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

It is currently 23 Jul 2014, 10:27

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 |p−6|+p=6, which of the following must be true?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1095
Followers: 71

Kudos [?]: 413 [0], given: 99

Premium Member CAT Tests
If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 06:32
Expert's post
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  45% (medium)

Question Stats:

50% (01:53) correct 50% (00:55) wrong based on 231 sessions
If |p−6|+p=6, which of the following must be true?

A. p=0
B. p=-6
C. p=6
D. p>-6
E. p<=6


Bunuel-Can you please explain! and Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?
[Reveal] Spoiler: OA

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || NEW !!! GMAC's IR Prep Tool

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)


Last edited by bagdbmba on 26 Jun 2013, 06:51, edited 1 time in total.
Expert Post
5 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [5] , given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 06:43
5
This post received
KUDOS
Expert's post
debayan222 wrote:
If |p−6|+p=6, which of the following must be true?

A. p=0
B. p=-6
C. p=6
D. p>-6
E. p<=6


Bunuel-Can you please explain! and Can we write |p−6|= (p-6) and -(p-6)?


|p-6|+p=6 --> |p-6|=6-p --> |p-6|=-(p-6).

|x|=-x means, that x\leq{0}. So, p-6\leq{0} --> p\leq{6}.

Answer: E.

_________________

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

Expert Post
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1095
Followers: 71

Kudos [?]: 413 [0], given: 99

Premium Member CAT Tests
Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 06:57
Expert's post
Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || NEW !!! GMAC's IR Prep Tool

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [1] , given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 07:04
1
This post received
KUDOS
Expert's post
Expert Post
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1095
Followers: 71

Kudos [?]: 413 [0], given: 99

Premium Member CAT Tests
Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 07:31
Expert's post
Bunuel wrote:
debayan222 wrote:
Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?


When p\leq{6}, then |p-6|=-(p-6)=6-p.
When p\geq{6}, then |p-6|=p-6.


So, only 6 satisfies both |p−6|= (p-6) and |p−6|=-(p-6)

Then why the answer is not ONLY 6 for the above qs?

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || NEW !!! GMAC's IR Prep Tool

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [0], given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 07:34
Expert's post
debayan222 wrote:
Bunuel wrote:
debayan222 wrote:
Bunuel-Can we write |p−6| as (p-6) and -(p-6)( I mean when modulus is withdrawn) ?


When p\leq{6}, then |p-6|=-(p-6)=6-p.
When p\geq{6}, then |p-6|=p-6.


So, only 6 satisfies both |p−6|= (p-6) and -(p-6)

Then why the answer is not 6 for the above qs?


These are not simultaneous equations.

If...
If...

Since given that |p-6|=-(p-6)=6-p, then p\leq{6}.

_________________

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

Expert Post
BSchool Forum Moderator
avatar
Joined: 27 Aug 2012
Posts: 1095
Followers: 71

Kudos [?]: 413 [0], given: 99

Premium Member CAT Tests
Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 07:43
Expert's post
Ah! got it... :) so the question itself already limits the scope of modulus.

Is it below 700 qs?

BTW,don't get the "If....If...." part in your above reply ! :o

_________________

UPDATED : e-GMAT SC Resources-Consolidated || ALL RC Resources-Consolidated || ALL SC Resources-Consolidated || UPDATED : AWA compilations-109 Analysis of Argument Essays || NEW !!! GMAC's IR Prep Tool

GMAT Club guide - OG 11-12-13 || Veritas Blog || Manhattan GMAT Blog


KUDOS please, if you like the post or if it helps :-)

Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [0], given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 26 Jun 2013, 07:47
Expert's post
debayan222 wrote:
Ah! got it... :) so the question itself already limits the scope of modulus.

Is it below 700 qs?

BTW,don't get the highlighted part in your above reply ! :o


I think it's a sub-600 question, because it's about basic property (definition) of absolute value:

When x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}.

When x\geq{0} then |x|=x, or more generally when some \ expression\geq{0} then |some \ expression|={some \ expression}.

P.S. What highlighted part?

_________________

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

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

Kudos [?]: 44 [0], given: 134

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 30 Jun 2013, 17:08
If |p−6|+p=6, which of the following must be true?

There are two ways to solve, one of which is to just pick numbers.

The other way:
|p-6|+p=6
|p-6| = 6-p
|p-6| = -(p-6)
|x| = -x (i.e. the value inside the absolute value bars is negative)
So, (p-6) is negative when p≤6

(E)


A. p=0
B. p=-6
C. p=6
D. p>-6
E. p<=6
Intern
Intern
avatar
Joined: 09 Jun 2013
Posts: 4
Followers: 0

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

GMAT ToolKit User
Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 01 Jul 2013, 13:39
without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6?
the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

thanks!
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [0], given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 01 Jul 2013, 13:42
Expert's post
nancerella wrote:
without plugging in numbers, how would you know that this |p-6| = -(p-6) would be p<=6 and not just p<6?
the way i'm solving it, this |x| = -x condition would be met when (p-6)<0 and therefore -(p-6)<0 yields p<6. but why also p=6?

thanks!


Because when x\leq{0} then |x|=-x, or more generally when some \ expression\leq{0} then |some \ expression|={-(some \ expression)}.

We have |p-6|=-(p-6), thus p-6\leq{0} --> p\leq{6}.

_________________

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

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

Kudos [?]: 44 [0], given: 134

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 09 Jul 2013, 22:07
Why can't we (or how would we know not to) solve in the following manor:

If |p−6|+p=6, which of the following must be true?

|p−6|+p=6
p≥6
p-6+p=6
p=6

p<6
-(p-6)+p=6
-p+6+p=6
6=6

Thanks!
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [1] , given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 09 Jul 2013, 22:13
1
This post received
KUDOS
Expert's post
WholeLottaLove wrote:
Why can't we (or how would we know not to) solve in the following manor:

If |p−6|+p=6, which of the following must be true?

|p−6|+p=6
p≥6
p-6+p=6
p=6

p<6
-(p-6)+p=6
-p+6+p=6
6=6

Thanks!


Actually we can. You got the correct result.

When p<6, you got that the equation holds for any value of p.
When p≥6, you got that the equation holds for p=6.

So, the equation holds for p<6 and p=6 --> p<=6.

Hope it's clear.

_________________

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

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

Kudos [?]: 44 [0], given: 134

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 10 Jul 2013, 08:27
Bunuel wrote:

So, the equation holds for p<6 and p=6 --> p<=6.

Hope it's clear.


because for p<6 and p≥6 the intersection is p ≤6, correct?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18703
Followers: 3236

Kudos [?]: 22271 [1] , given: 2610

Re: If |p−6|+p=6, which of the following must be true? [#permalink] New post 10 Jul 2013, 10:43
1
This post received
KUDOS
Expert's post
Re: If |p−6|+p=6, which of the following must be true?   [#permalink] 10 Jul 2013, 10:43
    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 |p−6|+p=6, 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®.