GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 20 Oct 2018, 02:33

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.

Close

Request Expert Reply

Confirm Cancel

If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?

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

Hide Tags

Manager
Manager
avatar
Joined: 19 Oct 2011
Posts: 104
Location: India
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post Updated on: 21 May 2018, 00:30
4
7
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

44% (02:02) correct 56% (02:35) wrong based on 342 sessions

HideShow timer Statistics

If \(8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}\), what is the value of xy?

(1) y > x
(2) x < 0

_________________

Encourage me by pressing the KUDOS if you find my post to be helpful.



Help me win "The One Thing You Wish You Knew - GMAT Club Contest"
http://gmatclub.com/forum/the-one-thing-you-wish-you-knew-gmat-club-contest-140358.html#p1130989


Originally posted by dvinoth86 on 23 Feb 2012, 20:27.
Last edited by Bunuel on 21 May 2018, 00:30, edited 5 times in total.
Edited the question and added the OA
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 24 Feb 2012, 00:18
9
9
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

General Discussion
Manager
Manager
User avatar
Joined: 25 Aug 2011
Posts: 141
Location: India
GMAT 1: 730 Q49 V40
WE: Operations (Insurance)
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 24 Dec 2012, 06:32
2
1

7. Algebra



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Intern
Intern
avatar
Joined: 18 Dec 2012
Posts: 1
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x?  [#permalink]

Show Tags

New post 25 Dec 2012, 13:18
Bunuel wrote:
If \(8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}\), what is the value of xy?

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

(1) y > x. Since \(y>x\), then \(y-x\neq{0}\), thus \(xy=0\). Sufficient.

(2) x < 0. Not sufficient.

Answer: A.


This solution does not answer to the question. Question asks about value xy.
if y>x then xy can't be equal 0. It can't be discussed.
Really I don't understand your solution please explain
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/ 2^-3,what is the value of x?  [#permalink]

Show Tags

New post 26 Dec 2012, 03:43
akshin wrote:
Bunuel wrote:
If \(8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}\), what is the value of xy?

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

(1) y > x. Since \(y>x\), then \(y-x\neq{0}\), thus \(xy=0\). Sufficient.

(2) x < 0. Not sufficient.

Answer: A.


This solution does not answer to the question. Question asks about value xy.
if y>x then xy can't be equal 0. It can't be discussed.
Really I don't understand your solution please explain


You should read a solution carefully.

From the stem we have that either \(xy=0\) or \(y-x=0\).

(1) says that y > x, so y - x > 0, which means that \(y-x\neq{0}\), thus \(xy=0\).
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Intern
Intern
User avatar
Joined: 25 May 2014
Posts: 46
GMAT ToolKit User Reviews Badge
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 14 Nov 2014, 06:23
1
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.


Hi Bunuel,

I did a blunder while reducing 8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3) but not sure the reason for that.
i started by cancelling out the xy from both sides to get (x-y)^2 = 0 at the end.
Why cant we cancel the x and y ? Please help.
_________________

Never Try Quitting, Never Quit Trying

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 14 Nov 2014, 06:28
1
2
Ankur9 wrote:
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.


Hi Bunuel,

I did a blunder while reducing 8x*y^3 + 8x^3*y = 2x^2*y^2 / 2^(-3) but not sure the reason for that.
i started by cancelling out the xy from both sides to get (x-y)^2 = 0 at the end.
Why cant we cancel the x and y ? Please help.


If you divide (reduce) 8x*y^3 + 8x^3*y = 2x^2*y^2/2^(-3), by xy you assume, with no ground for it, that xy does not equal to zero thus exclude a possible solution (notice that xy=0 satisfies the equation). Never reduce equation by variable (or expression with variable), if you are not certain that variable (or expression with variable) doesn't equal to zero. We can not divide by zero.

Check more tips on Algebra here: algebra-tips-and-hints-175003.html

Hope it helps.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Current Student
avatar
Joined: 09 Aug 2015
Posts: 85
GMAT 1: 770 Q51 V44
GPA: 2.3
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 13 Aug 2015, 18:19
I factored out the xy from both sides and that screwed up my equation. Note to self: dont factor out things when it may lead to division by zero!
Intern
Intern
avatar
S
Joined: 30 Sep 2017
Posts: 39
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
GPA: 3.7
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 22 Nov 2017, 09:24
1
St2: if x < 0, and y not equal to 0 , then LHS is negative but RHS is positive, which is not possible so y has to be 0.
and hence xy = 0. this sums to Answer D.

Where am I getting it wrong.

Bunuel wrote:
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.

_________________

If you like my post, motivate me by giving kudos...

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50004
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 22 Nov 2017, 09:34
Barui wrote:
St2: if x < 0, and y not equal to 0 , then LHS is negative but RHS is positive, which is not possible so y has to be 0.
and hence xy = 0. this sums to Answer D.

Where am I getting it wrong.

Bunuel wrote:
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.


You can always check your theoretical deduction by simple number plugging.

Fro (2) plug x = y = -1 or x = y = -2.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Intern
Intern
avatar
S
Joined: 30 Sep 2017
Posts: 39
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
GPA: 3.7
WE: Engineering (Energy and Utilities)
GMAT ToolKit User
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 30 Nov 2017, 06:00
Thanks

I understood now...


Bunuel wrote:
Barui wrote:
St2: if x < 0, and y not equal to 0 , then LHS is negative but RHS is positive, which is not possible so y has to be 0.
and hence xy = 0. this sums to Answer D.

Where am I getting it wrong.

Bunuel wrote:
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.


You can always check your theoretical deduction by simple number plugging.

Fro (2) plug x = y = -1 or x = y = -2.

_________________

If you like my post, motivate me by giving kudos...

Manager
Manager
User avatar
S
Status: The journey is always more beautiful than the destination
Affiliations: Computer Science
Joined: 24 Apr 2017
Posts: 54
Location: India
Concentration: Statistics, Strategy
GMAT 1: 570 Q40 V28
GPA: 3.14
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?  [#permalink]

Show Tags

New post 26 Mar 2018, 00:28
This is an excellent question.
The trick is in simplyfing the question. Once you paraphrase the question into simple terms, it becomes,
xy*(x-y)^2=0.


8x∗y3+8x3∗y=2x2∗y22(−3)8x∗y3+8x3∗y=2x2∗y22(−3), What is xy?


(1) y > x ==>. Sufficient. Because, if y is greater than 1)x then x can be equal to Y.
so only one equation left. xy=0.

(2) x < 0. Clearly not sufficient.

Answer: A.
_________________

Sky is the limit. 800 is the limit.

GMAT Club Bot
Re: If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? &nbs [#permalink] 26 Mar 2018, 00:28
Display posts from previous: Sort by

If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x?

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


Copyright

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

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.