number properties

[sud21]

xyz>0, is xy^2z^3>0 ?
1). y>0
2). x>0

[avik.ch]

We are given xyz > 0

we need to find whether xy^2z^3>0.

y^2 is always positive. x and z^3 can be both nagative and positive, depending on the value of x and z.

A. Y > 0 , the xyz > o : x and y has to be either both positive or both nagative. Hence
X and z^3 are of same sign. hence sufficient.

B. X > 0, xyz>0 : y and z has to be either both nagative or both positive.
Y^2 is always positive.
Z^3 can be positive or nagative. - the value of z will determine the inequality ( xy^2z^3>0) in this case.
this is insufficient.

hence A.