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REALLY need explanation!

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by linfongyu » Thu Dec 17, 2009 11:36 pm
What is the value fo x^2 + y^2?

1) x^2 + y^2 = 2xy + 1
2) x^2 + y^2 = 4 - 2xy

Here's the answer OA is E

Here's my logic. [spoiler]I think it's C. It's clear that stem 1 is equal to (x-y)^2 = 1, and stem 2 is (x+y)^2 = 4. Each on its own is insufficient. But if you can solve for 2xy, then you know the answer. Setting the 2 equations equal to each other and solving for xy, which is equal to 3/4, and thus the answer to x^2 + y^2 = 2*3/4 + 1 = 4 - 2*3/4. What's wrong with this logic?

Please help...[/spoiler]
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by Stuart@KaplanGMAT » Fri Dec 18, 2009 1:05 am
linfongyu wrote:What is the value fo x^2 + y^2?

1) x^2 + y^2 = 2xy + 1
2) x^2 + y^2 = 4 - 2xy

Here's the answer OA is E

Here's my logic. [spoiler]I think it's C. It's clear that stem 1 is equal to (x-y)^2 = 1, and stem 2 is (x+y)^2 = 4. Each on its own is insufficient. But if you can solve for 2xy, then you know the answer. Setting the 2 equations equal to each other and solving for xy, which is equal to 3/4, and thus the answer to x^2 + y^2 = 2*3/4 + 1 = 4 - 2*3/4. What's wrong with this logic?

Please help...[/spoiler]
What's the source and what's the official explanation?

Your logic seems sound to me.
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by linfongyu » Fri Dec 18, 2009 1:18 am
Jeff Sackmann's Challenging sets. His explanation is attached.


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by Stuart@KaplanGMAT » Fri Dec 18, 2009 1:28 am
linfongyu wrote:Jeff Sackmann's Challenging sets. His explanation is attached.


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Sounds like the moral of the story is: Jeff's challenging sets are too challenging for Jeff. Too bad, this is actually a very difficult question and the proper solution is interesting.

Never heard of him before, but I'm not impressed so far!
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by kevincanspain » Thu Dec 24, 2009 7:00 pm
linfongyu wrote:What is the value fo x^2 + y^2?

1) x^2 + y^2 = 2xy + 1
2) x^2 + y^2 = 4 - 2xy

Here's the answer OA is E

Here's my logic. [spoiler]I think it's C. It's clear that stem 1 is equal to (x-y)^2 = 1, and stem 2 is (x+y)^2 = 4. Each on its own is insufficient. But if you can solve for 2xy, then you know the answer. Setting the 2 equations equal to each other and solving for xy, which is equal to 3/4, and thus the answer to x^2 + y^2 = 2*3/4 + 1 = 4 - 2*3/4. What's wrong with this logic?

Please help...[/spoiler]
Nothing wrong with your logic: Jeff's explanation is also good, except for the fact that we are asked for x^2 + y^2 , not for the values of x and y.

Jeff's resources are actually quite good
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