NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 19:16 It is currently 24 Apr 2024, 19:16
Decision Tracker
My Rewards
New posts
New comers' posts

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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

For positive integers A and x, A^3 = 48x Find the least value of x

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [1]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
For positive integers A and x, A^3 = 48x Find the least value of x [#permalink] New post   29 May 2020, 08:43
1
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

25% (medium)

Question Stats:

74% (01:17) correct 26% (01:56) wrong based on 76 sessions
Hide Show timer Statistics
For positive integers A and x, \(A^3 = 48x\)

Find the least value of x

A) 4
B) 9
C) 36
D) 48
E) \(48^2\)

ShowHide Answer
Official Answer
C
User avatar
L
EgmatQuantExpert
e-GMAT Representative
Joined: 04 Jan 2015
Posts: 3726
Own Kudos [?]: 16832 [1]
Given Kudos: 165
Send PM
For positive integers A and x, A^3 = 48x Find the least value of x [#permalink] New post   Updated on: 29 May 2020, 09:21
1
Bookmarks
Expert Reply

Solution



Given
In this question, we are given that
    • For positive integers A and x, \(A^3 = 48x\)

To find
We need to determine
    • The least value of x

Approach and Working out
\(48 = 2^4 * 3^1\)
Hence, if 48x is a perfect cube, x must have at least \(2^2\) and \(3^2\) (so that the powers of 2 and 3 becomes a multiple of 3)
    • Therefore, least value of x = \(2^2 * 3^2 = 36\)

Thus, option C is the correct answer.

Correct Answer: Option C

Originally posted by EgmatQuantExpert on 29 May 2020, 09:09.
Last edited by EgmatQuantExpert on 29 May 2020, 09:21, edited 1 time in total.
User avatar
L
Archit3110
GMAT Club Legend
GMAT Club Legend
Joined: 18 Aug 2017
Status:You learn more from failure than from success.
Posts: 8018
Own Kudos [?]: 4096 [0]
Given Kudos: 242
Location: India
Concentration: Sustainability, Marketing
GMAT Focus 1:
545 Q79 V79 DI73
GPA: 4
WE:Marketing (Energy and Utilities)
Send PM
GMAT ToolKit User CAT Tests
Re: For positive integers A and x, A^3 = 48x Find the least value of x [#permalink] New post   29 May 2020, 09:17
GMATinsight wrote:
For positive integers A and x, \(A^3 = 48x\)

Find the least value of x

A) 4
B) 9
C) 36
D) 48
E) \(48^2\)



48 ; 2^4*3
for A^3 to be a +ve integer ; value of x has to be 2^2*3^2 ; 36
OPTION C
User avatar
L
GMATinsight
GMAT Club Legend
GMAT Club Legend
Joined: 08 Jul 2010
Status:GMAT/GRE Tutor l Admission Consultant l On-Demand Course creator
Posts: 5957
Own Kudos [?]: 13387 [2]
Given Kudos: 124
Location: India
GMAT: QUANT+DI EXPERT
Schools: IIM (A) ISB '24
GMAT 1: 750 Q51 V41
WE:Education (Education)
Send PM
Reviews Badge
Re: For positive integers A and x, A^3 = 48x Find the least value of x [#permalink] New post   31 May 2020, 22:28
2
Bookmarks
Expert Reply
GMATinsight wrote:
For positive integers A and x, \(A^3 = 48x\)

Find the least value of x

A) 4
B) 9
C) 36
D) 48
E) \(48^2\)

Source: https://www.GMATinsight.com


OFFICIAL EXPLANATION:



CONCEPT: A perfect cube \(A^3\) must have all exponents of its unique prime factors a multiple of 3


\(A^3 = 48x = 2^4*3*x\)

the exponent of 2 is 4 which needs to be increased by 2 to become 6 i.e. multiple of 3 i.e. x must have \(2^2\)
the exponent of 3 is 1 which needs to be increased by 2 to become 3 i.e. multiple of 3 i.e. x must have \(3^2\)

i.e. \(x_{min} = 2^2*3^2\) to make the \(48 x\) a perfect cube

i.e. \(x_{min} = 36\)

Answer: Option C
GMAT Club Bot
gmatclubot
Re: For positive integers A and x, A^3 = 48x Find the least value of x [#permalink]
31 May 2020, 22:28
Moderators:
Bunuel
Math Expert
92900 posts
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions