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Scoretop No. 4 - Q 15 - Squares

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Source: — Data Sufficiency |
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by beny » Sun Aug 26, 2007 6:27 am
Taking the two together, all you know is that x^2+y^2>2.

Therefore, I'd guess E.
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by scholardream » Tue May 01, 2012 4:55 pm
My answer is E
1. (x+y)^2 = x^2 + y^2 + 2xy > 6. We can't determine the value of 2xy -> Not sufficient
2. xy = 2 . x=1, y=2 -> x^2+y^2 < 6 buy x=1/6, y=6 absolutely has bigger value -> Not sufficient
1&2. x^2 + y^2 > 2 but it doesn't mean x^2+y^2 > 6 or <6 -> Not sufficient
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by Anurag@Gurome » Tue May 01, 2012 10:48 pm
akay wrote:Seems easy...but

Is x^2 + y^2 > 6

(1) (x+y)^2 > 6
(2) xy = 2
(1) (x + y)² > 6 implies x² + y² + 2xy > 6
If x² + y² = 5 and 2xy = 3, then x² + y² < 6
If x² + y² = 10 and 2xy = 3, then x² + y² > 6
No definite answer; NOT sufficient.

(2) xy = 2
If x = y = √2, then x² + y² = 4 < 6
If x = 10, y = 1/5, then x² + y² = 100 + 1/25 > 6
No definite answer; NOT sufficient.

Combining (1) and (2), x² + y² + 2xy > 6
x² + y² + 2(2) > 6
x² + y² + 4 > 6
x² + y² > 2
If x² + y² = 5, then x² + y² < 6
If x² + y² = 10 , then x² + y² > 6
No definite answer; NOT sufficient.

The correct answer is E.
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