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# if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4

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Senior Manager
Joined: 17 Aug 2005
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if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4 [#permalink]  16 Feb 2007, 16:07
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if 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
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Joined: 17 Dec 2006
Posts: 22
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Re: PS [#permalink]  16 Feb 2007, 16:41
buckkitty wrote:
if 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

Are you sure you copied the question right? 1s cancel off right away, doesnt look right
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Joined: 08 Nov 2006
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Location: Ann Arbor
Schools: Ross '10
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Re: PS [#permalink]  16 Feb 2007, 18:01
buckkitty wrote:
if 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

I think you mean 2^((x+y)^2)/2^((x-y)^2)

If this is the case, then

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

2^A/2^B=2^(A-B)

Substitute A and B and you get 2^(4xy)

If xy=1, then the expression becomes 2^4=16.

D.
Senior Manager
Joined: 12 Mar 2006
Posts: 367
Schools: Kellogg School of Management
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Re: PS [#permalink]  16 Feb 2007, 20:58
buckkitty wrote:
if 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

I think you mean 2^((x+y)^2)/2^((x-y)^2)

If this is the case, then

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

2^A/2^B=2^(A-B)

Substitute A and B and you get 2^(4xy)

If xy=1, then the expression becomes 2^4=16.

D.

this makes sense... the question as it is will not give a numerical solution...
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Location: Boston, MA
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[#permalink]  17 Feb 2007, 10:53
no wonder I couldnt solve it. I had this problem written in my error log incorrectly.

as ncprasad correctly pointed out, the question should be as follows:

if 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
[#permalink] 17 Feb 2007, 10:53
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# if xy=1, what is the value of 2(x+y)^2/2(x-y)^2? A. 2 B. 4

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