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Gmatfocus

by deltaforce » Fri Jul 17, 2009 5:48 am
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

ORG answer is c

I think A satisfies as well since xy are either positive or negative. and whichever way the sign of y is in relation to x and xy>0, the sign for Z has to be opposite.

thanks
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by tohellandback » Fri Jul 17, 2009 6:00 am
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
The powers of two are bloody impolite!!
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Thanks

by deltaforce » Fri Jul 17, 2009 7:53 am
lol...yeah so obvious...after doing a zillion of such calculations, I still screw up.

thanks for the feed back.
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Re: Thanks

by maihuna » Fri Jul 17, 2009 8:47 am
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
Charged up again to beat the beast :)
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by ghacker » Fri Jul 17, 2009 10:07 am
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
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by Ian Stewart » Fri Jul 17, 2009 11:40 am
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.
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by Jeff@TargetTestPrep » Tue Dec 12, 2017 5:08 pm
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

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