Problem Solving

You can certainly break this down into cases - that's a perfectly good approach here - but if xy > 0, and yz < 0, then (xy)(yz) is the product of a positive and a negative, so must be negative. Notice of course that (xy)(yz) = x(y^2)z = Answer Choice C.

deltaforce wrote:This is a gmatquant focus problem


IF XY>0 and YZ<0, Which of the following must be negative?

A) XYZ
B) XYZ^2
C) XY^2Z
D) XY^2Z^2

Since xy > 0 and yz < 0, we see the following:

When xy > 0:

x = positive and y = positive

or

x = negative and y = negative

When yz < 0:

y = negative and z = positive

or

y = positive and z = negative

Putting our two statements together:

1) When x is positive, y is positive and z is negative

2) When x is negative, y is negative and z is positive.

Using those two statements, let's determine which answer choice must be true.

A) Is xyz negative?

Using statement two, we see that xyz does not have to be negative.

B) Is (x)(y)(z^2) negative?

In order for answer choice B to be true, xy must be negative. However, both statements one and two prove that xy is not negative.

C) Is (x)(y^2)(z) negative?

In order for answer choice C to be true, xz must be negative. Looking at both statements one and two, we see that in either statement xz is negative. Thus, answer choice C is true. We can stop here.

Answer: C