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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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Joined: 12 Sep 2015
Posts: 1842

Kudos [?]: 2600 [0], given: 362

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
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Difficulty:

35% (medium)

Question Stats:

73% (01:10) correct 27% (02:03) wrong based on 124 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

[Reveal] Spoiler:
[Reveal] Spoiler: OA

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Brent Hanneson – Founder of gmatprepnow.com

Kudos [?]: 2600 [0], given: 362

Manager
Joined: 04 Jan 2014
Posts: 120

Kudos [?]: 39 [1], given: 15

GMAT 1: 660 Q48 V32
GMAT 2: 630 Q48 V28
GMAT 3: 680 Q48 V35
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
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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

Kudos [?]: 39 [1], given: 15

Math Expert
Joined: 02 Sep 2009
Posts: 42247

Kudos [?]: 132677 [0], given: 12331

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

[Reveal] Spoiler:

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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Kudos [?]: 132677 [0], given: 12331

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Posts: 15690

Kudos [?]: 282 [0], given: 0

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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Kudos [?]: 282 [0], given: 0

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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