Though goyalsau and beat_gmat_09 provided effective and easy solution to the question, I want to provide some insight into the question. Picking numbers and cross checking the statements is a very common strategy to attack GMAT problems. But don't practice them directly. If you are going for that method then you've to choose the numbers carefully! My suggestion is: First go through the basics, Strengthen your concepts and then go for the shortcuts. If your concepts are clear, you'll never make a wrong assumption.
Statement 1: 2x - 2y = 1
Implies (x - y) = 1/2. This means the only case that is not possible is x negative and y positive. In that case the LHS will be negative always! So the possible cases are (with examples),
- (1) x positive, y positive (x = 4.5, y = 4)
(2) x positive, y negative (x = 0.25, y = -0.25)
(3) x = 0.5, y = 0
(4) x = 0 , y = -0.5
(5) x negative, y negative (x = -4, y = -4.5)
(Note : In each case there is also some constraints. Like in the 1st case, not for all positive x, y the relation will hold! x must be equal to (y + 0.5) etc.)
Not sufficient.
Statement 2: (x/y) > 1
Again this implies any one of the following two cases,
- (1) Both of them are positive and x > y
(2) Both of them are negative and x < y
Not sufficient.
1 & 2 Together: Statement 2 limits the number of possible cases to two. Let's analyze them again with the help of statement 1.
- (1) Both of them are positive and x > y => (x - y) = 0.5 is possible.
(2) Both of them are negative and x < y => (x - y) will be always negative. Not possible.
Thus, x and y are both positive.
Sufficient.
The correct answer is C.
