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:

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