Data Sufficiency

if x^2>y^2, is x>y

1) IxI>y
2) IyI<x.

x^2 > y^2 tells you that |x| > |y|
It doesn't tell you whether either one is positive or negative.

How do we figure out whether x is bigger than y?
In this case it all depends on x.
If x is positive, it will be bigger than y, regardless of the sign of y.
If x is negative, it will be smaller than y, regardless of the sign of y.
These statements are true because x has the bigger absolute value, so it is farther from zero, whether to the left (neg) or to the right (pos).

Statement 1 [spoiler]doesn't tell us the sign of x, so it's insufficient.[/spoiler] [spoiler]It's pretty easy to find examples one way or the other here. x = 1 or -1, y = 0.[/spoiler]

Statement 2 does tell us that x is positive, and that it is bigger than abs(y), [spoiler]which means it will be bigger than y, regardless of the sign of y, since y can't be any bigger than |y|. [/spoiler]Sufficient.