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# Is x^2 equal to xy? (1) x^2-y^2 = (x + 5)(y - 5) (2) x = y

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Is x^2 equal to xy? (1) x^2-y^2 = (x + 5)(y - 5) (2) x = y [#permalink]  09 Feb 2006, 06:09
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Is x^2 equal to xy?
(1) x^2-y^2 = (x + 5)(y - 5)
(2) x = y
edited sorry for a typo
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Last edited by Yurik79 on 09 Feb 2006, 06:26, edited 1 time in total.
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[#permalink]  09 Feb 2006, 06:17
B..... (i believe there is a trick, too easy )
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[#permalink]  09 Feb 2006, 07:01
x^2-y^2 = (x + y)(x - y)
x^2-y^2 = (x + 5)(y - 5)
therefore y=5 and x=y; Statement 1 is sufficient

Statement 2 is also sufficient

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[#permalink]  09 Feb 2006, 07:08
trublu wrote:
x^2-y^2 = (x + y)(x - y)
x^2-y^2 = (x + 5)(y - 5)
therefore y=5 and x=y; Statement 1 is sufficient

Statement 2 is also sufficient

But you cannot determine that x=y from the first statement....
you get x^2-25=x^2-25, where x can be any number....

Second statement gives us the straight answer.....
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[#permalink]  09 Feb 2006, 09:19
Hey SimaQ, how did you get that x^2-25 = X^-25?

What's the OA?

If you expand the 1st statement:

x^2 - y^2 = xy - 5x +5y -25
so x^2 = xy -5x +5y -25 +y^2

So Can't we make sure that x^2 is not equal to xy??
Intern
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[#permalink]  09 Feb 2006, 09:35
if you plug in y=5,

you get x^2 = 25

and that case, x = + or - 5.

therefore you can't solve it with A.

is that right?
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[#permalink]  09 Feb 2006, 17:37
x^2 = xy
x^2 - xy = 0
x(x-y) = 0
x = 0 or x=y

So x^2 is equal to xy when x is 0 or x is y.

Statement 2 gives us the second condition. So we now need to evaluate statement 1.

x^2-y^2 = (x + 5)(y - 5)
x^2 - y^2 = xy -5x + 5y - 25
x^2 = y^2 + 5 (y - 5 - x)
x^2 = y^2 only when y-x = 5 which we do not know if this is so.

So statement 1 is insufficient.

Ans B
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[#permalink]  10 Feb 2006, 08:49
good job guys OA is B
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[#permalink]  10 Feb 2006, 09:00
ywilfred wrote:
x^2-y^2 = (x + 5)(y - 5)
x^2 - y^2 = xy -5x + 5y - 25
x^2 = y^2 + 5 (y - 5 - x)
x^2 = y^2 only when y-x = 5 which we do not know if this is so.
Ans B

Statement 2 is sufficient but I relly could not evalute statement 1!

ywilfred
x^2 - y^2 = xy -5x + 5y - 25
x^2 = y^2 + 5 (y - 5 - x) +xy

so analysis fails there!

Statement 1 si true for x=y=+5 or x=y=-5

But I can not say for sure that these are the only values which satisfy this equation!

And I can not come up with any values which justify this equation except above one!

Anyone has mathemitical proof why statement 1 will be sufficient or not!

What is OA/OE
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Re: DS from DS 1000 [#permalink]  11 Feb 2006, 18:43
Yurik79 wrote:
Is x^2 equal to xy?
(1) x^2-y^2 = (x + 5)(y - 5)
(2) x = y
edited sorry for a typo

So is the 1st statement not sufficient because x and y can be 5 or -5?
Re: DS from DS 1000   [#permalink] 11 Feb 2006, 18:43
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# Is x^2 equal to xy? (1) x^2-y^2 = (x + 5)(y - 5) (2) x = y

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