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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

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

now we can write eq as:- [square_root]xy=xy...... xy=(xy)^2.....ie (xy)^2-xy=0.....or xy(xy-1)=0.... so xy=0 or xy=1 i)x=-1/2..... substituting this value in xy we get (-1/2)y=0 ....so y=0... also (-1/2)y=0....y=-2.... not sufficient.... ii)y not equal to 0.... not sufficient... combining the two.... y=-2... sufficient
_________________

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.

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.

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.

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...

Re: If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink]

Show Tags

13 May 2014, 09:09

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.
_________________

Re: If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink]

Show Tags

22 Dec 2015, 09:41

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.
_________________

If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink]

Show Tags

09 Mar 2016, 17:52

Bunuel wrote:

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?

Last edited by atirajak on 09 Mar 2016, 21:08, edited 1 time in total.

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

Its been long time coming. I have always been passionate about poetry. It’s my way of expressing my feelings and emotions. And i feel a person can convey...

Written by Scottish historian Niall Ferguson , the book is subtitled “A Financial History of the World”. There is also a long documentary of the same name that the...

Post-MBA I became very intrigued by how senior leaders navigated their career progression. It was also at this time that I realized I learned nothing about this during my...