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

It is currently 29 Aug 2014, 04:06

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:
1 KUDOS received
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 909
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 15

Kudos [?]: 205 [1] , given: 18

GMAT Tests User
Is |x-y| = ||x|-|y|| [#permalink] New post 05 Oct 2009, 08:52
1
This post received
KUDOS
00:00
A
B
C
D
E

Difficulty:

  35% (medium)

Question Stats:

64% (02:03) correct 36% (01:17) wrong based on 124 sessions
Is |x-y| = ||x|-|y||

(1) x > y
(2) x< y < 0
[Reveal] Spoiler: OA

Last edited by Bunuel on 03 Jul 2013, 05:03, edited 1 time in total.
Edited the question and added the OA.
1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 18 Aug 2009
Posts: 333
Followers: 8

Kudos [?]: 162 [1] , given: 13

GMAT Tests User
Re: Absolutes [#permalink] New post 05 Oct 2009, 09:01
1
This post received
KUDOS
Answer B.

Statement 1) Not sufficient.

Consider, x is -ve, y is -ve: x = -1, y = -2
|x-y| = 1, | |x|-|y| | = 1;

Consider, x is +ve, y is +ve: x = 2, y = 1
|x-y| = 1, | |x|-|y| | = 1;

Consider, x is +ve, y is -ve: x = 1, y = -1
|x-y| = 2, | |x|-|y| | = 0;

Statement 2) Sufficient.

Consider, x is -ve, y is -ve: x = -2, y = -1
|x-y| = 1, | |x|-|y| | = 1;
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [1] , given: 2698

Re: Absolutes [#permalink] New post 05 Oct 2009, 09:44
1
This post received
KUDOS
Expert's post
Economist wrote:
Is |x-y| = | |x|-|y| |
1). x>y
2). x<y<0


Is |x - y| = ||x| - |y|| ?

(1) x > y. There can be the following three cases:

A. x>y>0
LHS=x-y; RHS=|x-y|=x-y

B. x>0>y
LHS=x-y; RHS=|x+y|=-x-y or =x+y (depending whether |x|>|y| or not).

Already clear that (1) is not sufficient, but still let's continue:

C. 0>x>y
LHS=x-y; RHS=|-x+y|=x-y

NOT SUFFICIENT.

(2) x < y < 0:

LHS=-x+y; RHS=|-x+y|=-x+y.

SUFFICIENT.

Answer: B.
_________________

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
User avatar
Joined: 07 Sep 2011
Posts: 65
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 4

Kudos [?]: 26 [0], given: 3

Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 15 May 2012, 22:23
Is |x-y|=||x|-|y||?

(1) x>y
(2) x<y<0
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 16 May 2012, 00:32
Expert's post
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.
_________________

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
User avatar
Joined: 07 Sep 2011
Posts: 65
Location: United States
Concentration: Strategy, International Business
GMAT 1: 640 Q39 V38
WE: General Management (Real Estate)
Followers: 4

Kudos [?]: 26 [0], given: 3

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 16 May 2012, 02:04
Great. Thanks Bunuel for both the replies.

Is there any other approach to solve such questions?

Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 16 May 2012, 02:08
Expert's post
manjeet1972 wrote:
Great. Thanks Bunuel for both the replies.

Is there any other approach to solve such questions?

Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


Different approaches are possible to solve absolute value questions.

DS questions on absolute value: search.php?search_id=tag&tag_id=37
PS questions on absolute value: search.php?search_id=tag&tag_id=58

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

Intern
Intern
avatar
Joined: 07 May 2011
Posts: 42
GMAT 1: Q V
GMAT 2: Q V
Followers: 0

Kudos [?]: 10 [0], given: 11

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 27 Nov 2012, 18:12
Bunuel,

I have noticed that you reason a lot of problems into their solution by simply picking a set of numbers. Other than positive, 0, negative and fractional numbers, do u follow some rule of thumb to directly see what numbers to plug. is there a more "right" number to plug in such that you arrive at solutions faster?
Any insight will be appreciated.

Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 28 Nov 2012, 03:36
Expert's post
koisun wrote:
Bunuel,

I have noticed that you reason a lot of problems into their solution by simply picking a set of numbers. Other than positive, 0, negative and fractional numbers, do u follow some rule of thumb to directly see what numbers to plug. is there a more "right" number to plug in such that you arrive at solutions faster?
Any insight will be appreciated.

Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


First of all: on DS questions when plugging numbers, goal is to prove that the statement is not sufficient. So we should try to get a YES answer with one chosen number(s) and a NO with another.

Now, number picking strategy can vary for different problems. Generally it's good to test negative/positive/zero as well as integer/fraction to get a YES and a NO answers. If you deal with two variables it's also helpful to test x<y and x>y in addition to the former.
_________________

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: 26 Dec 2011
Posts: 117
Followers: 1

Kudos [?]: 9 [0], given: 17

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 29 Nov 2012, 12:34
I tried to solve it in this way, however I am not sure if my tght process is right. Bunuel, your input will be highly appreciated.

|x-y| = ||x|-|y||===> squaring both (given that both sides are mod)===> x2 + y2 -2xy = |x2|+|y2| -2|x||y|===> xy = |x||y|===> this is possible only when either both x,y >0 or x,y <0 .. second condition satisfies..hence B.
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 30 Nov 2012, 03:10
Expert's post
pavanpuneet wrote:
I tried to solve it in this way, however I am not sure if my tght process is right. Bunuel, your input will be highly appreciated.

|x-y| = ||x|-|y||===> squaring both (given that both sides are mod)===> x2 + y2 -2xy = |x2|+|y2| -2|x||y|===> xy = |x||y|===> this is possible only when either both x,y >0 or x,y <0 .. second condition satisfies..hence B.


xy=|xy| when xy\geq{0}. Apart from this your solution is correct.
_________________

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: 28 Feb 2012
Posts: 115
Concentration: Strategy, International Business
Schools: INSEAD Jan '13
GPA: 3.9
WE: Marketing (Other)
Followers: 0

Kudos [?]: 18 [0], given: 17

GMAT ToolKit User
Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 30 Nov 2012, 04:26
Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


I am a little confused, as far as i understood in GMAT statements will not contradict to each other. But in this question in statement 1 x>y and vice versa in statement 2.

Bunnuel can you comment please.
_________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 30 Nov 2012, 04:30
Expert's post
ziko wrote:
Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


I am a little confused, as far as i understood in GMAT statements will not contradict to each other. But in this question in statement 1 x>y and vice versa in statement 2.

Bunnuel can you comment please.


You are right. The question is flawed in that respect.
_________________

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

Intern
Intern
avatar
Joined: 15 Nov 2012
Posts: 4
Location: United States
Concentration: General Management, Technology
GMAT Date: 12-05-2012
GPA: 3.82
WE: Business Development (Computer Software)
Followers: 0

Kudos [?]: 6 [0], given: 3

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 01 Dec 2012, 05:41
simple approach could be,

both sides should give an equal positive result

Consider x<y<0

x= -2 , y =-1

then,
|-2+1| = ||-2| - |-1||
|-1| = |2 - 1| since, modulus gives a positive result
1 = 1
Intern
Intern
avatar
Joined: 18 Mar 2012
Posts: 48
GMAT 1: 690 Q V
GPA: 3.7
Followers: 0

Kudos [?]: 29 [0], given: 117

GMAT Tests User
Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 10 Feb 2013, 06:33
Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


I tired to solve this question by using distances of x and y on the number line. My line of thinking was that I need to know where x and y sit with respect to zero. Is this a correct approach?

Thanks!
Manager
Manager
User avatar
Joined: 24 Sep 2012
Posts: 90
Location: United States
Concentration: Entrepreneurship, International Business
GMAT 1: 730 Q50 V39
GPA: 3.2
WE: Education (Education)
Followers: 3

Kudos [?]: 67 [0], given: 3

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 23 Feb 2013, 13:06
I believe this approach is not correct. Your theory is correct that the distance between 2 numbers in the number line is the absolute value of the difference between the two numbers. However, the distance cannot always be measured as the difference of the absolute values as done in this problem. It could sometimes be the sum of the values also.

For example, consider distance between -5 and 3. The distance is |-5-5|=8
however, |-5|-|3|=2 which is wrong

alexpavlos wrote:
Bunuel wrote:
Is |x-y|=||x|-|y||?

(1) x>y. If x=1 and y=0 then the answer is YES but if x=1 and y=-1 then the answer is NO. Not sufficient.

(2) x<y<0. Analyze left hand side (LHS) of the equation: as x<y then x-y<0 so |x-y|=-(x-y)=y-x. Analyze right hand side (RHS) of the equation: as both x and y are negative then ||x|-|y||=|-x-(-y)|=|-x+y|=|y-x|. Again as x<y then y-x>0 so |y-x|=y-x. So, we have that LHS=RHS. Sufficient.

Answer: B.


I tired to solve this question by using distances of x and y on the number line. My line of thinking was that I need to know where x and y sit with respect to zero. Is this a correct approach?

Thanks!

_________________

Thanks
Kris
Instructor at Aspire4GMAT

Visit us at http://www.aspire4gmat.com

Post your queries
Join our free GMAT course

New blog: How to get that 700+
New blog: Data Sufficiency Tricks


Press Kudos if this helps!

Senior Manager
Senior Manager
User avatar
Joined: 13 May 2013
Posts: 476
Followers: 1

Kudos [?]: 49 [0], given: 134

Re: Is |x-y|=||x|-|y||? (1) x>y (2) x<y<0 [#permalink] New post 30 Jun 2013, 10:07
Is |x-y|=||x|-|y||?

is x-y = |y|-|x|
OR
is x-y = |x|-|y|

(x-y)^2 = (|x|-|y|)^2?
(x-y)*(x-y) = (|x|-|y|)*(|x|-|y|)
x^2-2xy+y^2 = |x|^2 - 2|x|*|y| + |y|^2

-2xy = -2|xy|
xy = |xy|

That is only possible when xy = |xy| In other words, if xy were negative it wouldn't be equal to |xy|

(we cannot add 2xy to 2|xy| correct?)

(1) x>y

If x > y then |x-y| will always be positive. However, we don't know the sign of |x| and |y|
INSUFFICIENT

(2) x<y<0
x and y are both negative which means that xy = (-x)*(-y) which = (+xy)
SUFFICIENT

(B)

(just to make sure I understand it fully I will utilize Bunuel's approach as well)

#2) x<y<0
|x-y|=||x|-|y||
if x-y then |x-y| is negative: -(x-y) ===> (y-x)

if x and y are negative, then x, y are negative: (||x|-|y||) ===> | (-x) - (-y) | ===> |-x + y| ===> (y-x)
so: (y-x) = (y-x)
SUFFICIENT
1 KUDOS received
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1627
Location: United States
Concentration: Finance
GMAT 1: 710 Q48 V39
WE: Corporate Finance (Investment Banking)
Followers: 11

Kudos [?]: 155 [1] , given: 254

GMAT ToolKit User
Re: Absolutes [#permalink] New post 22 Apr 2014, 05:50
1
This post received
KUDOS
Bunuel wrote:
Economist wrote:
Is |x-y| = | |x|-|y| |
1). x>y
2). x<y<0


(1)
A. x>y>0
LHS=x-y RHS=|x-y|=x-y
B. x>0>y
LHS=x-y RHS=|x+y|=-x-y or =x+y (depending |x|>|y| or not)
Already clear that (1) is not sufficient, but let's continue to make the way of dealing such problems more clear.
C. 0>x>y
LHS=x-y RHS=|-x+y|=x-y
NOT SUFFICINT

(2) x<y<0
LHS=-x+y RHS=|-x+y|=-x+y
SUFFICIENT

Answer: B.


Is this approach valid?

Is |x-y| = | |x|-|y| |?

Square both sides and simplify
x^2-2xy+y^2 = x^2-2|x||y|+y^2?

We are down to is xy = |x||y|?

Statement 1 not sufficient
Statement 2 is sufficient and answer is thus yes

Therefore B stands

Please advice
Cheers!
J :)
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 22148
Followers: 3413

Kudos [?]: 24986 [0], given: 2698

Re: Absolutes [#permalink] New post 22 Apr 2014, 06:35
Expert's post
jlgdr wrote:
Bunuel wrote:
Economist wrote:
Is |x-y| = | |x|-|y| |
1). x>y
2). x<y<0


(1)
A. x>y>0
LHS=x-y RHS=|x-y|=x-y
B. x>0>y
LHS=x-y RHS=|x+y|=-x-y or =x+y (depending |x|>|y| or not)
Already clear that (1) is not sufficient, but let's continue to make the way of dealing such problems more clear.
C. 0>x>y
LHS=x-y RHS=|-x+y|=x-y
NOT SUFFICINT

(2) x<y<0
LHS=-x+y RHS=|-x+y|=-x+y
SUFFICIENT

Answer: B.


Is this approach valid?

Is |x-y| = | |x|-|y| |?

Square both sides and simplify
x^2-2xy+y^2 = x^2-2|x||y|+y^2?

We are down to is xy = |x||y|?

Statement 1 not sufficient
Statement 2 is sufficient and answer is thus yes

Therefore B stands

Please advice
Cheers!
J :)


Yes, your solution is perfectly fine.
_________________

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: 07 May 2013
Posts: 109
Followers: 0

Kudos [?]: 8 [0], given: 1

Re: Is |x-y| = ||x|-|y|| [#permalink] New post 04 Jun 2014, 19:26
Basically, the question is asking are both x and y +ve or both are -ve.
S1 does not give us any info regarding the signs i.e +ve or -ve.
S2 clearly states both are -ve.
Hence, B.
Re: Is |x-y| = ||x|-|y||   [#permalink] 04 Jun 2014, 19:26
    Similar topics Author Replies Last post
Similar
Topics:
2 Experts publish their posts in the topic Is xy + xy < xy ? nitin1negi 1 17 Jun 2014, 18:45
Is xy + xy < xy? Manhnip 0 05 Jun 2013, 14:12
4 Experts publish their posts in the topic Is xy + xy < xy ? mun23 5 02 Mar 2013, 12:03
3 Experts publish their posts in the topic Is xy > x/y? Naina1605 9 02 Dec 2011, 03:36
2 Experts publish their posts in the topic Is xy > x/y? naaga 5 25 Feb 2011, 07:15
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®.