mod x > mod y

[AshvinV429]

Can someone please provide a solution to this DS problem? source: GMATPrep practice test
Is |x| > |y| ?

(1) X^2 > y^2
(2) X > Y

[Sage Pearce-Higgins]

Statement 2 is easier to deal with, so I'll start there. With inequalities it's often best to test cases, so let me try:
We know that x > y, so we could have x=2 and y=1. Relating it back to the question, note that l2l>l1l, giving the answer "yes" to the question.
However, if we pick some negative numbers, say x=-1 and y=-2 (this agrees with the statement that x>y), we'd get the answer "no" to the question. So statement 2 is insufficient.
Let's test cases for statement 1 as well: e.g. x^2=9, y^2=4, so x=3 and y=2, giving answer "yes" to the question. In fact, even if you tried negative numbers, you wouldn't be able to find a case that gives answer "no" to the question. So statement 1 is sufficient and the answer to the problem is A.

If that last step still puzzles you, I suggest that you test some cases yourself (on paper) and then try to understand the rule that's operating in this situation.