Bunuel wrote:
Marcab wrote:
If a is non-negative, is x^2 + y^2 > 4a ?
(1) (x + y)^2 = 9a
(2) (x - y)^2 = a
Source: Jamboree
I am not convinced with the OA.
If a is non-negative, is x^2 + y^2 > 4a ?(1) (x + y)^2 = 9a --> x^2+2xy+y^2=9a. Clearly insufficient.
(2) (x – y)^2 = a --> x^2-2xy+y^2=a. Clearly insufficient.
(1)+(2) Add them up 2(x^2+y^2)=10a --> x^2+y^2=5a. Also insufficient as x, y, and a could be 0 and x^2 + y^2 > 4a won't be true, as LHS and RHS would be in that case equal to zero. Not sufficient.
Answer: E.
Hi Bunel,
Can you please explain where am I going wrong:
(x^2+y^2) = x^2+2xy+y^2 = 9a..........(1)
x^2+y^2 >= 2xy ..........(2)
Substitute equation 2 in 1
Thus, (x^2+y^2+x^2+y^2) = 2(x^2+y^2) >= 9a
2(x^2+y^2) >= 9a
Finally, (x^2+y^2) >= 4.5a. Sufficient
(2) (x – y)^2 = a --> x^2-2xy+y^2=a. Clearly insufficient.
Answer: A