Question

If x5y4z2 <0 , which of the following must be true?

I xy <0
II yz <0
III xz <0
A. I
B. II
C. III
D. I and II
E. None

Answer 1

interesting, this question is simple but also hardly to me.

x^5y^4z^2 <0
x(x^4y^4z^2) < 0
x (x^2 y^2 z)^2 < 0

here, x must be negative. while in parantheses can be positive or negative.

so,
if x^2 y^2 z positive, it means
x^2 y^2 z > 0
(xy)^2 z > 0
here, z must be positive and xy can + or -

if x^2 y^2 z negative, then
x^2 y^2 z < 0
(xy)^2 z < 0
here, z must be negative and xy can be po(+) or ne(-)

thus,
i would chose E, NONE