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

In order for the whole expression to be negative, either  (x⁵) 
or  (y⁴)  or  (z²)  must be negative.

But an even-numbered power can't be negative ... even if the base
is a negative number, any even-numbered power of it is positive.

So  (y⁴)  and  (z²)  are always positive.  The expression can be
negative if 'x' is negative, because  (x⁵)  will then be negative.

None of the proposed requirements is appropriate, so the
final answer is  E. None .