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If n is an integer and n3 is divisible by 24, what is the la

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GMAT Club Legend
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If n is an integer and n3 is divisible by 24, what is the la [#permalink] New post 12 Aug 2018, 15:46
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Question Stats:

37% (01:17) correct 62% (01:06) wrong based on 8 sessions
If n is an integer and \(n^3\) is divisible by 24, what is the largest number that must be a factor of n?

(A) 1
(B) 2
(C) 6
(D) 8
(E) 12
[Reveal] Spoiler: OA

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Re: If n is an integer and n3 is divisible by 24, what is the la [#permalink] New post 13 Aug 2018, 00:11
why 6 but not 12?
GMAT Club Legend
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Joined: 07 Jun 2014
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Re: If n is an integer and n3 is divisible by 24, what is the la [#permalink] New post 17 Aug 2018, 16:08
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Explanation

Start by considering the relationship between \(n\) and \(n^3\). Because \(n\) is an integer, for every prime factor \(n\) has, \(n^3\) must have three of them.

Thus, \(n^3\) must have prime numbers in multiples of 3. If \(n^3\) has one prime factor of 3, it must actually have two more, because \(n^3\)’s prime factors can only
come in triples.

The question says that \(n^3\) is divisible by 24, so \(n^3\)’s prime factors must include at least three 2’s and a 3.

But since \(n^3\) is a cube, it must contain at least three 3’s. Therefore, n must contain at least one 2 and one 3, or \(2 \times 3 = 6\).
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Re: If n is an integer and n3 is divisible by 24, what is the la   [#permalink] 17 Aug 2018, 16:08
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