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

It is currently 03 Sep 2015, 20:31
GMAT Club Tests

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

Is |x + y| < |x| + |y|?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Intern
Intern
User avatar
Joined: 21 Nov 2013
Posts: 41
Followers: 0

Kudos [?]: 31 [0], given: 3

Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 12:56
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

73% (02:02) correct 27% (01:37) wrong based on 83 sessions
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?
[Reveal] Spoiler: OA
Intern
Intern
avatar
Joined: 26 May 2013
Posts: 32
Location: United States
Surendra: Cherukuri
Concentration: Operations, Technology
GMAT 1: 670 Q48 V34
GMAT 2: 670 Q47 V35
GMAT 3: 720 Q50 V36
GPA: 4
WE: Research (Telecommunications)
Followers: 0

Kudos [?]: 18 [0], given: 10

GMAT ToolKit User
Re: Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 13:19
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?


The answer is B.
for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
in that case
|x+y| =|x|+|y|
3.x+ve and y -ve
in that case
|x+y| <|x|+|y|
4.x -ve and Y +ve
in that case
|x+y| <|x|+|y|
and if x=0 or y =0 (i.e. any one equal to zero)
|x+y| =|x|+|y|

so if x and y are of opposite signs then only |x + y| < |x| + |y|
now 1 gives
|x|=|y|
with this we cant answer the question as we donot know signs of x and y
2.| x – y | > | x + y |
this implies that x and y are of opposite signs. So with this we can answer the question.
Key point here is you should understand immediately after looking at the inequality that its valid only if x and y are of opposite signs.
Give me kudos if this helps
Intern
Intern
User avatar
Joined: 21 Nov 2013
Posts: 41
Followers: 0

Kudos [?]: 31 [0], given: 3

Re: Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 13:42
cherukuri1011 wrote:
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?


The answer is B.
for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
[....]


I am unsure with "ve" is... Thanks.
Intern
Intern
avatar
Joined: 26 May 2013
Posts: 32
Location: United States
Surendra: Cherukuri
Concentration: Operations, Technology
GMAT 1: 670 Q48 V34
GMAT 2: 670 Q47 V35
GMAT 3: 720 Q50 V36
GPA: 4
WE: Research (Telecommunications)
Followers: 0

Kudos [?]: 18 [0], given: 10

GMAT ToolKit User
Re: Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 14:00
BabySmurf wrote:
cherukuri1011 wrote:
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?


The answer is B.
for |x+y| <|x|+|y|
we have four cases
1.x +ve ,y+ve
in that case
|x+y| =|x|+|y|
2.x-ve ,y -ve
[....]


I am unsure with "ve" is... Thanks.

Hi BabySmurf,
I used a shorter expression X +ve means x is positive number and x -ve means if x is a negative number
Expert Post
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 5870
Location: Pune, India
Followers: 1485

Kudos [?]: 8005 [0], given: 190

Re: Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 21:02
Expert's post
2
This post was
BOOKMARKED
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?


This question can be done very easily if you are familiar with the properties of absolute value.
For all real x and y, \(|x + y| \leq |x| + |y|\)

\(|x + y| = |x| + |y|\) when x and y have the same sign (e.g. x = 4, y = 6 OR x = -2, y = -3) or at least one of them is 0.
When x and y have opposite signs, \(|x + y| < |x| + |y|\)

So the question asks us whether x and y have opposite signs or not.

(1) | x | ≠ | y |
Doesn't tell us anything about the signs of x and y. Not sufficient.

(2) | x – y | > | x + y |
When will | x – y | be greater than | x + y |? Only when x and y have opposite signs e.g. | x – y | = |3 - (-2)| = 5 but | x + y | = |3 - 2| = 1
If x and y have the same sign or one of them is 0, | x + y | will be greater or equal to | x – y |.
Hence this statement tells us that x and y have opposite signs. So it is sufficient alone.

Answer (B)
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 29205
Followers: 4751

Kudos [?]: 50291 [1] , given: 7540

Re: Is |x + y| < |x| + |y|? [#permalink] New post 23 Jan 2014, 23:53
1
This post received
KUDOS
Expert's post
BabySmurf wrote:
Is |x + y| < |x| + |y|?

(1) | x | ≠ | y |
(2) | x – y | > | x + y |





Appreciate views on how to solve this. Thank you.
I did this by picking numbers choosing various numbers positive, negative, fractions, 0.
Took make almost four minutes. Any other way?


Similar questions to practice:
is-x-y-x-y-87926.html
is-x-y-x-y-1-x-y-2-x-y-x-101660.html
is-x-y-x-y-123108.html
is-x-y-x-y-160531.html
is-x-y-x-z-1-y-z-2-x-86132.html
is-a-b-a-b-105457.html
is-x-y-x-y-1-x-y-2-x-y-132654.html
is-x-y-146991.html
is-x-y-x-y-137050.html
is-x-z-y-x-z-y-154245.html

Hope this helps.
_________________

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

PLEASE READ AND FOLLOW: 12 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 ; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) ; 12. Tricky questions from previous years.

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

GMAT Club Premium Membership - big benefits and savings

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 6205
Followers: 346

Kudos [?]: 71 [0], given: 0

Premium Member
Re: Is |x + y| < |x| + |y|? [#permalink] New post 27 Jul 2015, 18:34
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.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Re: Is |x + y| < |x| + |y|?   [#permalink] 27 Jul 2015, 18:34
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Is |x y| < |x| + |y|? venmic 12 08 Aug 2012, 21:08
1 Experts publish their posts in the topic Is x < y ? Naina1605 5 12 Feb 2012, 11:18
1 Is x < y? siddhans 3 22 Sep 2011, 22:32
Experts publish their posts in the topic Is x+y<1? vigneshpandi 6 21 Sep 2010, 21:57
2 Experts publish their posts in the topic Is -x < 2y ? devilmirror 10 30 Jan 2007, 20:25
Display posts from previous: Sort by

Is |x + y| < |x| + |y|?

  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®.