Statement 1: 2x - 2y = 1
Lets take an example: 4 - 3 = 1 OR (-4) - (-5) = 1.
Thus we can't say for sure if X and Y are positive.
Also: 1 - 0 = 1 and 0 - (-1) = 1. So, both need not be positive or negative simultaneously.

Statement 2: (x/y) > 1
This means that either both X and Y are positive (in which case X > Y) OR both X and Y are negative (in which case X < Y). Thus, we still can't say if both X and Y are positive.

Combining 1 and 2:
Firstly we eliminate 1 - 0 = 1 and 0 - (-1) = 1.
Two cases left: both are positive, and both are negative.

In the case where both numbers are negative, Y has to be less than X, but Statement 2 does not allow that. It is only in the case where both numbers are positive that both the equations hold true.

Thus C is the OA.

ps: You might want to attach a smaller file for a screen shot; 2.5 MB does take some time to download.