Last visit was: 19 Nov 2025, 23:18 It is currently 19 Nov 2025, 23:18
Home
GMAT
Messages
Tests
Schools
Events
Rewards
Chat
My Profile
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.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
Back to Forum
Create Topic
805+ Level|   Algebra|      
User avatar
dvinoth86
User avatar
Joined: 19 Oct 2011
Last visit: 06 Dec 2015
Posts: 87
Own Kudos:
1,328
 [58]
Given Kudos: 33
Location: India
Posts: 87
Kudos: 1,328
 [58]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? Updated on: 21 May 2018, 00:30
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
7
Kudos
Add Kudos
51
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
A
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

95% (hard)

Question Stats:

43% (02:14) correct 57% (02:37) wrong based on 675 sessions

History

Date
Time
Result
Not Attempted Yet
If \(8xy^3 + 8x^3y=\frac{2x^2y^2}{2^{-3}}\), what is the value of xy?

(1) y > x
(2) x < 0
ShowHide Answer
Official Answer
A
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
 [32]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
 [32]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 24 Feb 2012, 00:18
13
Kudos
Add Kudos
19
Bookmarks
Bookmark this Post
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
 [8]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
 [8]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 24 Dec 2012, 06:32
2
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post

7. Algebra



Check below for more:
ALL YOU NEED FOR QUANT ! ! !
Ultimate GMAT Quantitative Megathread
General Discussion
User avatar
devinawilliam83
User avatar
Joined: 25 Aug 2011
Last visit: 01 Mar 2013
Posts: 113
Own Kudos:
1,642
 [1]
Given Kudos: 11
Location: India
GMAT 1: 730 Q49 V40
WE:Operations (Insurance)
GMAT 1: 730 Q49 V40
Posts: 113
Kudos: 1,642
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 16 Mar 2012, 00:04
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
if the question stem says y=x and option A says y>x.. How can er say xy=0 . am unable to understand

Bunuel
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.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
 [1]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 16 Mar 2012, 02:18
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
devinawilliam83
if the question stem says y=x and option A says y>x.. How can er say xy=0 . am unable to understand

Bunuel
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.
Show more

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.
avatar
akshin
avatar
Joined: 18 Dec 2012
Last visit: 25 Feb 2013
Posts: 1
Posts: 1
Kudos: 0
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 25 Dec 2012, 13:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 26 Dec 2012, 03:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
akshin
Bunuel
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
Show more

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 \(xy=0\).
User avatar
Ankur9
User avatar
Joined: 25 May 2014
Last visit: 11 May 2016
Posts: 43
Own Kudos:
52
 [2]
Given Kudos: 125
Products:
My Reviews
Posts: 43
Kudos: 52
 [2]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 14 Nov 2014, 06:23
1
Kudos
Add Kudos
1
Bookmarks
Bookmark this Post
Bunuel
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.
Show more

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.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
 [4]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
 [4]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 14 Nov 2014, 06:28
1
Kudos
Add Kudos
3
Bookmarks
Bookmark this Post
Ankur9
Bunuel
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.
Show more

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.
User avatar
ggurface
User avatar
Joined: 09 Aug 2015
Last visit: 12 Jul 2020
Posts: 72
Own Kudos:
79
 [2]
Given Kudos: 7
Schools: Schulich Jan '18 (A)
GMAT 1: 770 Q51 V44
GPA: 2.3
Schools: Schulich Jan '18 (A)
GMAT 1: 770 Q51 V44
Posts: 72
Kudos: 79
 [2]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 13 Aug 2015, 18:19
2
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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!
User avatar
Aim800score
User avatar
Joined: 30 Sep 2017
Last visit: 09 Dec 2018
Posts: 29
Own Kudos:
52
 [1]
Given Kudos: 27
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
GPA: 3.7
WE:Engineering (Energy)
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
Posts: 29
Kudos: 52
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 22 Nov 2017, 09:24
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
Show more
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 22 Nov 2017, 09:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Barui
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
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
Show more

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

Fro (2) plug x = y = -1 or x = y = -2.
User avatar
Aim800score
User avatar
Joined: 30 Sep 2017
Last visit: 09 Dec 2018
Posts: 29
Own Kudos:
52
Given Kudos: 27
Location: India
Concentration: Entrepreneurship, General Management
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
GPA: 3.7
WE:Engineering (Energy)
Schools: IIM Udaipur '17
GMAT 1: 700 Q50 V37
Posts: 29
Kudos: 52
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 30 Nov 2017, 06:00
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks

I understood now...


Bunuel
Barui
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
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
Show more
User avatar
Nixondutta
User avatar
Joined: 24 Apr 2017
Last visit: 10 Aug 2018
Posts: 40
Own Kudos:
78
Given Kudos: 83
Status:The journey is always more beautiful than the destination
Affiliations: Computer Science
Location: India
Concentration: Statistics, Strategy
Schools: Columbia EMBA"19 Simon '19 Mason '19
GMAT 1: 570 Q40 V28
GPA: 3.14
Schools: Columbia EMBA"19 Simon '19 Mason '19
GMAT 1: 570 Q40 V28
Posts: 40
Kudos: 78
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 26 Mar 2018, 00:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
avatar
strawberryjelly
avatar
Joined: 24 Mar 2019
Last visit: 10 Jan 2021
Posts: 28
Own Kudos:
30
 [1]
Given Kudos: 34
Location: United Kingdom
Schools: Stanford '22 (A) HBS '22 (M) Booth '22 (A) Wharton '22 (A)
Schools: Stanford '22 (A) HBS '22 (M) Booth '22 (A) Wharton '22 (A)
Posts: 28
Kudos: 30
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 13 Apr 2019, 04:55
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
Show more

This may be me being extremely dim but can someone explain why \(xy\): \(xy(y^2+x^2-2xy)=0\); factors to \(xy(y-x)^2=0\) and not \(xy(x-y)^2=0\) I've written it out a lot and it seems to have the same product?
avatar
kri93
avatar
Joined: 02 Dec 2016
Last visit: 03 Mar 2020
Posts: 6
Own Kudos:
1
Given Kudos: 250
Posts: 6
Kudos: 1
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 28 Dec 2019, 21:01
Kudos
Add Kudos
Bookmarks
Bookmark this Post
strawberryjelly
Bunuel
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.

This may be me being extremely dim but can someone explain why \(xy\): \(xy(y^2+x^2-2xy)=0\); factors to \(xy(y-x)^2=0\) and not \(xy(x-y)^2=0\) I've written it out a lot and it seems to have the same product?
Show more


I have the same question
User avatar
DhruvS
User avatar
Joined: 09 May 2018
Last visit: 07 May 2022
Posts: 40
Own Kudos:
77
Given Kudos: 121
Location: India
Posts: 40
Kudos: 77
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 03 Mar 2020, 07:43
Kudos
Add Kudos
Bookmarks
Bookmark this Post
strawberryjelly
Bunuel
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.

This may be me being extremely dim but can someone explain why \(xy\): \(xy(y^2+x^2-2xy)=0\); factors to \(xy(y-x)^2=0\) and not \(xy(x-y)^2=0\) I've written it out a lot and it seems to have the same product?
Show more

The bigger question is would it really matter in this case?

If it is xy(x-y)^2 =0 or it is xy(y-x)^2 =0 ???

Nope it will not matter, as eventually both the expressions will boil down to xy=0 or x=y. :) ;)

Posted from my mobile device
User avatar
puneetfitness
User avatar
Joined: 02 Aug 2022
Last visit: 08 Jul 2023
Posts: 40
Own Kudos:
5
 [1]
Given Kudos: 23
Posts: 40
Kudos: 5
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 07 Feb 2023, 12:14
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.
Show more

Hi Bunuel please advise the way we factor out 8 on both side of equation why are we not factoring out xy from both sides of equation

xy^3+x^3y=2x^2*y^2
Xy(Y^2+x^2)=2xy * xy
Y^2+x^2= 2xy
(Y-x)^2=0

I can see that we don't anything to related with xy from this but. I still curious to find out we cannot factor out xy

Bunuel

Posted from my mobile device
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 19 Nov 2025
Posts: 105,401
Own Kudos:
778,406
 [1]
Given Kudos: 99,987
Products:
GMAT Club Tests Forum Quiz
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 105,401
Kudos: 778,406
 [1]
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 07 Feb 2023, 12:27
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
puneetfitness
Bunuel
\(8x*y^3 + 8x^3*y = \frac{2x^2*y^2}{2^{(-3)}}\), 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.

Hi Bunuel please advise the way we factor out 8 on both side of equation why are we not factoring out xy from both sides of equation

xy^3+x^3y=2x^2*y^2
Xy(Y^2+x^2)=2xy * xy
Y^2+x^2= 2xy
(Y-x)^2=0

I can see that we don't anything to related with xy from this but. I still curious to find out we cannot factor out xy

Bunuel

Posted from my mobile device
Show more

You can factor out xy but you cannot reduce by xy and as to why you cannot do that is explained here: https://gmatclub.com/forum/if-8xy-3-8x- ... l#p1442635

Hope it helps.
User avatar
bumpbot
User avatar
Non-Human User
Joined: 09 Sep 2013
Last visit: 04 Jan 2021
Posts: 38,591
Own Kudos:
1,079
Posts: 38,591
Kudos: 1,079
If 8xy^3 + 8x^3*y=2x^2*y^2/2^-3, what is the value of x? 19 Mar 2024, 23:59
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
Moderators:
Bunuel
Math Expert
105398 posts
kingbucky
496 posts