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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]  26 Feb 2007, 16:38
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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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Re: DS [#permalink]  26 Feb 2007, 17:40
jjhko wrote:
Is x^2 equal to xy?

1) x^2 - y^2 = (x+5)(y-5)

2) x=y

Since #2 is self-explanatory, the answer has to be B or D. I tried to work out #1 and wasn't able to simplify the expression to make the answer obvious. Can someone show the simplification for #1?

Thanks!

Last edited by nervousgmat on 28 Feb 2007, 18:27, edited 1 time in total.
Senior Manager
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Quote:
Is x^2 equal to xy?

1) x^2 - y^2 = (x+5)(y-5)

2) x=y

S1: x^2-y^2=(x+y)(x-y)=(x+5)(y-5)
=>x-y=x+5=>y=-5
x+y=y+x=y-5=>x=-5
suff

S2:x=y=>x*x=x*y
suff

Hence D
Senior Manager
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Sumithra wrote:
Quote:
Is x^2 equal to xy?

1) x^2 - y^2 = (x+5)(y-5)

2) x=y

S1: x^2-y^2=(x+y)(x-y)=(x+5)(y-5)
=>x-y=x+5=>y=-5
x+y=y+x=y-5=>x=-5
suff

Hence D

Sumithra, Can you please explain this step.
Manager
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Yeah I'm not sure how that works either.
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wall street...bulls, bears, people from connecticut

Senior Manager
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Sure

Since (x+y)(x-y)=(x+5)(y-5)
I equated x+y=y-5 and x-y=x+5 as the signs match and is less complicated
Hence x+y=y-5 =>x=-5 and x-y=x+5=>-y=5 or y=-5

Guess, I'm clear
Senior Manager
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whats the OA?

I think it should be B
Senior Manager
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Here...

x^2 - y^2 = (x+5)(y-5)
=> x^2 - y^2 = xy-5^2
=>x^2=xy

Or

x^2 - y^2 = (x+5)(y-5)
x^2+xy-xy-y^2=xy-5x+5y-5^2
For this to be true x^2=xy and 5x=5y or x=y
Either way I believe S1 is suff

Explain me if/where I'm wrong
Senior Manager
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I would say D.

Sumithra is right.
Senior Manager
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st1 is not sufficient:
consider x=-5 y=5 ; x=5 y=5
in both cases st1 holds but stem is either "yes" or "no"...

so this is the ultimate proof of insufficiency of st1.

it is a bit difficult to expand st1 algebraicly and people here did various mistakes....
x^2-y^2 = (x+5)(y-5) = xy + 5y - 5x -25 ..... leads to nothing.

it is of utmost importance in gmat to know when to stop seeking algebraic expansions/solutions (and start look at other directions for the answer).
in this case the (something +5)*(something -5) is put as diversion that leads you to make mistakes - either doing wrong algebraic operations or assuming wrong things....
in fact this was a "red alert" for me. the stem doesn't say anything about specific numbers, just x and y. and then comes statement 1 and adds numbers to the equation... this sounded ood to me and made me extra alerted.
Senior Manager
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Quote:
st1 is not sufficient:
consider x=-5 y=5 ; x=5 y=5
in both cases st1 holds but stem is either "yes" or "no"...

It is pretty straight forward. I'm over thinking.
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