Is x^2 + y^2 6? (1) (x + y)^2 6 (2) xy = 2

Question

Is x^2 + y^2 > 6?

(1) (x + y)^2 > 6
(2) xy = 2

Donnie84 · Answer

St1: (x + y)^2 > 6 If x = 1 and y = 2, (x + y)^2 > 6 but x^2 + y^2 < 6. We have a no. If x = 100 and y = 200, (x + y)^2 > 6 and x^2 + y^2 > 6. We have a yes. Insufficient. St2: xy = 2 If x = 1 and y = 2, (x + y)^2 > 6 but x^2 + y^2 < 6. We have a no. If x = 4 and y = 1/2, (x + y)^2 > 6 and x^2 + y^2 > 6. We have a yes. Insufficient. St1 + St2: Since (x + y)^2 = x^2 + y^2 + 2xy (x + y)^2 > 6 x^2 + y^2 + 2xy > 6 x^2 + y^2 + 4 > 6 x^2 + y^2 > 2 Insufficient. Answer (E).

Maverickhemant · Answer

Lets go with a different approach with this question
Try solving it with C
x^2+y^2+2xy>6
x^2+y^2+2.2>6
x^2+y^2>2

Clearly after putting everything in the equation ,you still can't have definately yes or definately no
So E

DharLog · Answer

(1) (x + y)^2 > 6 ---> x^2 + y^2 + 2x*y > 6 
We can see that if 2x*y < 0 then x^2 + y^2 > 6 (because in this case y^2 + 2x*y > 6 + something positive)
In other scenario we can not tell anything ---> insuff

(2) xy = 2 
We have already analyzed this case. It is insuff

So the answer is E.

If (2) were xy = -2, the answer would be C

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Is x^2 + y^2 > 6? (1) (x + y)^2 > 6 (2) xy = 2

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