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To answer this question, it might be useful to use a number line to show the different cases that follow from each statement.

Statement 1: The product of P and Q is greater than 0
i.e., the product is positive. So:
case a) either P & Q are both negative
case b) P & Q are both positive

On a number line, we get:
case a) _____P_Q____0__________
case b) ____________0________P_Q__

Since we have no information about Z, we cannot answer the target question with any certainty.
So, statement 1 is NOT SUFFICIENT


Statement 2: The product of P and Z is less than 0
i.e., the product is negative.
So one is positive and one is negative

On a number line, we get:
case a) _____P______0____Z______
case b) _____Z______0____P______

Since we have no information about Q, we cannot answer the target question with any certainty.
So, statement 2 is NOT SUFFICIENT


Statements 1& 2:
Several cases are possible. Here are two:

On a number line, we get:
case a) _____Z______0____P__Q____ (P is between Q and Z)
case b) _____Z______0____Q__P____ (P is not between Q and Z)
Since we cannot answer the target question with certainty, statements 1 & 2 are NOT SUFFICIENT, so the answer is E

Cheers,
Brent

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Brent Hanneson - GMAT Prep Now instructor
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