SOLUTION: If (x^2)(y^3)z < 0, which of the following statements must be true? I. yz < 0 II. xz < 0 III. xy < 0 A) I only B) I and II only C) I and III only D) II and III only E)

Algebra ->  Exponents -> SOLUTION: If (x^2)(y^3)z < 0, which of the following statements must be true? I. yz < 0 II. xz < 0 III. xy < 0 A) I only B) I and II only C) I and III only D) II and III only E)       Log On


   

Question 472217: If (x^2)(y^3)z < 0, which of the following statements must be true?
I. yz < 0
II. xz < 0
III. xy < 0
A) I only
B) I and II only
C) I and III only
D) II and III only
E) I, II, III
Please explain how I could approach this (ie. plugging in numbers?...) and why the answer is correct.
Thanks!
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
II and III do not have to be true, since x could be either positive or negative, and whatever sign y has, x could have that same sign, and xy > 0.

However, I has to be true. Divide both sides by (x^2)(y^2) (a positive number), and you will obtain yz < 0.