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

It is currently 21 Aug 2014, 12:44

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 |x|-|y|=|x+y|, then which of the following must be true?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 590 [1] , given: 62

GMAT ToolKit User GMAT Tests User Premium Member
If |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 21 Oct 2012, 22:42
1
This post received
KUDOS
Expert's post
00:00
A
B
C
D
E

Difficulty:

(N/A)

Question Stats:

83% (01:41) correct 17% (02:15) wrong based on 28 sessions
If |x|-|y|=|x+y|, then which of the following must be true?

A. x-y>0
B. x-y<0
C. x+y>0
D. xy>0
E. xy<0

I was unable to find its answer. Hence after trying, I guess the answer is x+y>0.
Please correct me if I am wrong.
Source: Jamboree
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1226
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 65

Kudos [?]: 656 [0], given: 116

GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 21 Oct 2012, 23:18
If x & y are both equal to 0. Then none of the options are true. So if want to find which MUST be true then answer is none. Question should be missing some part i guess.

If the question states that x and y are non zero. Then we can see that x and y should be off opposite polarity to satisfy the equation.
Illustration :

x = 5, y = -1

1)true 2)false 3)true 4) false 5) true

x= -5, y = 1

1)false 2)true 3)false 4) false 5)true

So, answer should be

xy<0

Answer is E
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 590 [1] , given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 01:34
1
This post received
KUDOS
Expert's post
Thanx for the reply Macfauz. Agree to your illustration but it will be great if you can go with the algebraic method.
Such modulus questions are painful if one doesn't the knows the correct approach.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

1 KUDOS received
Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 68

Kudos [?]: 499 [1] , given: 43

GMAT Tests User
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 02:24
1
This post received
KUDOS
Marcab wrote:
if |x|-|y|=|x+y|, then which of the following must be true?
1) x-y>0
2) x-y<0
3) x+y>0
4) xy>0
5) xy<0

I was unable to find its answer. Hence after trying, I guess the answer is x+y>0.
Please correct me if I am wrong.
Source: Jamboree


The correct answer is E, but should be xy\leq{0} and not xy<0. Otherwise, none of the answers is correct.
The given equality holds for x=y=0, for which none of the given answers is correct.

The given equality can be rewritten as |x| = |y| + |x + y|.
If y=0, the equality becomes |x|=|x|, obviously true.
From the given answers, D cannot hold, and A,B or C holds, depending on the value of x. Corrected E holds.
If y>0, then necessarily x must be negative, because if x>0, then |x+y|>|x| (x+y>x), and the given equality cannot hold.
If y<0, then necessarily x must be positive, because if x<0, then again |x+y|>|x| (-x-y>-x) and the given equality cannot hold.
It follows that x and y must have opposite signs or y=0.

Answer corrected version of E \,\,xy\leq{0}.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

2 KUDOS received
Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1226
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 65

Kudos [?]: 656 [2] , given: 116

GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 02:28
2
This post received
KUDOS
Marcab wrote:
Thanx for the reply Macfauz. Agree to your illustration but it will be great if you can go with the algebraic method.
Such modulus questions are painful if one doesn't the knows the correct approach.


Squaring both sides we get :

(|x| - |y|)^2 = (|x + y|)^2

|x|^2 + |y|^2 - 2|x||y| = x^2 + y^2 + 2xy

So.,

|x||y| = -xy

So -xy is positive (since modulus cannot be negative) and hence xy should be negative.
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 590 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 02:57
Expert's post
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1425
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 127

Kudos [?]: 590 [0], given: 62

GMAT ToolKit User GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 03:02
Expert's post
EvaJager wrote:
Marcab wrote:
if |x|-|y|=|x+y|, then which of the following must be true?
1) x-y>0
2) x-y<0
3) x+y>0
4) xy>0
5) xy<0

I was unable to find its answer. Hence after trying, I guess the answer is x+y>0.
Please correct me if I am wrong.
Source: Jamboree


The correct answer is E, but should be xy\leq{0} and not xy<0. Otherwise, none of the answers is correct.
The given equality holds for x=y=0, for which none of the given answers is correct.

The given equality can be rewritten as |x| = |y| + |x + y|.
If y=0, the equality becomes |x|=|x|, obviously true.
From the given answers, D cannot hold, and A,B or C holds, depending on the value of x. Corrected E holds.
If y>0, then necessarily x must be negative, because if x>0, then |x+y|>|x| (x+y>x), and the given equality cannot hold.
If y<0, then necessarily x must be positive, because if x<0, then again |x+y|>|x| (-x-y>-x) and the given equality cannot hold.
It follows that x and y must have opposite signs or y=0.

Answer corrected version of E \,\,xy\leq{0}.


Many thanks for the explanation.
It will be great if you elaborate on how to solve split modulus questions such as given above.
_________________

Prepositional Phrases Clarified|Elimination of BEING| Absolute Phrases Clarified
Rules For Posting
www.Univ-Scholarships.com

Director
Director
User avatar
Joined: 22 Mar 2011
Posts: 613
WE: Science (Education)
Followers: 68

Kudos [?]: 499 [0], given: 43

GMAT Tests User
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 03:26
MacFauz wrote:
Marcab wrote:
Thanx for the reply Macfauz. Agree to your illustration but it will be great if you can go with the algebraic method.
Such modulus questions are painful if one doesn't the knows the correct approach.


Squaring both sides we get :

(|x| - |y|)^2 = (|x + y|)^2

|x|^2 + |y|^2 - 2|x||y| = x^2 + y^2 + 2xy

So.,

|x||y| = -xy

So -xy is positive (since modulus cannot be negative) and hence xy should be negative.


OR 0, that's why the correct answer should be xy\leq{0}.
Otherwise, very nice solution.
_________________

PhD in Applied Mathematics
Love GMAT Quant questions and running.

Moderator
Moderator
User avatar
Joined: 02 Jul 2012
Posts: 1226
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 65

Kudos [?]: 656 [0], given: 116

GMAT Tests User Premium Member
Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink] New post 22 Oct 2012, 04:01
EvaJager wrote:
MacFauz wrote:
Marcab wrote:
Thanx for the reply Macfauz. Agree to your illustration but it will be great if you can go with the algebraic method.
Such modulus questions are painful if one doesn't the knows the correct approach.


Squaring both sides we get :

(|x| - |y|)^2 = (|x + y|)^2

|x|^2 + |y|^2 - 2|x||y| = x^2 + y^2 + 2xy

So.,

|x||y| = -xy

So -xy is positive (since modulus cannot be negative) and hence xy should be negative.


OR 0, that's why the correct answer should be xy\leq{0}.
Otherwise, very nice solution.


I was solving on the basis of my previous comment where I had just added the phrase "where x and y are non zero" to the question.

But seeing as how it is much more probable to leave out a <= sign than an entire sentence, I guess the question frame is right and the answer should be xy <= 0
_________________

Did you find this post helpful?... Please let me know through the Kudos button.

Thanks To The Almighty - My GMAT Debrief

GMAT Reading Comprehension: 7 Most Common Passage Types

Re: if |x|-|y|=|x+y|, then which of the following must be true?   [#permalink] 22 Oct 2012, 04:01
    Similar topics Author Replies Last post
Similar
Topics:
which of the following must be true? tejal777 2 06 Jun 2009, 03:57
2 Experts publish their posts in the topic If XY is divisible by 4, which of the following must be true bigfernhead 16 29 Nov 2008, 14:27
if X ____ = X, Which of the following must be true for all arjtryarjtry 8 26 Aug 2008, 09:41
Experts publish their posts in the topic Which of the following about triangle must be true? I. If a arjtryarjtry 10 31 Jul 2008, 20:06
which of the following must be true? (no restrictions of oops 8 29 May 2007, 16:07
Display posts from previous: Sort by

If |x|-|y|=|x+y|, then which of the following must be true?

  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®.