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If xy = 1

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by babachal » Thu Jun 12, 2008 3:23 pm
Hey, can you give us full question?
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by netigen » Thu Jun 12, 2008 3:38 pm
Question is what is the value of

2^(x + Y)^2)/2^(x - Y)^2
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by egybs » Thu Jun 12, 2008 4:02 pm
ahhhh.. in that case it's easy!

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

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

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

2^(4xy)

which as we know is equal to 2^4... so 16.
Last edited by egybs on Thu Jun 12, 2008 4:21 pm, edited 1 time in total.
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by babachal » Thu Jun 12, 2008 4:17 pm
egybs, you did mistake in the last step

2^(x^2+2xy+y^2-x^2+2xy-y^2)+2^4xy=2^4=16
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by egybs » Thu Jun 12, 2008 4:20 pm
oops! yep. i did.
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by s_raizada » Fri Jun 13, 2008 1:36 am
Hi guys,
question is not what you are calculating. See the screenshot of the question and it is form GMAT prep
You do not have the required permissions to view the files attached to this post.
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by AleksandrM » Fri Jun 13, 2008 9:19 am
Undifined or 25/9????? :?
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by egybs » Fri Jun 13, 2008 9:32 am
Can you give us the answer options...
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by Ian Stewart » Fri Jun 13, 2008 11:23 am
As has been posted elsewhere, there's a typo in the question itself. The solution posted above by netigen, with the x and y terms in the exponents, presented the question in the way it's supposed to be written.
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by GMAT dreamer » Tue Nov 18, 2008 12:16 pm
We can make things simpler...
If xy=1; it tells that x=1 and y=1, right?

so, 2^(1+1)^2/2^(1-1)^2=
2^2^2/2^0^2=
2^4/2^0=
16/1= 16

Very simple we put numbers.
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by cramya » Tue Nov 18, 2008 3:40 pm
If xy=1; it tells that x=1 and y=1, right?
In general if xy=1 does not necessarily mean x=1 and y=1 unless there are other properties about x and y also given that confirms the fact that x=1 y=1

To quote a few:

x=-1 y=-1 xy=1

x=5 y=1/5 xy =1

x=-5 y=-1/5 xy=1

Unless it says x and y are positive integers and xy=1 we cannot assume
x=1 and y=1

Hope this helps!
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by rochy81 » Sun Aug 16, 2009 1:02 pm
Ahh, I was just stuck on this. I'm kicking myself...
Anyone happen to know what the difficulty of this question is?
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