Is xyz 0 ? (1) xy + yz 0 (2) xz 0

Question

Is xyz > 0 ?

(1) xy + yz > 0

(2) xz > 0

Bunuel · Answer

Notice that both statements hold true if all unknowns are positive as well if all unknowns are negative. Now, if x, y, and z are positive then xyz > 0 but if x, y, and z are negative then xyz < 0.

Answer: E.

rango · Answer

xyz>o
= x; y; z # 0
1- xy +yz >0
=y (x+z) >0
= either y> 0 and x+z>0 or both are < 0
Hence NOT SUFFICIENT

2- xz>0
= x >0; z>0 or both are <0
Again no information about y
hence Not sufficient

Taking 1 and 2 together
same scenario exist Hence NOT SUFFICIENT
Ans - E

avohden · Answer

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.

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bumpbot · Answer

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Is xyz > 0 ? (1) xy + yz > 0 (2) xz > 0

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