Max@Math Revolution wrote:Is xyz > 0?
1) xy > 0
2) yz > 0
Target question: Is xyz > 0?
Statement 1: xy > 0
Since there's no information about z,
we cannot determine whether xyz > 0.
Since we cannot answer the
target question with certainty, statement 1 is NOT SUFFICIENT
Statement 2: yz > 0
Since there's no information about x,
we cannot determine whether xyz > 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 xy > 0
There are two possible scenarios:
scenario 1: x and y are both positive
scenario 2: x and y are both negative
Statement 2 tells us that yz > 0
There are two possible scenarios:
scenario 3: y and z are both positive
scenario 4: y and z are both negative
So, when we consider the statements COMBINED, we see that EITHER scenarios 1 and 3 can occur, OR scenarios 2 and 4 can occur.
Let's see what happens with each possible pair:
Scenarios 1 and 3: x, y, and z are all positive, in which case xyz = (POSITIVE)(POSITIVE)(POSITIVE) = POSITIVE. In other words,
xyz > 0
Scenarios 2 and 4: x, y, and z are all negative, in which case xyz = (NEGATIVE)(NEGATIVE)(NEGATIVE) = NEGATIVE. In other words,
xyz < 0
Since we cannot answer the
target question with certainty, the combined statements are NOT SUFFICIENT
Answer:
C
RELATED VIDEO
- Operations with signed numbers - part II:
https://www.gmatprepnow.com/module/gmat ... video/1060
