS NOT a multiple of 3; 345,136 can’t be a multiple of 6^k for any positive integer value of k. So k must equal zero and 6^0 - 0 = 1 - 0 = 1.

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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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02 Jul 2017, 22:10
Just did attention that 345,136 is not divisible by 3, even though should be because 6=3*2

So, only option is that k=0 meaning 6^0-0=1

D
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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12 Jan 2019, 14:15
Am I missing something here or is anything like $$x^{y-y}$$ always = 1
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Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is  [#permalink]

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14 Jan 2019, 08:47
1
ghnlrug wrote:
Am I missing something here or is anything like $$x^{y-y}$$ always = 1

as we dont have a bracket in the term I think its $$x^{y}-y$$
Re: If k is a non-negative integer, and 6^k is a factor of 345,136 what is   [#permalink] 14 Jan 2019, 08:47
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