bobdylan wrote:How do we attack this kind of problem????

Is | x^2 + y^2| > | x^2 - y^2|?
(1) x > y
(2) x > 0

The inequality | x^2 + y^2| > | x^2 - y^2| does not hold true when either one or both of x and y are equal to 0.
When x = 0,
|0 + y^2| = |0 - y^2|

When y = 0,
|x^2 + 0| = |x^2 - 0|

When both x and y are non-zero,
|x^2 + y^2| > |x^2 - y^2|

Therefore, the answer to the question is YES when both x and y are non-zero. If one of them is 0, the answer is NO.

Statement(1):
Does not tell if x or y are 0 or not.
INSUFFICIENT

Statement(2):
x is NOT equal to 0, but y can be 0.
INSUFFICIENT

Let's combine,
x > 0 AND x > y
y can still be 0 or not.
INSUFFICIENT

[spoiler](E)[/spoiler] is correct.