GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
close

It is currently 18 Jan 2020, 20:13
Register
GMAT Club Tests
Decision Tracker
My Rewards
New comers' posts
New posts
Unanswered

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
CLICK HERE TO HIDE/SHOW EVENTS

If x and y are positive integers, and 4x^2=3y, then which of the follo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
First unread post
Print view
 
  Sort by Date Sort by Kudos  
Search for:
 
PREVIOUS TOPIC
NEXT TOPIC
Author Message
TAGS:

Hide Tags

Find Similar Topics 
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 60480
CAT Tests
Top Member of the Month
If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

Show Tags

New post 01 Nov 2019, 05:39
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

46% (02:03) correct 54% (02:01) wrong based on 82 sessions

HideShow timer Statistics

If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
Spoiler: OA

_________________
New to the GMAT CLUB Forum?
Posting Rules: QUANTITATIVE | VERBAL. Guides and Resources: QUANTITATIVE | VERBAL | Ultimate GMAT Quantitative Megathread | All You Need for Quant

Questions' Banks and Collection:
PS: Standard deviation | Tough Problem Solving Questions With Solutions | Probability and Combinations Questions With Solutions | Tough and tricky exponents and roots questions | 12 Easy Pieces (or not?) | Bakers' Dozen | Algebra set | Mixed Questions | Fresh Meat
DS: DS Standard deviation | Inequalities | 700+ GMAT Data Sufficiency Questions With Explanations | Tough and tricky exponents and roots questions | The Discreet Charm of the DS | Devil's Dozen!!! | Number Properties set | New DS set
MIXED: GMAT Club's Complete Questions' Bank | SEVEN SAMURAI OF 2012 | Tricky questions from previous years. | Special Questions' Directory | Best Of The Best Of 2017 | The Best Of Quant of 2016 | 20 hardest and 20 best questions of 2015 | 15 best topics of 2015 | Seven Samurai of 2012 | GMAT Probability Questions

What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
Signature Read More
Intern
Intern
User avatar
B
Joined: 21 Sep 2016
Posts: 21
Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

Show Tags

New post 01 Nov 2019, 06:28
1
Since x and y are positive integers therefore,

y = 12*n^2
And
x = 3n
Where n is a positive integer.

This implies that x^2,y^2 and xy are multiple of 9 for sure.

Therefore, answer is (E).

Posted from my mobile device
VP
VP
avatar
V
Joined: 20 Jul 2017
Posts: 1233
Location: India
Concentration: Entrepreneurship, Marketing
WE: Education (Education)
Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

Show Tags

New post 01 Nov 2019, 07:04
1
Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions


\(4x^2=3y\)
--> \(x^2 = 3y/4\)
--> \(x\) is a multiple of 3 & \(y\) is also a multiple of 3 (only then \(x\) will be a positive integer)
--> \(x = 3p\), \(y = 3q\), for any positive integers \(p\) & \(q\)
--> \(x^2 = 9*p^2\) --> I is true
\(y^2 = 9*q^2\) --> II is true
\(x*y = 3p*3q = 9*p*q\) --> III is also true

IMO Option E
Board of Directors
User avatar
D
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4856
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User
Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

Show Tags

New post 01 Nov 2019, 08:02
1
Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions


Let, \(4x^2=3y = 36\)

So, \(x^2 = 9\) Or, \(x = +3 , -3\)

And, \(y = 12\)

(I) \(\frac{x^2}{9}\) = \(\frac{9}{9} = 1\)
(II) \(\frac{y^2}{9} = 12*12/9 = 16\)
(III) \(xy/9 = 12*3/9 = 4\)

Thus, Answer must be (E) I, II and III
_________________
Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )
Signature Read More
GMAT Club Legend
GMAT Club Legend
User avatar
V
Joined: 18 Aug 2017
Posts: 5693
Location: India
Concentration: Sustainability, Marketing
GPA: 4
WE: Marketing (Energy and Utilities)
GMAT ToolKit User Premium Member
Re: If x and y are positive integers, and 4x^2=3y, then which of the follo  [#permalink]

Show Tags

New post 01 Nov 2019, 08:08
given
4*x^2/3y =1
x^2 has to be 3 ; and y = 12
4*3^2/3*12 = 1
in that case all given conditions are valid

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

IMO E

Bunuel wrote:
If x and y are positive integers, and \(4x^2=3y\), then which of the following must be a multiple of 9?

I. \(x^2\)
II. \(y^2\)
III. \(xy\)

A. I only
B. II only
C. III only
D. I and II only
E. I, II and III


Are You Up For the Challenge: 700 Level Questions: 700 Level Questions
GMAT Club Bot
Re: If x and y are positive integers, and 4x^2=3y, then which of the follo   [#permalink] 01 Nov 2019, 08:08
Print view
First unread post
Display posts from previous: Sort by

If x and y are positive integers, and 4x^2=3y, then which of the follo

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  

Moderators: chetan2u, VeritasKarishma, Gladiator59, Bunuel, generis

Search for:
PREVIOUS TOPIC
NEXT TOPIC





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