Hi pims,

This DS question is perfect for TESTing VALUES.

We're asked if XY > 0? This is a YES/NO question.

Fact 1: X - Y > - 2

This can rewritten as:

X + 2 > Y

If X = 1, Y = 1, XY = 1 and the answer to the question is YES
If X = 1, Y = 0, XY = 0 and the answer to the question is NO
Fact 1 is INSUFFICIENT

Fact 2: X - 2Y < -6

This can be rewritten as:

X + 6 < 2Y

If X = 0, Y = 4, then XY = 0 and the answer to the question is NO
If X = 1, Y = 4, then XY = 4 and the answer to the question is YES
Fact 2 is INSUFFICIENT

Combined, we know:
X + 2 > Y
X + 6 < 2Y

2Y - 6 > X > Y - 2

From this, with a bit of "tinkering", we can deduce that...

Y CANNOT be 0, since -6 > X > -2 is impossible
Y CANNOT be negative (it would create the same "impossible" situation)
Y MUST be > 4

Since Y > 4, then X > 2

This means that X and Y are BOTH POSITIVE, so the answer to the question is ALWAYS YES.
Combined, SUFFICIENT

Final Answer: C

GMAT assassins aren't born, they're made,
Rich

pims wrote:Is xy > 0?

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

Target question: Is xy > 0?

Statement 1: x - y > -2
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 1, in which case xy = (1)(1) = 1. Here, xy > 0
Case b: x = 1 and y = -1, in which case xy = (1)(-1) = -1. Here, xy < 0
Since we cannot answer the target question with certainty, statement 1 is NOT SUFFICIENT

Statement 2: x - 2y < -6
There are several values of x and y that satisfy this condition. Here are two:
Case a: x = 1 and y = 10, in which case xy = (1)(10) = 10. Here, xy > 0
Case b: x = -10 and y = 1, in which case xy = (-10)(1) = -10. Here, xy < 0
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Statements 1 and 2 combined
Statement 1: x - y > -2
Statement 2: x - 2y < -6

IMPORTANT: We can solve this system of inequalities (through addition) as long as we get the INEQUALITIES FACING THE SAME DIRECTION first.

Keep statement 1 as is: x - y > -2
Multiply statement 2 by -1 to get: -x + 2y > 6
ADD the inequalities to get: y > 4
In other words, y IS POSITIVE

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Let's do this one more time.
Statement 1: x - y > -2
Statement 2: x - 2y < -6

Multiply statement 1 by 2 to get: 2x - 2y > -4
Multiply statement 2 by -1 to get: -x + 2y > 6
ADD the inequalities to get: x > 2
In other words, x IS POSITIVE

If x and y are BOTH POSITIVE, we can be certain that xy > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent