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# If n is the greatest integer such that 6^n is a divisor of 86,420, the

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CEO
Joined: 12 Sep 2015
Posts: 2561
If n is the greatest integer such that 6^n is a divisor of 86,420, the [#permalink]

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26 Aug 2016, 12:51
Top Contributor
3
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Difficulty:

35% (medium)

Question Stats:

73% (01:05) correct 27% (01:47) wrong based on 150 sessions

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If n is the greatest integer such that $$6^n$$is a divisor of 86,420, then $$2^n - n^2$$ =
A) 0
B) 1
C) 7
D) 28
E) 79

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Brent Hanneson – Founder of gmatprepnow.com

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Joined: 04 Jan 2014
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GMAT 1: 660 Q48 V32
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Re: If n is the greatest integer such that 6^n is a divisor of 86,420, the [#permalink]

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26 Aug 2016, 19:37
1
2
86420 is divisible by 2 but not by 3. There is only one possibility for 6^n to be a factor of 86420:

If n = 0, 6^n = 6^0 = 1
1 is a factor of every integer.

Plugging n = 0 in the formula:

2^n - n^2
= 2^0 - 0^2
= 1 - 0
= 1

Math Expert
Joined: 02 Sep 2009
Posts: 46194
Re: If n is the greatest integer such that 6^n is a divisor of 86,420, the [#permalink]

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27 Aug 2016, 02:17
GMATPrepNow wrote:
If n is the greatest integer such that $$6^n$$is a divisor of 86,420, then $$2^n - n^2$$ =
A) 0
B) 1
C) 7
D) 28
E) 79

Similar question to practice: if-n-is-a-non-negative-integer-such-that-6-n-is-a-divisor-of-84885.html
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Posts: 7006
Re: If n is the greatest integer such that 6^n is a divisor of 86,420, the [#permalink]

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27 Sep 2017, 07:05
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Re: If n is the greatest integer such that 6^n is a divisor of 86,420, the   [#permalink] 27 Sep 2017, 07:05
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