IMO C
XY>0 i.e x and y positive OR x and y negative
and YZ<0 i.e y positive and z negative OR y negative and z postive
so cases:
1)x,y positive and z negative
2)x,y negative and z positive
answer options:

A) XYZ - positive when we use the 2nd case
B) XYZ^2 -positive in any case
C) XY^2Z -correct
D) XY^2Z^2 -positive when we use the 1st case

lol...yeah so obvious...after doing a zillion of such calculations, I still screw up.

thanks for the feed back.

deltaforce wrote:lol...yeah so obvious...after doing a zillion of such calculations, I still screw up.

thanks for the feed back.

XYZ can be viewed in this way: YZ<0, X can be positive or negative so not a must.

Thinking XYZ as (XY)Z do create issue

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

XY >0 -------------> X and Y are of the same sign

YZ <0 ------------------> Y and Z are of different signs , that means Y and X are of different signs

We know that X, Y or Z to the power 2 > 0 so lets look at the answer choices

It must Be a must



A ----------> XYZ , XY>0 so X and Y can be negative hence Z can be positive so A can be positive , there is no must --------> A is out

B -----------> XYZ^2 we know that XY >0 and Z^2 >0 so B is definitely not the answer

C --------> XY^2Z = XY*YZ but XY and YZ are of opposite sign hence C is always <0 hence C is the answer

D --------> XY^2Z^2 = X(YZ)^2 but (YZ)^2 is always >0 and X can be positive or negative so D is not a must

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