 It is currently 24 Mar 2019, 13:09 ### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here. # If n is an integer and n3 is divisible by 24, what is the la  Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

If n is an integer and n3 is divisible by 24, what is the la [#permalink]
Expert's post 00:00

Question Stats: 33% (01:17) correct 66% (01:01) wrong based on 9 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

_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test

Intern Joined: 02 Aug 2018
Posts: 1
Followers: 0

Kudos [?]: 1 , given: 1

Re: If n is an integer and n3 is divisible by 24, what is the la [#permalink]
why 6 but not 12?
GRE Prep Club Legend  Joined: 07 Jun 2014
Posts: 4857
GRE 1: Q167 V156 WE: Business Development (Energy and Utilities)
Followers: 105

Kudos [?]: 1783 , given: 397

Re: If n is an integer and n3 is divisible by 24, what is the la [#permalink]
Expert's post
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 $$2 \times 3 = 6$$.
_________________

Sandy
If you found this post useful, please let me know by pressing the Kudos Button

Try our free Online GRE Test Re: If n is an integer and n3 is divisible by 24, what is the la   [#permalink] 17 Aug 2018, 16:08
Display posts from previous: Sort by

# If n is an integer and n3 is divisible by 24, what is the la  Question banks Downloads My Bookmarks Reviews Important topics  Powered by phpBB © phpBB Group Kindly note that the GRE® test is a registered trademark of the Educational Testing Service®, and this site has neither been reviewed nor endorsed by ETS®.