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

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If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink] New post 05 Sep 2009, 18:30
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If sqrt(xy)=xy , what is the value of x + y?

(1) x = -1/2
(2) y is not equal to zero
[Reveal] Spoiler: OA
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Re: MGMAT- Algebra 700-800 [#permalink] New post 05 Sep 2009, 19:08
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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.
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Last edited by Bunuel on 05 Sep 2009, 20:07, edited 1 time in total.
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Re: MGMAT- Algebra 700-800 [#permalink] New post 05 Sep 2009, 19:58
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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
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 03:12
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[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
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 05:44
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?
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 05:53
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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..
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 06:07
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.
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 07:54
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.

Hope that made sense
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 09:38
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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
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 12:42
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.
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Re: MGMAT- Algebra 700-800 [#permalink] New post 06 Sep 2009, 13:11
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Re: MGMAT- Algebra 700-800 [#permalink] New post 28 Sep 2009, 03:11
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...
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Re: MGMAT- Algebra 700-800 [#permalink] New post 28 Sep 2009, 03:47
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.
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Re: MGMAT- Algebra 700-800 [#permalink] New post 28 Sep 2009, 04:51
dhushan wrote:
If sqrt(xy)=xy , what is the value of x + y?
(1) x = -1/2
(2) y is not equal to zero

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
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Re: MGMAT- Algebra 700-800 [#permalink] New post 29 Sep 2009, 09:18
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.
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Re: MGMAT- Algebra 700-800 [#permalink] New post 29 Sep 2009, 18:16
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deepakraam wrote:
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.


Simple and clear solution
thanku
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Re: If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink] New post 13 May 2014, 09:09
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Re: If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2   [#permalink] 13 May 2014, 09:09
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