Consider first (1) alone.
Let x = 1 and y = ½.
Here 2x - 2y = 1 and x and y are both positive.
Next let x = -1/2 and y = -1.
Here 2x - 2y = 1 and both x and y are negative.
So nothing definite can be said from (1) alone.
Next consider (2) alone.
Let x = 4 and y = 2.
So x/y = 2 > 1 and x and y are both positive.
Next let x = -4 and y = -2.
So x/y = 2 > 1 and x and y are both negative.
So nothing definite can be said from (2) alone.
Next combine both the statements together and check.
On combining we get that x = y + ½.
Or (y + ½)/y > 1.
Or 1/2y > 0.
Or y > 0.
Or x = y + ½ > ½ > 0.
Or x >0.
So on combining we get that both x and y are positive.
The correct answer is (C).