Is xyz>0?

[Max@Math Revolution]

Is xyz>0?
1) xy>0
2) yz>0

[Brent@GMATPrepNow]

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

[Max@Math Revolution]

==>In the original condition, the answer is highly likely to be E with 3 variables (x,y,z). If you do 1)&2), you get x=y=z=1 yes, and x=y=z=-1, hence no, and not suffi. Thus, the answer is E.

Answer: E

- Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a solution.

[Scott@TargetTestPrep]

Is xyz>0?
1) xy>0
2) yz>0

We need to determine whether xyz > 0.

Statement One Alone:

xy>0

We see that either:

x = negative and y = negative

OR

x = positive and y = positive

However, without any information regarding z, we cannot answer the question.

Statement Two Alone:

yz > 0

We see that either:

y = negative and z = negative

OR

y = positive and z = positive

However, without any information regarding x, we cannot answer the question.

Statements One and Two Together:

Using our statements together, we see:

When x = negative, y = negative, and z = negative, xyz is less than zero.

When x = positive, y = positive, and z = positive, xyz is greater than zero.

So, statements one and two together are not sufficient to answer the question.

Answer: E