GMATPrep : Is x > 0 ?

[BlindVision]

Is x > 0 ?

1) xy > 0

2) x + y > 0

OA = C

[Anurag@Gurome]

Is x > 0 ?

1) xy > 0

2) x + y > 0

OA = C

(1) xy > 0 implies that both x and y should be positive or both x and y should be negative. This means x can be positive or negative. Since we don't have a unique answer, so (1) alone is NOT sufficient.

(2) x + y > 0 again implies that x can be positive or negative. So, (2) is alone is NOT sufficient.

Combining (1) and (2), we know that x and y, both cannot be negative becuse if both are negative then x + y < 0, which will be a contradiction. Example: x = -2, y = -3 implies xy = (-2)(-3) = 6 > 0 but x + y = -2 - 3 = -5 < 0.
Hence, we get that x and y have to be positive, or we can say that x > 0. SUFFICIENT.

The correct answer is C.

[gmatboost]

I'm going to use more spoiler tags [spoiler](like this)[/spoiler] so readers can have an additional moment to think on their own before reading the entire explanation. Let me know if this is good or annoying.

Is x > 0 ?
1) xy > 0
2) x + y > 0

Statement 1: If the product of two numbers is positive then the two numbers must ... have the same sign (both positive or both negative). So x could be positive or negative. Insufficient.

Statement 2: If the sum of two numbers is positive, then ... at least one of them must be positive, otherwise the sum would be negative (Neg + Neg = Neg). [spoiler]But, as long as y is big enough to compensate, x could be negative. For example, y = 4, x = -2. Of course, both could be positive. Insufficient.[/spoiler]

Combined: If both have the same sign (Statement 1) and at least one must be positive (Statement 2), then they both must be positive. Sufficient.