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# Is X^2 equal to xy? I. x^2 - y^2 = (x+5)(y-5) II. x=y

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Is X^2 equal to xy? I. x^2 - y^2 = (x+5)(y-5) II. x=y [#permalink]

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16 Apr 2008, 10:27
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Is X^2 equal to xy?

I. x^2 - y^2 = (x+5)(y-5)
II. x=y
Current Student
Joined: 27 Mar 2008
Posts: 416
Schools: Kellogg Class of 2011
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Kudos [?]: 42 [0], given: 1

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16 Apr 2008, 10:38
(2) x = y
Thus x^2 = xy. Sufficient

(1) (x+y)(x-y) = (x+5)(y-5)
This is in the form (a+b)(b-a). Thus, we cannot make the assumption that x=y=5.
Insufficient
Manager
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16 Apr 2008, 10:42
1)
x^2-y^2=(x-5)(y-5)
x^2-y^2=xy-5x-5y+25
xy=x^2-y^2+5x+5y-25
insufficient

2)
x^2=xy?
Sub y for x
x^2=x*x
x^2=x^2
sufficient

B
Current Student
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16 Apr 2008, 12:51
zhenmaster wrote:
Is X^2 equal to xy?

I. x^2 - y^2 = (x+5)(y-5)
II. x=y

i get D...

1) (x-y)(x+y)=(x+5)(y-5)...x=y=5

sufficient..
Current Student
Joined: 27 Mar 2008
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16 Apr 2008, 12:59
fresinha,

(x+5)(y-5) is not the same as (x+y)(x-y).

(x+5)(y-5) is (x+y)(y-x) or -(x+y)(x-y).

That extra negative sign makes your assumption invalid.

If (1) had been (x+5)(5-y) then (1) would have been sufficient.
Current Student
Joined: 28 Dec 2004
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Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 273 [0], given: 2

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16 Apr 2008, 13:03
yellowjacket wrote:
fresinha,

(x+5)(y-5) is not the same as (x+y)(x-y).

(x+5)(y-5) is (x+y)(y-x) or -(x+y)(x-y).

That extra negative sign makes your assumption invalid.

If (1) had been (x+5)(5-y) then (1) would have been sufficient.

we are told in (1)

(x+y)(x-y)=(x+5)(y-5)

this can only hold if x=y=5?
or maybe i am missing something..
Re: DS: X^2   [#permalink] 16 Apr 2008, 13:03
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