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

It is currently 21 Oct 2014, 08:53

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:
Intern
Intern
avatar
Joined: 25 Oct 2009
Posts: 6
Followers: 0

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

If zy < xy < 0 is |x-z| + |x| = |z| [#permalink] New post 17 Jan 2010, 10:42
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (02:10) correct 49% (01:16) wrong based on 49 sessions
If zy < xy < 0 is |x-z| + |x| = |z|

(1) z < x
(2) y > 0
[Reveal] Spoiler: OA
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 23355
Followers: 3604

Kudos [?]: 28713 [1] , given: 2820

Re: please help me with this ds problem [#permalink] New post 17 Jan 2010, 13:14
1
This post received
KUDOS
Expert's post
bharat2384 wrote:
If zy<xy<0 is |x-z|+|x|=|z|
1.z<x
2.y>0


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

Manager
Manager
avatar
Joined: 27 Apr 2008
Posts: 191
Followers: 1

Kudos [?]: 32 [0], given: 1

Re: please help me with this ds problem [#permalink] New post 17 Jan 2010, 10:48
This should be asked in the DS forum.
Intern
Intern
avatar
Joined: 11 Dec 2012
Posts: 14
Followers: 0

Kudos [?]: 0 [0], given: 21

GMAT ToolKit User
Re: If zy<xy<0 is |x-z|+|x|=|z| 1.z<x 2.y>0 A. [#permalink] New post 09 Jan 2013, 10:30
If zy<xy<0 is |x-z|+|x|=|z|
1.z<x
2.y>0

A. Statement (1) ALONE is sufficient, but statement (2) alone is not sufficient.
B. Statement (2) ALONE is sufficient, but statement (1) alone is not sufficient.
C. BOTH statements TOGETHER are sufficient, but NEITHER statement ALONE is
sufficient.
D. EACH statement ALONE is sufficient.
E. Statements (1) and (2) TOGETHER are NOT sufficient.


Bunuel is right we don't need stmts (1) or (2) or both to solve this problem. Here how can we come to it.

squre both sides of the equation:

|x-z|+|x|=|z|
|x-z|=|z|-|x|
x^2-2xz+z^2=x^2-2|xz|+z^2
after that we have:

-2xz=-2|xz| divding this equation by -2 we have:
xz=|xz| which means that question asks us: is xz=|xz|? here everything is clear
i.e.If zy<xy<0 y must be positive or negative. If y positive x and z must be both negative or vice versa which means that if y is negative both x and z must be positive where the inequality zy<xy<0 will be correct.

So we don't need any statements to solve this problem
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 43

Kudos [?]: 597 [0], given: 135

Premium Member
Re: If zy < xy < 0 is |x-z| + |x| = |z| [#permalink] New post 01 Feb 2013, 04:57
Expert's post
Given that zy < xy < 0 . Thus, xy-zy>0 = y(x-z)>0.

(1) z < x . Thus, from above y has to be positive. Hence, sufficient.

(2) y > 0. Similarly from above, (x-z)>0. Also sufficient.

D.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Intern
Intern
avatar
Joined: 12 Dec 2012
Posts: 2
Followers: 0

Kudos [?]: 0 [0], given: 2

Re: If zy < xy < 0 is |x-z| + |x| = |z| [#permalink] New post 05 Feb 2013, 23:20
zy<xy<0 (for y<0).....z..................x...................|..................x..................z....(for y>0)

so |x-z| + |x| = |z| -----> |delta| + |x| = |z| -------> LHS=RHS (take a look at the no. line i have drawn above)
This is a conditional identity and will always hold true
Re: If zy < xy < 0 is |x-z| + |x| = |z|   [#permalink] 05 Feb 2013, 23:20
    Similar topics Author Replies Last post
Similar
Topics:
16 Experts publish their posts in the topic If zy < xy < 0, is |x-z| + |x| = |z|? zaarathelab 7 28 Jan 2010, 01:50
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  


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®.