If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? : GMAT Problem Solving (PS)
Check GMAT Club App Tracker for the Latest School Decision Releases http://gmatclub.com/AppTrack

 It is currently 07 Dec 2016, 01:31

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:

### Hide Tags

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

Kudos [?]: 224 [2] , given: 32

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

### Show Tags

15 Oct 2012, 03:17
2
KUDOS
13
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

66% (02:44) correct 34% (02:23) wrong based on 186 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
Math Expert
Joined: 02 Sep 2009
Posts: 35909
Followers: 6849

Kudos [?]: 90008 [4] , given: 10402

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

### Show Tags

15 Oct 2012, 03:22
4
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 $$xy=3$$ --> $$x=\frac{3}{y}$$ --> $$x^2=\frac{9}{y^2}$$.

Hope it's clear.
_________________
Senior Manager
Joined: 22 Dec 2011
Posts: 298
Followers: 3

Kudos [?]: 224 [0], given: 32

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

### Show Tags

15 Oct 2012, 03:38
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 $$xy=3$$ --> $$x=\frac{3}{y}$$ --> $$x^2=\frac{9}{y^2}$$.

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
Math Expert
Joined: 02 Sep 2009
Posts: 35909
Followers: 6849

Kudos [?]: 90008 [1] , given: 10402

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

### Show Tags

15 Oct 2012, 03:44
1
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 $$xy=3$$ --> $$x=\frac{3}{y}$$ --> $$x^2=\frac{9}{y^2}$$.

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

Kudos [?]: 414 [2] , given: 11

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

### Show Tags

10 Dec 2012, 22:57
2
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 $$6$$

$$xy = 3$$
$$x^2 = 9/y^2$$

_________________

Impossible is nothing to God.

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

Kudos [?]: 414 [0], given: 11

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

### Show Tags

18 Dec 2012, 20:45
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.

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

_________________

Impossible is nothing to God.

Intern
Joined: 11 Oct 2013
Posts: 18
Location: United Kingdom
GMAT 1: 490 Q32 V25
GPA: 3.9
WE: Other (Other)
Followers: 0

Kudos [?]: 21 [0], given: 34

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

### Show Tags

16 Dec 2013, 18:21
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 $$xy=3$$ --> $$x=\frac{3}{y}$$ --> $$x^2=\frac{9}{y^2}$$.

Hope it's clear.

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

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
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 55 [0], given: 185

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

### Show Tags

11 Jun 2015, 02:21
I don't understand why you can not divide by y^2 here? Pls help
Math Expert
Joined: 02 Sep 2009
Posts: 35909
Followers: 6849

Kudos [?]: 90008 [0], given: 10402

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

### Show Tags

11 Jun 2015, 02:36
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.
_________________
Manager
Joined: 07 Apr 2015
Posts: 188
Followers: 2

Kudos [?]: 55 [0], given: 185

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

### Show Tags

11 Jun 2015, 03:34
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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7069
Location: Pune, India
Followers: 2086

Kudos [?]: 13291 [1] , given: 222

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

### Show Tags

11 Jun 2015, 20:45
1
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
Joined: 09 Sep 2013
Posts: 12884
Followers: 561

Kudos [?]: 158 [0], given: 0

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

### Show Tags

13 Sep 2016, 10:49
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.
_________________
Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ?   [#permalink] 13 Sep 2016, 10:49
Similar topics Replies Last post
Similar
Topics:
11 If x and y are positive and x^2+y^2=100, then for which of the followi 8 14 Jun 2015, 04:01
4 If x^2 - y^2 = 101, find the value of x^2 + y^2, given that 2 12 Sep 2013, 23:26
If x and y are positive integers and x^2 + y^2 = 100 3 18 Aug 2012, 14:22
13 If x and y are positive and x^2*y^2 = 18 - 3xy, then x^2 = 10 17 Oct 2010, 05:34
14 If x and y are positive and x^2 * y^2 = 18 – 3xy, then x^2 = 9 23 Jun 2008, 17:44
Display posts from previous: Sort by