It is currently 17 Nov 2018, 04:40
My Tests

Close

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
Your Progress

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 k is a multiple of 24 but not a multiple of 16, which of

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [0], given: 375

CAT Tests
If k is a multiple of 24 but not a multiple of 16, which of [#permalink] New post 12 Aug 2018, 15:36
Expert's post
00:00

Question Stats:

75% (01:13) correct 25% (00:00) wrong based on 4 sessions
If k is a multiple of 24 but not a multiple of 16, which of the following cannot be an integer?

(A) \(\frac{k}{8}\)
(B) \(\frac{k}{9}\)
(C) \(\frac{k}{32}\)
(D) \(\frac{k}{36}\)
(E) \(\frac{k}{81}\)
[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

1 KUDOS received
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 07 Jun 2014
Posts: 4710
GRE 1: Q167 V156
WE: Business Development (Energy and Utilities)
Followers: 91

Kudos [?]: 1612 [1] , given: 375

CAT Tests
Re: If k is a multiple of 24 but not a multiple of 16, which of [#permalink] New post 15 Aug 2018, 08:12
1
This post received
KUDOS
Expert's post
Explanation

If k is a multiple of 24, it contains the prime factors of 24: 2, 2, 2, and 3. (It could also contain other prime factors, but the only ones for certain are the prime factors contained in 24.)

If k were a multiple of 16, it would contain the prime factors of 16: 2, 2, 2, and 2.

Thus, if k is a multiple of 24 but not of 16, k must contain 2, 2, and 2, but not a fourth 2 (otherwise, it would be a multiple of 16).

Thus: k definitely has 2, 2, 2, and 3. It could have any other prime factors (including more 3’s) except for more 2’s.

An answer choice in which the denominator contains more than three 2’s would guarantee a non-integer result. Only choice (C) works. Since k has fewer 2’s than 32, can never be an integer.

Alternatively, list multiples of 24 for k: 24, 48, 72, 96, 120, 144, 168, etc. Then, eliminate multiples of 16 from this list: 24, , 72, , 120, , 168, etc.

A pattern emerges: k = (an odd integer) \(\times 24\):

(A) can be an integer, for example when \(k = 24.\)

(B) can be an integer, for example when \(k = 72.\)

(C) is correct by process of elimination.

(D) can be an integer, for example when \(k = 72.\)

(E) can be an integer, for example when \(k = 81 \times 24.\)
_________________

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

Try our free Online GRE Test

Re: If k is a multiple of 24 but not a multiple of 16, which of   [#permalink] 15 Aug 2018, 08:12
Display posts from previous: Sort by

If k is a multiple of 24 but not a multiple of 16, which of

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GRE Prep Club Forum Home| About| Terms and Conditions and Privacy Policy| GRE Prep Club Rules| Contact

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®.