Last visit was: 08 Jul 2025, 20:18 It is currently 08 Jul 2025, 20:18
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
User avatar
dhushan
Joined: 30 Jul 2009
Last visit: 17 Sep 2009
Posts: 13
Own Kudos:
27
 [12]
Given Kudos: 18
Posts: 13
Kudos: 27
 [12]
1
Kudos
Add Kudos
11
Bookmarks
Bookmark this Post
Most Helpful Reply
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,581
 [12]
6
Kudos
Add Kudos
6
Bookmarks
Bookmark this Post
General Discussion
User avatar
chetan2u
User avatar
GMAT Expert
Joined: 02 Aug 2009
Last visit: 08 Jul 2025
Posts: 11,296
Own Kudos:
41,617
 [1]
Given Kudos: 333
Status:Math and DI Expert
Products:
Expert
Expert reply
Posts: 11,296
Kudos: 41,617
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
User avatar
yezz
User avatar
Retired Moderator
Joined: 05 Jul 2006
Last visit: 26 Apr 2022
Posts: 837
Own Kudos:
1,641
 [1]
Given Kudos: 49
Posts: 837
Kudos: 1,641
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
[quote="dhushan"]If sqrt(xy)=xy , what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero


XY=(XY)^2........ie: x,y have the same sign and they could be (0,anything)(1,1),(-1,-1) receprocals

from 1

no info about y......x,y could be (0,-1/2) or receprocals
from 2
insuff

both

receprocals..........suff
User avatar
dhushan
Joined: 30 Jul 2009
Last visit: 17 Sep 2009
Posts: 13
Own Kudos:
27
 [1]
Given Kudos: 18
Posts: 13
Kudos: 27
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?
avatar
gmate2010
Joined: 25 Aug 2009
Last visit: 26 Nov 2009
Posts: 96
Own Kudos:
251
 [1]
Given Kudos: 12
Posts: 96
Kudos: 251
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dhushan
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?

You cancelled out a root of the equation which is incorrect..you should consider each and every real root of the equation..
User avatar
dhushan
Joined: 30 Jul 2009
Last visit: 17 Sep 2009
Posts: 13
Own Kudos:
Given Kudos: 18
Posts: 13
Kudos: 27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
gmate2010
dhushan
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?

You cancelled out a root of the equation which is incorrect..you should consider each and every real root of the equation..

Sorry, I still don't follow. what do you mean by "cancelled out a root of the equation" - I still have x and y in the equation.
User avatar
sfeiner
Joined: 05 Jun 2009
Last visit: 27 Dec 2009
Posts: 43
Own Kudos:
Given Kudos: 1
Posts: 43
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
for a function the square root of xy is only equal to xy if the function is equal to 0 or 1, you can do the math and find the roots by squaring but I just accept that it can only equal 0 or 1. So if we know X is not 0 and is in fact a #, we know Y can only be 0 or the multiplicative reciporcal of X so that XY=1 or 0. When we get statement 2 we know that X*Y can not be equal to 0 so we know that XY= 1 and if we know what X is we can calculate what Y is.

Hope that made sense
User avatar
yezz
User avatar
Retired Moderator
Joined: 05 Jul 2006
Last visit: 26 Apr 2022
Posts: 837
Own Kudos:
1,641
 [1]
Given Kudos: 49
Posts: 837
Kudos: 1,641
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dhushan
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?

x,y are both interrelated ( roots ie: the solution is a unique combination of x,y value.s but not any of them on its own),

you can never cancell out a VARIABLE, because its unique value in the combination xy or x^2y^2 makes the equation valid.

think of it as if there are 2 conditions for the equation to be true the first is the value of x and the second is values of y but not any of them alone.

hope am clear
User avatar
dhushan
Joined: 30 Jul 2009
Last visit: 17 Sep 2009
Posts: 13
Own Kudos:
Given Kudos: 18
Posts: 13
Kudos: 27
Kudos
Add Kudos
Bookmarks
Bookmark this Post
yezz
dhushan
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?

x,y are both interrelated ( roots ie: the solution is a unique combination of x,y value.s but not any of them on its own),

you can never cancell out a VARIABLE, because its unique value in the combination xy or x^2y^2 makes the equation valid.

think of it as if there are 2 conditions for the equation to be true the first is the value of x and the second is values of y but not any of them alone.

hope am clear

Thanks, I finally get it in this situation. However, does the same hold true in other questions, for example

x^2y^2 = x^2 (so here I would have determine whether, x = 0 and y = 0, or x and y = 1)

Thanks for everyone's help, it is greatly appreciated.
User avatar
Bunuel
User avatar
Math Expert
Joined: 02 Sep 2009
Last visit: 08 Jul 2025
Posts: 102,594
Own Kudos:
Given Kudos: 97,452
Products:
Expert
Expert reply
Active GMAT Club Expert! Tag them with @ followed by their username for a faster response.
Posts: 102,594
Kudos: 739,581
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Here you'll have:

x^2y^2 -x^2 = 0 --> x^2(y^2-1)=0 --> x^2(y-1)(y+1)=0

One of the multiples must be zero --> x=0, y=1 or y=-1.
User avatar
sunny4frenz
Joined: 26 Jul 2009
Last visit: 09 Oct 2009
Posts: 15
Own Kudos:
Given Kudos: 8
Posts: 15
Kudos: 51
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dhushan
yezz
dhushan
Thanks guys, I see how your answers work, but I was wondering what is wrong with solving the problem this way.

sqrt(xy) = xy

xy = x^2y^2
1/x = y

therefore if y = 1/x, and from the info in (1), couldn't we deduce that y = =-2 by substituting -1/2 in for x?

Therefore A would be the answer?

x,y are both interrelated ( roots ie: the solution is a unique combination of x,y value.s but not any of them on its own),

you can never cancell out a VARIABLE, because its unique value in the combination xy or x^2y^2 makes the equation valid.

think of it as if there are 2 conditions for the equation to be true the first is the value of x and the second is values of y but not any of them alone.

hope am clear

Thanks, I finally get it in this situation. However, does the same hold true in other questions, for example

x^2y^2 = x^2 (so here I would have determine whether, x = 0 and y = 0, or x and y = 1)

Thanks for everyone's help, it is greatly appreciated.


Here is the catch .....

In mathematics ... division by zero is not allowed ...
so
xy = x^2Y^2 => x^2y^2 - xy = 0 => xy(xy - 1) = => xy = 0 or xy = 1 => x is not zero therefor y = 0 or y =1/x

in ur second case .....

x^2y^2 = x^2 => x^2y^2 - x^2 = 0 => x^2(y^2 - 1) = 0 => x^2 = 0 or y^2 = 1 => x = 0 or y = 1 or y = -1...
User avatar
deepakraam
Joined: 15 Sep 2009
Last visit: 27 Oct 2011
Posts: 54
Own Kudos:
Given Kudos: 2
Posts: 54
Kudos: 53
Kudos
Add Kudos
Bookmarks
Bookmark this Post
statement 1:
==========
x = -1/2 .so y can be 0 or -2.Nt suff

Statement 2:
==========
y is not equal to zero. Nt suff

Combining both we can get x = -1/2 y = -2.
User avatar
maratikus
Joined: 01 Jan 2008
Last visit: 22 Jul 2010
Posts: 257
Own Kudos:
Given Kudos: 1
Posts: 257
Kudos: 340
Kudos
Add Kudos
Bookmarks
Bookmark this Post
dhushan
If sqrt(xy)=xy , what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero

Can some please explain this, the answer is C.

sqrt(xy)=xy -> two solutions: xy = 0 or xy = 1.

1: insufficient: y = -2 or y = 0
2: insufficient: x = 1/y

1+2: sufficient y = -2, x = -1/2 -> x+y = -2.5 -> C
User avatar
pleonasm
Joined: 01 Mar 2009
Last visit: 29 Aug 2011
Posts: 265
Own Kudos:
Given Kudos: 24
Location: PDX
Concentration: Entrepreneurship
 Q44  V40
Posts: 265
Kudos: 158
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Hey guys - Just a quick clarification

Why can't we divide the equation by \sqrt{xy} to yield the following:

1 = \sqrt{xy}

Based on this .. just option 1 would be sufficient because if x is -1/2 y has to be -2 to satisfy this above equation.
avatar
atirajak
Joined: 03 Jan 2016
Last visit: 05 Apr 2017
Posts: 1
Given Kudos: 8
Posts: 1
Kudos: 0
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(\sqrt{xy} = xy\) what is the value of x + y?

\(\sqrt{xy} = xy\) --> \(xy=x^2y^2\) --> \(x^2y^2-xy=0\) --> \(xy(xy-1)=0\) --> either \(xy=0\) or \(xy=1\).

(1) x = -1/2 --> either \(-\frac{1}{2}*y=0\) --> \(y=0\) and \(x+y=-\frac{1}{2}\) OR \(-\frac{1}{2}*y=1\) --> \(y=-2\) and \(x+y=-\frac{5}{2}\). Not sufficient.

(2) y is not equal to zero. Clearly not sufficient.

(1)+(2) Since from (2) \(y\neq{0}\), then from (1) \(y=-2\) and \(x+y=-\frac{5}{2}\). Sufficient.

Answer: C.


On combining both the statements, we still wouldn't know the value of x. What if x is 0?
User avatar
ENGRTOMBA2018
Joined: 20 Mar 2014
Last visit: 01 Dec 2021
Posts: 2,329
Own Kudos:
Given Kudos: 816
Concentration: Finance, Strategy
GMAT 1: 750 Q49 V44
GPA: 3.7
WE:Engineering (Aerospace and Defense)
Products:
GMAT 1: 750 Q49 V44
Posts: 2,329
Kudos: 3,784
Kudos
Add Kudos
Bookmarks
Bookmark this Post
atirajak
Bunuel
If \(\sqrt{xy} = xy\) what is the value of x + y?

\(\sqrt{xy} = xy\) --> \(xy=x^2y^2\) --> \(x^2y^2-xy=0\) --> \(xy(xy-1)=0\) --> either \(xy=0\) or \(xy=1\).

(1) x = -1/2 --> either \(-\frac{1}{2}*y=0\) --> \(y=0\) and \(x+y=-\frac{1}{2}\) OR \(-\frac{1}{2}*y=1\) --> \(y=-2\) and \(x+y=-\frac{5}{2}\). Not sufficient.

(2) y is not equal to zero. Clearly not sufficient.

(1)+(2) Since from (2) \(y\neq{0}\), then from (1) \(y=-2\) and \(x+y=-\frac{5}{2}\). Sufficient.

Answer: C.


What if x is 0? On combining both the statements, we still wouldn't know the value of x.

Your question is confusing. On one hand you are assuming that x=0 and on the other hand you are saying that you dont know the value of x. Can you rephrase your question?

As for this question, when you combine both the statements, x=-0.5 and as y \(\neq\) 0 ---> this thus rules out the case when xy=0, leaving you with unique values of y and x. Hence C is the correct answer.

Also, S2 alone does leave the door open for assuming x=0 but then again it can very well be \(\neq\) 0, making statement 2 not sufficient.

Hope this helps.
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 08 Jul 2025
Posts: 4,847
Own Kudos:
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,847
Kudos: 8,620
Kudos
Add Kudos
Bookmarks
Bookmark this Post
When I first looked at this question, especially the bit on √xy=xy , I knew that plugging in the values of 1 and 0 for xy would be the fastest approach since these are the only two values that satisfy the equation given.
Remember that if the question says √xy=xy or something similar, it’s telling you that the values under the root can be 1 or 0.

So if √xy=xy , it means xy = 1 or xy = 0. If xy=1, x=y=1 or x=y=-1; if xy=0, at least one of the numbers is 0.
With this, let us analyse the statements.

From statement I alone, we know x = -\(\frac{1}{2}\). If xy=1, value of y will be -2 and if xy=0, value of y will be 0. Since we do not know the exact value of xy, statement I alone is insufficient to find the value of y and hence the value of x+y.
Answer options A and D can be eliminated. Possible answer options are B, C or E.

From statement II alone, we know that y is not equal to 0. This eliminates the possibility of y being 0. However, we still do not know the exact values of x and y and hence cannot find the value of x+y. Statement II alone is insufficient.
Answer option B can be eliminated. Possible answer options are C or E.

Combining both statements I and II, we have the following:
From statement II alone, we know that xy≠0. Coupling this with the data given in the question, we can say that xy HAS TO be equal to 1.
From statement I alone, we know that x = -\(\frac{1}{2}\).
Since xy=1 and x=-\(\frac{1}{2}\), we can say that y=-2. Since we know x and y uniquely, we can calculate the value of x+y. The combination of statements is sufficient.
The correct answer option is C.

Hope that helps!
User avatar
CrackverbalGMAT
User avatar
Major Poster
Joined: 03 Oct 2013
Last visit: 08 Jul 2025
Posts: 4,847
Own Kudos:
8,620
 [1]
Given Kudos: 225
Affiliations: CrackVerbal
Location: India
Expert
Expert reply
Posts: 4,847
Kudos: 8,620
 [1]
1
Kudos
Add Kudos
Bookmarks
Bookmark this Post
pleonasm
Hey guys - Just a quick clarification

Why can't we divide the equation by \sqrt{xy} to yield the following:

1 = \sqrt{xy}

Based on this .. just option 1 would be sufficient because if x is -1/2 y has to be -2 to satisfy this above equation.


Hello Pleonasm,

Consider that the value of sq.root(xy) can be 0. As such, you cannot just divide both sides by sq.root(xy) since that would tantamount to division by ZERO, which is not allowed on the GMAT.

In general, you should avoid cancellations and cross-multiplications (yes, even when there's an equation) when you know that certain quantities can be ZERO. A better approach would be to take all terms on to the LHS, keeping the RHS as zero and simplifying the expression on the LHS to yield roots, as Bunuel has done in his response to this query.

Hope that helps!
User avatar
puneetfitness
Joined: 02 Aug 2022
Last visit: 08 Jul 2023
Posts: 40
Own Kudos:
Given Kudos: 23
Posts: 40
Kudos: 4
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Bunuel
If \(\sqrt{xy} = xy\) what is the value of x + y?

\(\sqrt{xy} = xy\) --> \(xy=x^2y^2\) --> \(x^2y^2-xy=0\) --> \(xy(xy-1)=0\) --> either \(xy=0\) or \(xy=1\).

(1) x = -1/2 --> either \(-\frac{1}{2}*y=0\) --> \(y=0\) and \(x+y=-\frac{1}{2}\) OR \(-\frac{1}{2}*y=1\) --> \(y=-2\) and \(x+y=-\frac{5}{2}\). Not sufficient.

(2) y is not equal to zero. Clearly not sufficient.

(1)+(2) Since from (2) \(y\neq{0}\), then from (1) \(y=-2\) and \(x+y=-\frac{5}{2}\). Sufficient.

Answer: C.


Hi Bunuel when we have xy=(xy)^2 why we cannot assume that (xy)^2/xy=1 why should we do (xy)^2 -xy=o

My question is how do we know when the power on two side of equality should cancel out to simplify and when should we perform subtract as done above

Posted from my mobile device
 1   2   
Moderator:
Math Expert
102594 posts