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8xy^3 + 8x^3y = 2x^2*y^2 / 2^(-3), What is xy?

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8xy^3 + 8x^3y = 2x^2*y^2 / 2^(-3), What is xy? [#permalink] New post 23 Feb 2012, 20:27
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8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3), What is xy?

(1) y > x
(2) x < 0
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Last edited by Bunuel on 24 Feb 2012, 00:20, edited 2 times in total.
Edited the question and added the OA
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Re: DS: Inequalities [#permalink] New post 23 Feb 2012, 21:32
Could you reformat the question? A lot of things are unclear.
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Re: DS: Inequalities [#permalink] New post 24 Feb 2012, 00:18
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8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3), What is xy?

8xy^3+8x^3y=\frac{2x^2*y^2}{2^{-3}} --> 8xy^3+8x^3y=2x^2*y^2*8 --> reduce by 8: xy^3+x^3y=2x^2*y^2 --> rearrange: xy^3+x^3y-2x^2*y^2=0 --> factor out xy: xy(y^2+x^2-2xy)=0 --> xy(y-x)^2=0 --> either xy=0 or y-x=0 (x=y).

(1) y > x --> y\neq{x}, which means that xy=0. Sufficient.
(2) x < 0. Clearly not sufficient.

Answer: A.

Hope it's clear.

P.S. dvinoth86 please check the questions before posting and format them correctly. Thank you.
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Re: 8xy^3 + 8x^3y = 2x^2*y^2 / 2^(-3), What is xy? [#permalink] New post 24 Feb 2012, 09:47
wil follow from next time
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Re: DS: Inequalities [#permalink] New post 16 Mar 2012, 00:04
if the question stem says y=x and option A says y>x.. How can er say xy=0 . am unable to understand

Bunuel wrote:
8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3), What is xy?

8xy^3+8x^3y=\frac{2x^2*y^2}{2^{-3}} --> 8xy^3+8x^3y=2x^2*y^2*8 --> reduce by 8: xy^3+x^3y=2x^2*y^2 --> rearrange: xy^3+x^3y-2x^2*y^2=0 --> factor out xy: xy(y^2+x^2-2xy)=0 --> xy(y-x)^2=0 --> either xy=0 or y-x=0 (x=y).

(1) y > x --> y\neq{x}, which means that xy=0. Sufficient.
(2) x < 0. Clearly not sufficient.

Answer: A.

Hope it's clear.

P.S. dvinoth86 please check the questions before posting and format them correctly. Thank you.
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Re: DS: Inequalities [#permalink] New post 16 Mar 2012, 02:18
devinawilliam83 wrote:
if the question stem says y=x and option A says y>x.. How can er say xy=0 . am unable to understand

Bunuel wrote:
8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3), What is xy?

8xy^3+8x^3y=\frac{2x^2*y^2}{2^{-3}} --> 8xy^3+8x^3y=2x^2*y^2*8 --> reduce by 8: xy^3+x^3y=2x^2*y^2 --> rearrange: xy^3+x^3y-2x^2*y^2=0 --> factor out xy: xy(y^2+x^2-2xy)=0 --> xy(y-x)^2=0 --> either xy=0 or y-x=0 (x=y).

(1) y > x --> y\neq{x}, which means that xy=0. Sufficient.
(2) x < 0. Clearly not sufficient.

Answer: A.

Hope it's clear.

P.S. dvinoth86 please check the questions before posting and format them correctly. Thank you.


The stem DOES NOT say that x=y, it says: EITHER xy=0 OR x=y.

(1) says y > x, which means that x=y is not possible, hence xy=0.

Hope it's clear.
_________________

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

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. NEW!!!

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. NEW!!!


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Re: DS: Inequalities   [#permalink] 16 Mar 2012, 02:18
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