There is no math at all!
The question and answer choces are as easy as possible
(1) x > y indicates that y is positive, so x > |y| is true. So (1) is sufficient
(2) if y < 0 then x is positive and |x|>|y|. Suficient
I don't understand your explanation. In (1), y does not have to be positive. Consider x = 2 and y = -1. In (2), just because X is positive doesn't explani why x > |y|.
Here is my solution:
We are given x + y > 0. This is the same as
x > -y
(1) x > y. If x > y AND x > -y, then x > |y|
(2) y < 0. This means that |y| = -y. Hence, substituting into x > -y we get x > |y|.
Former Senior Instructor, Manhattan GMAT and VeritasPrep
Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993