Find all School-related info fast with the new School-Specific MBA Forum

It is currently 26 Sep 2016, 07:18
GMAT Club 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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

2 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 207 [2] , given: 32

If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 15 Oct 2012, 04:17
2
This post received
KUDOS
11
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

66% (02:47) correct 34% (02:23) wrong based on 165 sessions

HideShow timer Statistics

If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 =?

A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34859
Followers: 6483

Kudos [?]: 82665 [3] , given: 10114

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 15 Oct 2012, 04:22
3
This post received
KUDOS
Expert's post
Jp27 wrote:
If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 =?

A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2


\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).

Answer: D.

Hope it's clear.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Senior Manager
Senior Manager
avatar
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 207 [0], given: 32

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 15 Oct 2012, 04:38
Bunuel wrote:
Jp27 wrote:
If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 =?

A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2


\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).

Answer: D.

Hope it's clear.


Hi Bunuel - thanks for your swift response.

Where I can get similar question like these for practice?

I have done the roots and equation set in your signature, are there any other sets that I can use for practice? Sincere thanks!

cheers
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34859
Followers: 6483

Kudos [?]: 82665 [1] , given: 10114

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 15 Oct 2012, 04:44
1
This post received
KUDOS
Expert's post
Jp27 wrote:
Bunuel wrote:
Jp27 wrote:
If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 =?

A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2


\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).

Answer: D.

Hope it's clear.


Hi Bunuel - thanks for your swift response.

Where I can get similar question like these for practice?

I have done the roots and equation set in your signature, are there any other sets that I can use for practice? Sincere thanks!

cheers


Check our question banks (viewforumtags.php) for more questions.

DS algebra questions: search.php?search_id=tag&tag_id=29
PS algebra questions: search.php?search_id=tag&tag_id=50

Hope it helps.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

2 KUDOS received
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 394 [2] , given: 11

GMAT ToolKit User
Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 10 Dec 2012, 23:57
2
This post received
KUDOS
\(x^2y^2 + 3xy = 18\)
\(xy (xy + 3) = 18\)

I thought of 2 positive numbers such as \(n\) and \(n + 3\) whose product is 18 --> \(3\) and \(6\)

\(xy = 3\)
\(x^2 = 9/y^2\)

Answer: D
_________________

Impossible is nothing to God.

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 25

Kudos [?]: 394 [0], given: 11

GMAT ToolKit User
Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 18 Dec 2012, 21:45
1
This post was
BOOKMARKED
\(x^2y^2+3xy-18=0\)
\((xy)^2+3xy-18=0\)
\((xy - 3)(xy + 6)=0\)
\(xy = 3 & xy = -6\) Since x and y are positive, we choose xy = 3.

\(xy = 3\)
\(x = \frac{3}{y}\)
\(x^2 = \frac{9}{y^2}\)

Answer: D
_________________

Impossible is nothing to God.

Intern
Intern
User avatar
Joined: 11 Oct 2013
Posts: 18
Location: United Kingdom
Concentration: General Management, Leadership
GMAT 1: 490 Q32 V25
GPA: 3.9
WE: Other (Other)
Followers: 0

Kudos [?]: 19 [0], given: 34

GMAT ToolKit User
Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 16 Dec 2013, 19:21
Bunuel wrote:
Jp27 wrote:
If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 =?

A. (18-3y)/y^3
B. 18/y^2
C. 18/(y^2+3y)
D. 9/y^2
E. 36/y^2


\((xy)^2+3(xy)-18=0\) --> solving for \(xy\) --> \(xy=-6\) (not a valid solution: \(xy\) must be positive as both unknowns are positive) or \(xy=3\) --> so \(xy=3\) --> \(x=\frac{3}{y}\) --> \(x^2=\frac{9}{y^2}\).

Answer: D.

Hope it's clear.


very elegant&simple...if you spot one variable in two :wink:
like it :wink:
_________________

Good things come to those who wait… greater things come to those who get off their ass and do anything to make it happen...

Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 49 [0], given: 185

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 11 Jun 2015, 03:21
I don't understand why you can not divide by y^2 here? Pls help
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 34859
Followers: 6483

Kudos [?]: 82665 [0], given: 10114

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 11 Jun 2015, 03:36
Manager
Manager
avatar
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 49 [0], given: 185

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 11 Jun 2015, 04:34
Bunuel wrote:
noTh1ng wrote:
I don't understand why you can not divide by y^2 here? Pls help


If you divide x^2 * y^2 = 18 – 3xy by y^2 you get x^2 = 18/y^2 - 3/y = (18-3y)/y^2. We don't have (18-3y)/y^2 among answer choices, thus we need other approach.


I sometimes don't get the GMAC..

just because it's not among the answer choices doesnt make it wrong imho
Expert Post
1 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6910
Location: Pune, India
Followers: 1989

Kudos [?]: 12360 [1] , given: 221

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 11 Jun 2015, 21:45
1
This post received
KUDOS
Expert's post
noTh1ng wrote:
Bunuel wrote:
noTh1ng wrote:
I don't understand why you can not divide by y^2 here? Pls help


If you divide x^2 * y^2 = 18 – 3xy by y^2 you get x^2 = 18/y^2 - 3/y = (18-3y)/y^2. We don't have (18-3y)/y^2 among answer choices, thus we need other approach.


I sometimes don't get the GMAC..

just because it's not among the answer choices doesnt make it wrong imho


If an expression is not in the options, it doesn't make the expression wrong. You might just need to manipulate it further.

Here, dividing by y^2 doesn't work: \(x^2 * y^2 = 18 – 3xy\)
When you divide by y^2, you get \(x^2 = 18/y^2 – 3x/y\)
How do you separate the x and y since you need to write x^2 in terms of y only?
You will need to divide by xy and then solve for it.

By the way, GMAC is absolutely reasoning based. If something confuses you, especially in Quant, it means you have missed a point.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 11684
Followers: 527

Kudos [?]: 143 [0], given: 0

Premium Member
Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink]

Show Tags

New post 13 Sep 2016, 11:49
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 Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ?   [#permalink] 13 Sep 2016, 11:49
    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic If x and y are positive and x^2+y^2=100, then for which of the followi reto 7 14 Jun 2015, 05:01
3 Experts publish their posts in the topic If x^2 - y^2 = 101, find the value of x^2 + y^2, given that kulkarnios 2 13 Sep 2013, 00:26
Experts publish their posts in the topic If x and y are positive integers and x^2 + y^2 = 100 metallicafan 3 18 Aug 2012, 15:22
13 Experts publish their posts in the topic If x and y are positive and x^2*y^2 = 18 - 3xy, then x^2 = samark 10 17 Oct 2010, 06:34
14 Experts publish their posts in the topic If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 = jimmyjamesdonkey 9 23 Jun 2008, 18:44
Display posts from previous: Sort by

If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ?

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


GMAT Club MBA Forum Home| About| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.