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

 It is currently 20 Jul 2018, 11:44

### 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

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

# If (xy)^)(1/2) = xy , what is the value of x + y?

Author Message
TAGS:

### Hide Tags

Intern
Joined: 30 Jul 2009
Posts: 18
If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

05 Sep 2009, 19:30
1
4
00:00

Difficulty:

55% (hard)

Question Stats:

61% (01:11) correct 39% (01:07) wrong based on 367 sessions

### HideShow timer Statistics

If $$\sqrt{xy} = xy$$ what is the value of x + y?

(1) x = -1/2
(2) y is not equal to zero
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

Updated on: 05 Sep 2009, 21:07
5
6
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.

_________________

Originally posted by Bunuel on 05 Sep 2009, 20:08.
Last edited by Bunuel on 05 Sep 2009, 21:07, edited 1 time in total.
##### General Discussion
Math Expert
Joined: 02 Aug 2009
Posts: 6258
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

05 Sep 2009, 20:58
1
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
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

GMAT online Tutor

Retired Moderator
Joined: 05 Jul 2006
Posts: 1734
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 04:12
1
[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
Intern
Joined: 30 Jul 2009
Posts: 18
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 06:44
1
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?
Manager
Joined: 25 Aug 2009
Posts: 169
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 06:53
1
dhushan wrote:
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..
Intern
Joined: 30 Jul 2009
Posts: 18
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 07:07
gmate2010 wrote:
dhushan wrote:
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.
Manager
Joined: 05 Jun 2009
Posts: 74
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 08:54
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.

Retired Moderator
Joined: 05 Jul 2006
Posts: 1734
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 10:38
1
dhushan wrote:
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
Intern
Joined: 30 Jul 2009
Posts: 18
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 13:42
yezz wrote:
dhushan wrote:
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.
Math Expert
Joined: 02 Sep 2009
Posts: 47157
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

06 Sep 2009, 14:11
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.
_________________
Intern
Joined: 26 Jul 2009
Posts: 17
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

28 Sep 2009, 04:11
dhushan wrote:
yezz wrote:
dhushan wrote:
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...
Manager
Joined: 15 Sep 2009
Posts: 118
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

28 Sep 2009, 04:47
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.
Director
Joined: 01 Jan 2008
Posts: 601
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

28 Sep 2009, 05:51
dhushan wrote:
If sqrt(xy)=xy , what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero

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
Senior Manager
Joined: 01 Mar 2009
Posts: 348
Location: PDX
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

29 Sep 2009, 10:18
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.
_________________

In the land of the night, the chariot of the sun is drawn by the grateful dead

Intern
Joined: 03 Jan 2016
Posts: 4
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

Updated on: 09 Mar 2016, 22:08
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.

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

Originally posted by atirajak on 09 Mar 2016, 18:52.
Last edited by atirajak on 09 Mar 2016, 22:08, edited 1 time in total.
Current Student
Joined: 20 Mar 2014
Posts: 2641
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

09 Mar 2016, 19:12
atirajak wrote:
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.

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.
Non-Human User
Joined: 09 Sep 2013
Posts: 7312
Re: If (xy)^)(1/2) = xy , what is the value of x + y?  [#permalink]

### Show Tags

21 Sep 2017, 17:48
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 (xy)^)(1/2) = xy , what is the value of x + y? &nbs [#permalink] 21 Sep 2017, 17:48
Display posts from previous: Sort by

# Events & Promotions

 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®.