Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Re: GMATprep Inequalities [#permalink]
28 Jan 2010, 02:51

6

This post received KUDOS

An easy way to approach this ineq will be to analyze that: |x-z| + |x| = |z| means |z-x| = |z| - |x|. |z-x| is the distance between z and x on number line. It can only be equal to |z| - |x| if both z and x have the same signs.

a) z < x - implies that y > 0 because zy < xy. If y > 0 then z < x < 0. Therefore both have same signs. SUFF

b) y>0 then z < x < 0. Therefore both have same signs. SUFF

Re: GMATprep Inequalities [#permalink]
28 Jan 2010, 05:14

5

This post received KUDOS

Expert's post

1

This post was BOOKMARKED

This question was discussed before here is my post from there:

This is not a good question, as neither of statement is needed to answer the question, stem is enough to do so.

If \(zy<xy<0\) is \(|x-z|+|x| = |z|\)

Look at the inequality \(zy<xy<0\):

We can have two cases:

A. If \(y<0\) --> when reducing we should flip signs and we'll get: \(z>x>0\). In this case: as \(z>x\) --> \(|x-z|=-x+z\); as \(x>0\) and \(z>0\) --> \(|x|=x\) and \(|z|=z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(-x+z+x=z\) --> \(0=0\), which is true.

And:

B. If \(y>0\) --> when reducing we'll get: \(z<x<0\). In this case: as \(z<x\) --> \(|x-z|=x-z\); as \(x<0\) and \(z<0\) --> \(|x|=-x\) and \(|z|=-z\).

Hence in this case \(|x-z|+|x|=|z|\) will expand as follows: \(x-z-x=-z\) --> \(0=0\), which is true.

So knowing that \(zy<xy<0\) is true, we can conclude that \(|x-z|+|x| = |z|\) will also be true. Answer should be D even not considering the statements themselves.

As for the statements:

Statement (1) says that \(z<x\), hence we have case B.

Statement (2) says that \(y>0\), again we have case B.

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink]
17 Dec 2013, 03:17

I solved this question on number line, we can first analyze this eq |x-z| + |x| = |z|? This equality is only possible, if x and z are on the same side of the number line.

(-) ----z----x----0--- or ---0-----x----z---- (+)

|distance between xandz| + |distance of x from origin| = |distance of z from origin|

given zy<xy<0 which can happen in two case.

z x y - - + zy negative xy negative < both less than 0 + + - zy negative xy negative < both less than 0

Therefore we don't even need option 1 and 2 to validate this |x-z| + |x| = |z|.

Answer : D _________________

Piyush K ----------------------- Our greatest weakness lies in giving up. The most certain way to succeed is to try just one more time. ― Thomas A. Edison Don't forget to press--> Kudos My Articles: 1. WOULD: when to use?| 2. All GMATPrep RCs (New) Tip: Before exam a week earlier don't forget to exhaust all gmatprep problems specially for "sentence correction".

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink]
10 May 2014, 11:04

using Statement 1 : from the question , zy < xy y(z-x)<0 ------- (A) Now statement 1 tells me that (z-x)< 0 . This implies Y>0 So, if zy < xy < 0 and Y>0 This implies Z & X < 0 mod (x-z) + mod (x) = X-Z (since Z-X<0) + (-X) = -Z = |Z|

Using Statement 2 : From (A), y(z-x)<0 Since from Statement 2 we know that y > 0 That implies (z-x)< 0 .

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink]
16 May 2015, 06:49

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________

Hey, everyone. After a hectic orientation and a weeklong course, Managing Groups and Teams, I have finally settled into the core curriculum for Fall 1, and have thus found...

MBA Acceptance Rate by Country Most top American business schools brag about how internationally diverse they are. Although American business schools try to make sure they have students from...

For the past couple of weeks I’ve been winding down my affairs in New York by working on consulting projects, trying every exotic sandwich there is and then intensely...