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# XY = 1, What is the value of 2(X+Y)^2 / 2(X-Y)^2 a)2. b)4.

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Manager
Joined: 13 Oct 2004
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XY = 1, What is the value of 2(X+Y)^2 / 2(X-Y)^2 a)2. b)4. [#permalink]  22 Jul 2005, 21:32
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XY = 1, What is the value of 2(X+Y)^2 / 2(X-Y)^2
a)2. b)4. c)8 d)16 e)32
Senior Manager
Joined: 29 Nov 2004
Posts: 486
Location: Chicago
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Kudos [?]: 11 [0], given: 0

Re: ETS PS -- Algebra [#permalink]  23 Jul 2005, 06:06
prep_gmat wrote:
XY = 1, What is the value of 2(X+Y)^2 / 2(X-Y)^2
a)2. b)4. c)8 d)16 e)32

The data is insufficient, x and y could be a lot of different numbers (or both equal to 1 or -1), so in each case the answer will be different....The answer will probably never be an integer, if i am not wrong.
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Fear Mediocrity, Respect Ignorance

Senior Manager
Joined: 30 May 2005
Posts: 277
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This is an very interesting exercises But tricky

2(x+y)^2/2(x+y)^2 =
cancel 2 OUT

(x+y)^2/2(x+y)^2 = x^2+y^2+2xy/x^2+y^2-2xy

xy=1

y =1/X

but i tried this other approach
2(x+y)^2/2(x+y)^2 =0
Cross solving

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

2xy+2xy=0

4xy=0
xy=1

FOUND 4

Plz correct me if i am wrong thanks
Director
Joined: 27 Dec 2004
Posts: 908
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Mandy, do you notice that the equation is 2(x + y)^2 / 2(x - y)^2 not 2(x + y)^2 / 2(x + y)^2 ?

@ Ranga, i couldn't solve this either.
Senior Manager
Joined: 30 May 2005
Posts: 277
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Kudos [?]: 11 [0], given: 0

Folaa3 wrote:
Mandy, do you notice that the equation is 2(x + y)^2 / 2(x - y)^2 not 2(x + y)^2 / 2(x + y)^2 ?

@ Ranga, i couldn't solve this either.

sorry just a tipo mistakes from the rush paper to the screen
on my rush paper and all my detailled calculations i do have this 2(x + y)^2 / 2(x - y)^2
Senior Manager
Joined: 27 Aug 2005
Posts: 332
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Kudos [?]: 47 [0], given: 0

OE says 16, but I'm not getting it either.

For example, take two numbers x and y where xy=1. For sake of simplicty, plug in x=2 and y=1/2:
2(2+1/2)^2/2(2-1/2)^2 = 12.5/4.5 = 25/9 = ~2.78. That's none of the choices listed, clearly.

As another example, let x=3 and y=1/3:
2(3+1/3)^2/2(3-1/3)^2 = ~ 1.56. Different answer again, and not any of the choices.

Has it pretty much been concluded that there's something wrong with this problem?
Senior Manager
Joined: 27 Aug 2005
Posts: 332
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Kudos [?]: 47 [0], given: 0

The problem showed up on a practice CAT test on the new GMATPrep software.
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