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1. (x+y) / 2 > 0 => x+y>0 With e.g. Above condn is satisifed for the following (x,y) pairs: (2,-1), (1,2), (-1,2) So, in one case x>y and in the other two, y>x Hence, insufficient.

2.(y-x)(y+x) > 0 With e.g. Above can be re-written as y^2>x^2. There can be 4 pairs of (x,y) which will satisfy this condn, viz. (-1,-2), (1,2), (-1,2), (1,-2) Hence, insufficent

Combining both 1 & 2, we get 2 choices for (x,y) : (1,2) & (-1,2). In both cases y>x.

I used co-ordinate axis to solve this. To look at my approach, please have a look at the similar problem, where I have explained my method with a diagram. http://www.gmatclub.com/forum/7-t63218