If you're experiencing a roadblock with one of the Manhattan Prep GRE math strategy guides, help is here!
franalej
Students
 
Posts: 21
Joined: Mon Jun 24, 2013 5:59 pm
 

GRE 5 lb. Guide - Chapter 33, Problem 5, page 1158

by franalej Wed Sep 18, 2013 6:33 pm

The problem asks the following QC question:

xy>0 and yz<0

Quantity A

xz

Quantity B

0



According to the book the answer is B, however I get answer D and my logic is as fallows:

Since xy>0 then x and y have the same sign, either ++ or --

Since yz<0, then y and z have oppositive signs, either +- or -+.

For xz, from the previous could x be positive (because x can be + or -) and z be also positive (because z can be + or -), and then xz can also be positive: ++ or --? If so, then the answer is D because xz can be less than 0 (negative) or more than 0 (positive), but not equal to 0. Is this right?

Thanks,

-f
chicku11
Students
 
Posts: 1
Joined: Mon Sep 09, 2013 3:02 pm
 

Re: GRE 5 lb. Guide - Chapter 33, Problem 5, page 1158

by chicku11 Thu Sep 19, 2013 2:46 am

Since both conditions apply simultaneously, I have the following reasoning-
yz < 0
Case 1- y is negative and z is positive.
Since y is negative and xy > 0 must mean x is also negative.
thus xz < 0
Case 2- y is positive and z is negative.
As y is positive and xy > 0 must mean x is also positive.
so xz < 0.
In both cases xz<0 justifying the answer given.
Hope this helps.
franalej
Students
 
Posts: 21
Joined: Mon Jun 24, 2013 5:59 pm
 

Re: GRE 5 lb. Guide - Chapter 33, Problem 5, page 1158

by franalej Thu Sep 19, 2013 9:52 am

Thanks chicku11, your explanation helps.

-f

chicku11 Wrote:Since both conditions apply simultaneously, I have the following reasoning-
yz < 0
Case 1- y is negative and z is positive.
Since y is negative and xy > 0 must mean x is also negative.
thus xz < 0
Case 2- y is positive and z is negative.
As y is positive and xy > 0 must mean x is also positive.
so xz < 0.
In both cases xz<0 justifying the answer given.
Hope this helps.
tommywallach
Manhattan Prep Staff
 
Posts: 1917
Joined: Thu Mar 31, 2011 11:18 am
 

Re: GRE 5 lb. Guide - Chapter 33, Problem 5, page 1158

by tommywallach Wed Sep 25, 2013 2:48 pm

Hey Frana,

Indeed. It should be obvious that x cannot simultaneously be both negative and positive. If they discuss the same variable in two different places, it's always the same variable, so cannot contradict itself in terms of its properties.

Good luck!

-t