Data sufficiency question:

Are x and y both positive?

1) 2x - 2y = 1

2) x/y > 1

I thought the answer choice is (E), but it is not correct as per GMATPrep software.

My reasoning was as follows:

Statement (1) can be simplified as

x - y = 1/2. This is NOT SUFFICIENT.

Statement (2) can be re-written as x > y. This is NOT SUFFICIENT

Combining the above 2 statements and taking an example as shown below.

x = -3/2 and y = -2. In this case x > y as per the second statement and x - y = 1/2 as per the second statement. Similarly I could also have an example that satisfies x and y as positive. So I went ahead with answer choice (E).

However what I failed to realize in the above example was that it actually doesn't satisfy the original condition x/y > 1. Because -3/2 divided by -2 will give 3/4 which is less than 1.

So is it correct to re-write the inequality x/y > 1 to x > y?