Find all School-related info fast with the new School-Specific MBA Forum

It is currently 23 Aug 2014, 05:28

Close

GMAT Club Daily Prep

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.

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

If zy < xy < 0, is |x-z| + |x| = |z|?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
5 KUDOS received
Manager
Manager
avatar
Joined: 17 Aug 2009
Posts: 238
Followers: 4

Kudos [?]: 86 [5] , given: 25

GMAT Tests User
If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink] New post 28 Jan 2010, 01:50
5
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  65% (hard)

Question Stats:

30% (02:33) correct 70% (01:39) wrong based on 222 sessions
If zy < xy < 0, is |x-z| + |x| = |z|?

(1) z < x
(2) y > 0

[Reveal] Spoiler:
For zy < xy < 0 to be true, I am counting two possible scenarios

x y z
-ve +ve -ve -------------------1
+ve -ve +ve--------------------2

Statement 1
rules out scenario 2 but scenario 1 is possible.
Now when i substitute the signs of x and z and take them out from the modulus, i get -

(-x + z) + (-x) = (-z)
-2x = -2z
x=z - - -
Therefore in the original equation, |x-z| = 0
and |x| = |z|

-hence sufficient


Statement 2

Again eliminates the possibility of the scenario 2
and hence is sufficient


Am i correct here?
[Reveal] Spoiler: OA
6 KUDOS received
Manager
Manager
avatar
Status: Applying Now
Joined: 21 Nov 2009
Posts: 65
WE: Project Management (Manufacturing)
Followers: 3

Kudos [?]: 45 [6] , given: 3

Re: GMATprep Inequalities [#permalink] New post 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

D is the answer i think
_________________

http://gmatclub.com/forum/insead-campus-visit-debrief-91669.html#p702796

If you like my post, consider giving me a kudos. THANKS!

Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19052
Followers: 3374

Kudos [?]: 24570 [3] , given: 2680

Re: GMATprep Inequalities [#permalink] New post 28 Jan 2010, 05:14
3
This post received
KUDOS
Expert's post
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.

Hope it helps.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

COLLECTION OF QUESTIONS:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS ; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

1 KUDOS received
Intern
Intern
avatar
Joined: 31 Jan 2010
Posts: 14
Followers: 0

Kudos [?]: 1 [1] , given: 0

Re: GMATprep Inequalities [#permalink] New post 31 Jan 2010, 11:40
1
This post received
KUDOS
wow, I solved this question by myself:)
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 152 [1] , given: 254

GMAT ToolKit User
Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink] New post 27 Nov 2013, 07:32
1
This post received
KUDOS
zaarathelab wrote:
If zy < xy < 0, is |x-z| + |x| = |z|?

(1) z < x
(2) y > 0

[Reveal] Spoiler:
For zy < xy < 0 to be true, I am counting two possible scenarios

x y z
-ve +ve -ve -------------------1
+ve -ve +ve--------------------2

Statement 1
rules out scenario 2 but scenario 1 is possible.
Now when i substitute the signs of x and z and take them out from the modulus, i get -

(-x + z) + (-x) = (-z)
-2x = -2z
x=z - - -
Therefore in the original equation, |x-z| = 0
and |x| = |z|

-hence sufficient


Statement 2

Again eliminates the possibility of the scenario 2
and hence is sufficient


Am i correct here?


Rearrange question |-(-x+z)|=|z-x| = |z|-|x|?
By property they will be equal when both x and z have the same sign

Statement 1
If x>z, then with zy < xy < 0, x and z are both positive. Same sign. Suff

Statement 2.
If y>0 then same with zy < xy < 0, x and z both positive. Same sign Suff

Answer is (D)

Hope it helps
Cheers!
J :)
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 22 Mar 2013
Posts: 883
Location: India
GPA: 3.51
WE: Information Technology (Computer Software)
Followers: 17

Kudos [?]: 240 [0], given: 185

Premium Member CAT Tests
Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink] New post 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".

Manager
Manager
User avatar
Joined: 10 Mar 2013
Posts: 195
Followers: 0

Kudos [?]: 5 [0], given: 1494

CAT Tests
Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink] New post 16 Apr 2014, 21:28
(1) z < x => y > 0
(2) Same as (1)

(1) or (2)
x < 0
z < 0

0 < x-z
abs(x-z) + abs(x) = abs(z)?
x-z + -x = -z
S

D
Intern
Intern
avatar
Joined: 08 Jan 2014
Posts: 20
Location: United States
Concentration: General Management, Entrepreneurship
GMAT Date: 06-30-2014
GPA: 3.99
WE: Analyst (Consulting)
Followers: 1

Kudos [?]: 14 [0], given: 4

Re: If zy < xy < 0, is |x-z| + |x| = |z|? [#permalink] New post 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 .

Hence D.
Re: If zy < xy < 0, is |x-z| + |x| = |z|?   [#permalink] 10 May 2014, 11:04
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If zy < xy < 0 is |x-z| + |x| = |z| bharat2384 5 17 Jan 2010, 10:42
If zy < xy < 0, is |x-z| + |x| = |z|? (1) z<x (2) tarek99 9 31 Jul 2008, 05:24
If zy < xy < 0, is |x-z| + |x| = |z|? (1) z<x>0 kookoo4tofu 13 13 May 2007, 11:40
2 Experts publish their posts in the topic ZY<XY<0 is |X-Z| + |x| = |Z| doc14 14 25 Apr 2007, 03:18
If zy<xy<0 is |x-z| + |x| = |z|? 1. z<x>0 2. successstory 5 02 Feb 2007, 18:01
Display posts from previous: Sort by

If zy < xy < 0, is |x-z| + |x| = |z|?

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

GMAT Club MBA Forum Home| About| Privacy Policy| Terms and Conditions| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group and phpBB SEO

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.