We can rewrite the given information as xyz < 0 < wxyabhasjha wrote:wxy > 0 ; xyz<0
Is Z>0 ?
(1) x > 0
(2) y > 0
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
