Data Sufficiency

Is xy > 0 ?

1. x - y > -2
2. x - 2y < -6

Target question: Is xy>0?

Statement 1: x-y > -2
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 5 and y = 1, in which case xy is greater than 0
Case b: x = 5 and y = -1, in which case xy is not greater than 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y < -6
There are several pairs of numbers that meet this condition. Here are two:
Case a: x = 1 and y = 5, in which case xy is greater than 0
Case b: x = -1 and y = 5, in which case xy is not greater than 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined:
Here's what we know:
x-y > -2
x-2y < -6

Since both inequalities have an x, let's isolate x in both of them to get:
y-2 < x
x < 2y-6

Aside: Notice that I rewrote them so that the 2 inequality symbols are pointing in the same direction.

Now we can combine these inequalities to get: y-2 < x < 2y-6
Next, remove the x to get: y-2 < 2y-6
Then subtract y from both sides and add 6 to both sides to get: 4 < y
Great, we now know that y is positive.
Also, if y-2 < x (and y>4), then we know that x must also be positive
Since we now know that x and y are positive, we can be certain that xy is greater than 0

So, the answer is C

Cheers,
Brent

Mitch, I think you accidentally posted the solution to the wrong question!

I'll add 2 things to Brent's great explanation:

a) As I'm sure you know, any time you see an inequality relative to 0, frame your question in terms of positives and negatives.
Is xy > 0?
Rephrased question: do x and y have the same sign?

Brent gave good examples of testing numbers to prove that x and y could have the same sign or different signs with each statement individually.

b) If you'd prefer not to isolate x first, you can combine the inequalities by simply flipping the second one around:
x - 2y < -6 --> -6 > x - 2y

Now, line up the inequalities and you can add them together:

x - y > -2
-6 > x - 2y
_______________
x - y - 6 > x - 2y - 2

Simplify: -y - 6 > -2y - 2
y - 6 > -2
y > 4

Substitute:
x - (grt 4) > -2
x > 2

x and y are both positive, so together the statements are sufficient.