NEW HERE? LEARN MORE
closeclose
Last visit was: 24 Apr 2024, 10:09 It is currently 24 Apr 2024, 10:09
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

If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and

SORT BY:
Date
Kudos
Tags:
Find Similar Topics 
Show Tags
Hide Tags
User avatar
L
Bunuel
Math Expert
Joined: 02 Sep 2009
Posts: 92902
Own Kudos [?]: 618773 [8]
Given Kudos: 81587
Send PM
CAT Tests Forum Quiz Mode
If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink] New post   06 Jul 2020, 04:51
8
Bookmarks
Expert Reply
00:00
A
B
C
D
E

Difficulty:

15% (low)

Question Stats:

85% (02:29) correct 15% (02:39) wrong based on 180 sessions
Hide Show timer Statistics
If \(\sqrt[3]{90x}\) and \(\sqrt{\frac{y}{75}}\) are positive integers, and both x and y are integers, what is the least possible value of \(xy\) ?

A. 20500
B. 21500
C. 22500
D. 23500
E. 24500
ShowHide Answer
Official Answer
C
User avatar
L
yashikaaggarwal
Senior Moderator - Masters Forum
Joined: 19 Jan 2020
Posts: 3137
Own Kudos [?]: 2769 [1]
Given Kudos: 1510
Location: India
Schools: Cranfield (A) Warwick MiM "23 (M)
GPA: 4
WE:Analyst (Internet and New Media)
Send PM
Re: If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink] New post   06 Jul 2020, 04:57
1
Kudos
³√90x and √y/75 are positive integers

Least value of ³√90x = (3*3*2*5*x)^1/3
X has to be 3*2*2*5*5 for ³√90x to be an integer.

Value of X = 300
And Y has to be 75

Value of xy = 300*75 = 22500

Answer should be C

Posted from my mobile device
User avatar
L
rajatchopra1994
VP
VP
Joined: 16 Feb 2015
Posts: 1080
Own Kudos [?]: 1024 [2]
Given Kudos: 30
Location: United States
Send PM
Re: If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink] New post   06 Jul 2020, 05:18
1
Kudos
1
Bookmarks
(90x)^1/3 : (2*3*3*5x)^1/3 : x has to be : 4x3x25 = 300 for integer value
√y/75 : y= 75 for integer value

xy least value : 300 x 75
= 22500

IMO-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
If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink] New post   06 Jul 2020, 05:41
2
Bookmarks
Expert Reply
Bunuel wrote:
If \(\sqrt[3]{90x}\) and \(\sqrt{\frac{y}{75}}\) are positive integers, and both x and y are integers, what is the least possible value of \(xy\) ?

A. 20500
B. 21500
C. 22500
D. 23500
E. 24500


\(\sqrt[3]{90x}\) is an Integer i.e. 90x must be a PERFECT CUBE

CONCEPT: For a number to be a perfect cube, all prime factors must have exponents which are multiples of 3


i.e. \(90x = 2*3^2*5*x\)

ie.. x must be minimum \(2^2*3*5^2\)


\(\sqrt{\frac{y}{75}}\) is an Integer i.e. \(\frac{y}{75}\) must be a PERFECT SQUARE

CONCEPT: For a number to be a perfect square, all prime factors must have exponents which are multiples of 2


i.e. \(\frac{y}{75} = 1\)

ie.. y must be minimum \(75\)

\(x*y_{min} = 2^2*3*5^2*75 = 22500\)



Answer: Option C
User avatar
bumpbot
Non-Human User
Joined: 09 Sep 2013
Posts: 32647
Own Kudos [?]: 821 [0]
Given Kudos: 0
Send PM
Re: If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink] New post   06 Apr 2022, 06:54
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
GMAT Club Bot
gmatclubot
Re: If (90x)^(1/3) and (y/75)^(1/2) are positive integers, and both x and [#permalink]
06 Apr 2022, 06:54
Moderators:
Bunuel
Math Expert
92902 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