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

It is currently 26 Nov 2014, 20:18

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

Which of the following inequalities is always true for any

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
avatar
Joined: 07 Nov 2012
Posts: 13
Followers: 0

Kudos [?]: 8 [0], given: 10

Which of the following inequalities is always true for any [#permalink] New post 09 Nov 2012, 10:03
2
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

74% (01:37) correct 26% (00:53) wrong based on 258 sessions
Which of the following inequalities is always true for any real number 'a' and 'b'?

(A) |a + b| = |a| + |b|
(B) |a + b| > |a| + |b|
(C) |a + b| <= |a| + |b|
(D) |a - b| <= |a| - |b|
(E) |a - b| > |a| - |b|
[Reveal] Spoiler: OA
2 KUDOS received
Intern
Intern
avatar
Status: Life begins at the End of your Comfort Zone
Joined: 31 Jul 2011
Posts: 47
Location: Tajikistan
Concentration: General Management, Technology
GPA: 3.86
Followers: 1

Kudos [?]: 22 [2] , given: 4

Re: Which of the following inequalities is always true for any [#permalink] New post 09 Nov 2012, 11:32
2
This post received
KUDOS
1
This post was
BOOKMARKED
It seems such an easy answer, but I would go with (C). No thinking here bro, you got to know one of the fundamental properties of absolute value, which is subadditivity in a nutshell means that sum of two any elements is something (some number) which is less than or equal to the sum of the each element taken on itself separately, i.e. |a + b| <= |a| + |b|

Please, correct me if I went awry
_________________

God loves the steadfast.

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24118
Followers: 3737

Kudos [?]: 31341 [0], given: 3345

Re: Which of the following inequalities is always true for any [#permalink] New post 10 Nov 2012, 04:04
Expert's post
1
This post was
BOOKMARKED
derekgmat wrote:
Which of the following inequalities is always true for any real number 'a' and 'b'?

(A) |a + b| = |a| + |b|
(B) |a + b| > |a| + |b|
(C) |a + b| <= |a| + |b|
(D) |a - b| <= |a| - |b|
(E) |a - b| > |a| - |b|


Property worth remembering:

1. Always true: |x+y|\leq{|x|+|y|}, note that "=" sign holds for xy\geq{0} (or simply when x and y have the same sign);

2. Always true: |x-y|\geq{|x|-|y|}, note that "=" sign holds for xy>{0} (so when x and y have the same sign) and |x|>|y| (simultaneously).

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

Take a Survey about GMAT Prep - Win Prizes!

Senior Manager
Senior Manager
avatar
Joined: 22 Nov 2010
Posts: 293
Location: India
GMAT 1: 670 Q49 V33
WE: Consulting (Telecommunications)
Followers: 5

Kudos [?]: 33 [0], given: 75

Re: Which of the following inequalities is always true for any [#permalink] New post 20 Nov 2012, 09:10
Please refer this brilliant resource (it includes the above mentioned properties and other relevant information)

gmat-math-book-in-downloadable-pdf-format-130609.html
_________________

YOU CAN, IF YOU THINK YOU CAN

Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 16

Kudos [?]: 216 [0], given: 11

GMAT ToolKit User
Re: Which of the following inequalities is always true for any [#permalink] New post 06 Dec 2012, 00:17
:wink:

One must memorize and understand this property by heart.
|x| + |y| >= |x+y|
_________________

Impossible is nothing to God.

Intern
Intern
avatar
Joined: 02 Nov 2012
Posts: 36
Followers: 0

Kudos [?]: 2 [0], given: 11

Re: Which of the following inequalities is always true for any [#permalink] New post 07 Jan 2013, 07:21
What is the prove for this properties? Can someone prove this? Pleaseee
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 24118
Followers: 3737

Kudos [?]: 31341 [0], given: 3345

Re: Which of the following inequalities is always true for any [#permalink] New post 08 Jan 2013, 02:57
Expert's post
KevinBrink wrote:
What is the prove for this properties? Can someone prove this? Pleaseee


Square |x+y|\leq{|x|+|y|} (we can safely do that since both sides are non-negative):

x^2+2xy+y^2\leq{x^2+2|xy|+y^2} --> 2xy\leq{2|xy|} --> xy\leq{|xy|} --> always true.

The same way for the second inequality.
_________________

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

Take a Survey about GMAT Prep - Win Prizes!

Manager
Manager
User avatar
Joined: 12 Jan 2013
Posts: 249
Followers: 0

Kudos [?]: 24 [0], given: 47

GMAT ToolKit User
Re: Which of the following inequalities is always true for any [#permalink] New post 16 Dec 2013, 11:29
Bunuel wrote:
derekgmat wrote:
Which of the following inequalities is always true for any real number 'a' and 'b'?

(A) |a + b| = |a| + |b|
(B) |a + b| > |a| + |b|
(C) |a + b| <= |a| + |b|
(D) |a - b| <= |a| - |b|
(E) |a - b| > |a| - |b|


Property worth remembering:

1. Always true: |x+y|\leq{|x|+|y|}, note that "=" sign holds for xy\geq{0} (or simply when x and y have the same sign);

2. Always true: |x-y|\geq{|x|-|y|}, note that "=" sign holds for xy>{0} (so when x and y have the same sign) and |x|>|y| (simultaneously).

Hope it helps.



Let me see if Ive interpreted you correctly:


|x+y|\leq{|x|+|y|} means that "!x! is always denoted in its positive value, and so is !y!, and thus !x+y!, which can take two values, can never be greater than the addition of the two positive values !x! and !y!"

By the same token:

|x-y|\geq{|x|-|y|} means that "since both !x! and !y! in the right hand side are denoted in their positive value, their subtracted value can never be bigger than !x - y!"

Is that interpretation correct? That is how I solved the question.
Re: Which of the following inequalities is always true for any   [#permalink] 16 Dec 2013, 11:29
    Similar topics Author Replies Last post
Similar
Topics:
If z - 4z > 5 then which of the following is always true tekno9000 4 15 Aug 2008, 07:40
If z - 4z > 5 then which of the following is always true yogeshsheth 10 04 Nov 2006, 09:57
If z - 4z > 5 then which of the following is always true u2lover 2 14 Jul 2006, 14:15
Which of the following must be true? I. Any of two lines rao_raghunath 5 28 Mar 2006, 16:26
If z - 4z > 5 then which of the following is always true svrkpally 4 26 May 2005, 02:38
Display posts from previous: Sort by

Which of the following inequalities is always true for any

  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®.