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

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If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 15 Oct 2012, 03:17
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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
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 15 Oct 2012, 03:22
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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.
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Senior Manager
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 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}.

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
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 15 Oct 2012, 03:44
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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 MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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.


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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 10 Dec 2012, 22:57
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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
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 18 Dec 2012, 20:45
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
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ? [#permalink] New post 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}.

Answer: D.

Hope it's clear.


very elegant&simple...if you spot one variable in two :wink:
like it :wink:
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Re: If x and y are positive and x^2y^2 = 18 – 3xy, then x^2 ?   [#permalink] 16 Dec 2013, 18:21
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