yeahwill wrote:

Is \(x^3y^2z\)>0?

1. \(yz>0\)

2. \(xz<0\)

a. Statement (1) ALONE is sufficient, but Statement (2) ALONE is not sufficient

b. Statement (2) ALONE is sufficient, but Statement (1) ALONE is not sufficient

c. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is sufficient

d. EACH statement ALONE is sufficient

e. Statements (1) and (2) TOGETHER are NOT sufficient

Statement (1) by itself is insufficient. It allows \(x=0\) .

Statement (2) by itself is insufficient. It allows \(y>0\) and \(y<0\) .

Statements (1) and (2) combined are sufficient. S1 and S2 give that is not 0 and thus \(x^3y^2z\)>0 .

The correct answer is C.

Can someone please simplify this for me?

I am completely stumped even after reading the explanation

Because x has an odd exponent, x^3 can be negative or positive or 0

Because y has an even exponent y^2 will be positive or 0

z can be positive or negative or 0

1. yz > 0 means both are positive or both negative but we know nothing about x, which can be positive, negative, or 0

2. xz< 0 means one is negative and one is positive which would make you think you have sufficient information because y^2 will also be positive, but it can also be zero in which case you don't have enough information

Together we know nothing is zero.