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

 It is currently 10 Mar 2014, 15:21

### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

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

Author Message
TAGS:
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1427
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 107

Kudos [?]: 483 [1] , given: 62

If |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  21 Oct 2012, 22:42
1
KUDOS
Expert's post
00:00

Difficulty:

5% (low)

Question Stats:

80% (01:51) correct 20% (02:15) wrong based on 5 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
_________________
Moderator
Joined: 02 Jul 2012
Posts: 1119
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 48

Kudos [?]: 499 [2] , given: 90

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  22 Oct 2012, 02:28
2
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

Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1427
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 107

Kudos [?]: 483 [1] , given: 62

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  22 Oct 2012, 01:34
1
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.
_________________
Director
Joined: 22 Mar 2011
Posts: 610
WE: Science (Education)
Followers: 63

Kudos [?]: 409 [1] , given: 43

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  22 Oct 2012, 02:24
1
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.

Moderator
Joined: 02 Jul 2012
Posts: 1119
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 48

Kudos [?]: 499 [0], given: 90

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  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

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

Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1427
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 107

Kudos [?]: 483 [0], given: 62

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  22 Oct 2012, 02:57
Expert's post
Macfauz , the solution was perfect. Thanks.
_________________
Verbal Forum Moderator
Status: Preparing for the another shot...!
Joined: 03 Feb 2011
Posts: 1427
Location: India
Concentration: Finance, Marketing
GPA: 3.75
Followers: 107

Kudos [?]: 483 [0], given: 62

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  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.
_________________
Director
Joined: 22 Mar 2011
Posts: 610
WE: Science (Education)
Followers: 63

Kudos [?]: 409 [0], given: 43

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  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
Joined: 02 Jul 2012
Posts: 1119
Location: India
Concentration: Strategy
GMAT 1: 740 Q49 V42
GPA: 3.8
WE: Engineering (Energy and Utilities)
Followers: 48

Kudos [?]: 499 [0], given: 90

Re: if |x|-|y|=|x+y|, then which of the following must be true? [#permalink]  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 Replies Last post
Similar
Topics:
which of the following must be true? (no restrictions of 8 29 May 2007, 16:07
Which of the following about triangle must be true? I. If a 10 31 Jul 2008, 20:06
if X ____ = X, Which of the following must be true for all 8 26 Aug 2008, 09:41
Which of the following must be true about x? 2 29 Dec 2008, 15:32
which of the following must be true? 2 06 Jun 2009, 03:57
Display posts from previous: Sort by