if xy > 0 both x and y has to have same sign,clearly from either statements we cannot conclude this.
combining
x>y-2 and x<2y-6

so 2y-6>y-2
or y>4..so y is positive

x>4-2 or x>2..hence x is also positive..so xy>0..sufficient

Ans option C

liferocks wrote:if xy > 0 both x and y has to have same sign,clearly from either statements we cannot conclude this.
combining
x>y-2 and x<2y-6

so 2y-6>y-2
or y>4..so y is positive

x>4-2 or x>2..hence x is also positive..so xy>0..sufficient

Ans option C

LR how did u decide X>4-2???

since y > 4
he substituted the value of y in the inequality x > y - 2
x > 4 - 2
x > 2
hence C

Liferock's explanation is great.

An alternative in merging statements is to do the following:

(1) x-y > -2
(2) x-2y < -6

Multiply (1) by -2 to get -2x+2y < 4. Add this to (2) and you'll end up with -x<-2 --> x>2
Multiply (2) by -1 to get -x+2y > 6. Add this to (1) and you'll end up with y>4

So x>2 and y>4. We have enough data to know that xy>0. The answer is C

A video solution is available at GMATPrep question 1125

Good luck,
-Patrick