Data Sufficiency

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Statement 1:
2x - 2y = 1
x - y = 1/2
x = y + 1/2

This tells us that x is a little bigger than y. It does not tell us about the sign of x or y. Insufficient.

Statement 2:
x/y > 1
This tells us that x/y is positive, which means that x and y have the same sign. It does not tell us about the sign of x or y. Insufficient.

Combined:
I like to look for opportunities to use algebra when combining two statements.

If we plug x = y + 1/2 (from Statement 1) into Statement 2, we get
(y + 1/2)/y > 1
y/y + (1/2)/y > 1
1 + (1/2)/y > 1
(1/2)/y > 0

Since (1/2)/y is positive, y must also be positive, or else (1/2)/y would be negative.
If y is positive, and x = y + 1/2, then x must also be positive. So, both are positive. Sufficient.

IMO:C