abhasjha wrote:wxy > 0 ; xyz<0

Is Z>0 ?

(1) x > 0
(2) y > 0

We can rewrite the given information as xyz < 0 < wxy
Since we know that wxy is POSITIVE, we can divide all three sides by wxy to get: xyz/wxy < 0 < 1
Simplify to get: z/w < 0 < 1
NOTICE that the x and y cancel out. This tells us that x and y don't affect the inequality. That's a great hint.

Target question: Is z > 0

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

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

Statements 1 and 2 combined
Statement 1 tells us that x is POSITIVE
Statement 2 tells us that y is POSITIVE
The GIVEN information tells us that xyz < 0
In other words, we have (POSITIVE)(POSITIVE)(z) < 0
From this, we can conclude, with certainty, that z is NEGATIVE
In other words, it is definitely NOT the case that z > 0
Since we can answer the target question with certainty, the combined statements are SUFFICIENT

Answer = C

Cheers,
Brent

Hi abhasjha,

This DS question is based heavily on Number Properties; if you're willing to do some thorough work "up front", you can handle the rest of the work rather quickly and easily.

We're told that XYZ < 0 < WXY. We're asked if Z > 0. This is a YES/NO question.

Notice that X and Y appear in both products, and that we're dealing with a product that is negative (XYZ) and a product that is positive (WXY).

For XYZ to be negative, EITHER all 3 terms are negative OR 1 is negative and 2 are positive.
For WXY to be positive, EITHER all 3 terms are positive OR 1 is positive and 2 are negative.

There are actually only 4 possible ways for the above inequality to be true.

1) W = Positive, X = Positive, Y = Positive, Z = Negative
2) W = Positive, X = Negative, Y = Negative, Z = Negative

3) W = Negative, X = Negative, Y = Positive, Z = Positive
4) W = Negative, X = Positive, Y = Negative, Z = Positive

With this "table" of data, we can now work through the rest of the prompt:

Fact: 1: X > 0

Since X is positive, we're limited to options 1 (Z is NEGATIVE; Answer is "NO") and 4 (Z is POSITIVE; Answer is "YES").
Fact 1 is INSUFFICIENT

Fact 2: Y > 0

Since Y is positive, we're limited to options 1 (Z is NEGATIVE: Answer is "NO") and 3 (Z is POSITIVE; Answer is "YES").
Fact 2 is INSUFFICIENT

Combined, we know that X and Y are both POSITIVE, which leave us with just one possibility: Option 1. The answer to the question is NO.
Combined, SUFFICIENT.

Final Answer: C

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