official explanation

answer E. In this Positive/Negative Number Properties problem, the question "is xyz > 0?" is really asking if any of the following are true: -All of x, y, and z are positive -Exactly two of x, y, and z are negative (with one as positive)

Those are the combinations that will lead to a positive product xyz (if one or three of the variables are negative, the product will be negative).

From statement 1, you can factor it to y(x + z) > 0, but this still allows for multiple possibilities: All could be positive, or all could be negative and the left side would look like:

Negative(Negative Sum) > 0 -----> So statement 1 is not sufficient.

For statement 2, this tells you that either:

-Both x and z are positive (which would allow for y to be either negative or positive, allowing for two different answers) or -Both x and z are negative (which would give a positive product for xyz if y were positive, or a negative product if y were negative) So statement 2 is not sufficient.

Even taking both statements together there remains a possibility of either product. If you go back to the factored inequality from statement 1: y(x + z) > 0

And incorporate what you learned from statement 2, that "x and z have the same sign":

If both x and z are positive, then y is positive and the product xyz is positive. If both x and z are negative, then y is negative and the product xyz is negative. Because both answers, positive and negative, are possible, you do not have sufficient information and the correct answer is E.