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If sqrt(xy)=xy , what is the value of x + y? (1) x = -1/2 [#permalink]
 05 Sep 2009, 19:30
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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
Can some please explain this, the answer is C.
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Re: MGMAT- Algebra 700-800 [#permalink]
05 Sep 2009, 20:08
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Last edited by Bunuel on 05 Sep 2009, 21:07, edited 1 time in total.
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Re: MGMAT- Algebra 700-800 [#permalink]
05 Sep 2009, 20:58
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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]
06 Sep 2009, 04:12
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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]
06 Sep 2009, 06:44
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]
06 Sep 2009, 06:53
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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]
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.
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Re: MGMAT- Algebra 700-800 [#permalink]
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.
Hope that made sense
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Re: MGMAT- Algebra 700-800 [#permalink]
06 Sep 2009, 10:38
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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]
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.
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Re: MGMAT- Algebra 700-800 [#permalink]
06 Sep 2009, 14:11
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Re: MGMAT- Algebra 700-800 [#permalink]
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...
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Re: MGMAT- Algebra 700-800 [#permalink]
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.
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Re: MGMAT- Algebra 700-800 [#permalink]
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
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]
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
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Re: MGMAT- Algebra 700-800 [#permalink]
29 Sep 2009, 19:16
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: MGMAT- Algebra 700-800
[#permalink]
29 Sep 2009, 19:16
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