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

It is currently 26 Mar 2015, 18:21

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 a, b, and c are constants, a > b > c, and x^3 - x = (x -

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26535
Followers: 4066

Kudos [?]: 38439 [3] , given: 4963

If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 19 Feb 2014, 00:19
3
This post received
KUDOS
Expert's post
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

68% (02:25) correct 32% (02:11) wrong based on 204 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3

Problem Solving
Question: 103
Category: Algebra Simplifying algebraic expressions
Page: 75
Difficulty: 650


GMAT Club is introducing a new project: The Official Guide For GMAT® Quantitative Review, 2ND Edition - Quantitative Questions Project

Each week we'll be posting several questions from The Official Guide For GMAT® Quantitative Review, 2ND Edition and then after couple of days we'll provide Official Answer (OA) to them along with a slution.

We'll be glad if you participate in development of this project:
1. Please provide your solutions to the questions;
2. Please vote for the best solutions by pressing Kudos button;
3. Please vote for the questions themselves by pressing Kudos button;
4. Please share your views on difficulty level of the questions, so that we have most precise evaluation.

Thank you!
[Reveal] Spoiler: OA

_________________

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

GMAT Club Premium Membership - big benefits and savings

Kaplan Promo CodeKnewton GMAT Discount CodesManhattan GMAT Discount Codes
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26535
Followers: 4066

Kudos [?]: 38439 [1] , given: 4963

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 19 Feb 2014, 00:19
1
This post received
KUDOS
Expert's post
SOLUTION

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3

As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too:

x=0 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=-abc, so one of the unknowns equals to zero;

x=1 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=(1-a)(1-b)(1-c), so one of the unknowns equals to 1;

x=-1 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=(-1-a)(-1-b)(-1-c), so one of the unknowns equals to -1.

As a > b > c then a=1, b=0 and c=-1.

Answer: C.
_________________

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

GMAT Club Premium Membership - big benefits and savings

1 KUDOS received
Senior Manager
Senior Manager
avatar
Joined: 20 Dec 2013
Posts: 273
Location: India
Followers: 0

Kudos [?]: 57 [1] , given: 29

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 19 Feb 2014, 01:54
1
This post received
KUDOS
Option C:
x^3-x can be re-written as:(x-1)*x*(x+1) in ascending order.
(x-1)*x*(x+1)=(x-a)*(x-b)*(x-c)
[As a>b>c=>-a<-b<-c => x-a<x-b<x-c]
Therefore,a=1
b=0
c=-1
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26535
Followers: 4066

Kudos [?]: 38439 [0], given: 4963

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 22 Feb 2014, 05:03
Expert's post
SOLUTION

If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3

As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too:

x=0 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=-abc, so one of the unknowns equals to zero;

x=1 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=(1-a)(1-b)(1-c), so one of the unknowns equals to 1;

x=-1 --> x^3-x=(x-a)(x-b)(x-c) becomes: 0=(-1-a)(-1-b)(-1-c), so one of the unknowns equals to -1.

As a > b > c then a=1, b=0 and c=-1.

Answer: C.
_________________

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

GMAT Club Premium Membership - big benefits and savings

3 KUDOS received
Intern
Intern
avatar
Joined: 02 Jan 2014
Posts: 12
Schools: INSEAD Jan '15
Followers: 0

Kudos [?]: 5 [3] , given: 15

GMAT ToolKit User
Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 01 May 2014, 07:27
3
This post received
KUDOS
Alternative SOLUTION
If a, b, and c are constants, a > b > c, and x^3 - x = (x - a)(x - b)(x - c) for all numbers x, what is the value of b ?

(A) - 3
(B) -1
(C) 0
(D) 1
(E) 3


x^3 - x = (x-a)(x-b)(x-c)
x(x^2 - 1) = (x-a)(x-b)(x-c)

Using (a-b)^2 = (a-b)(a+b) algebra form, the expression becomes ( x ) (x - 1)(x + 1) = (x-a)(x-b)(x-c)

Effectively, the solutions are 0, -1, and +1.
As we are given that a > b > c, the order is therefore +1 > 0 > -1
B is therefore 0.

Answer is C
1 KUDOS received
SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1828
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 19

Kudos [?]: 812 [1] , given: 193

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 17 Jul 2014, 00:07
1
This post received
KUDOS
x^3 - x = (x - a)(x - b)(x - c)

x (x^2 - 1) = (x - a)(x - b)(x - c)

(x + 0) (x+1) (x-1) = (x - a)(x - b)(x - c)

Given that a>b>c; so reorganising LHS of the equation

(x-1) (x + 0) (x+1) = (x - a)(x - b)(x - c)

b = 0

Answer = C
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 27 May 2014
Posts: 68
Followers: 0

Kudos [?]: 12 [0], given: 21

CAT Tests
Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 17 Jul 2014, 04:17
How do we know so is equal the numbers are -1,0,1. I know there consecutive but why not 2,3,4?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 26535
Followers: 4066

Kudos [?]: 38439 [0], given: 4963

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 17 Jul 2014, 04:43
Expert's post
bankerboy30 wrote:
How do we know so is equal the numbers are -1,0,1. I know there consecutive but why not 2,3,4?


Please check here: if-a-b-and-c-are-constants-a-b-c-and-x-3-x-x-167671.html#p1335360

As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too. Substituting these values you get the values of a, b, and c.
_________________

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

GMAT Club Premium Membership - big benefits and savings

SVP
SVP
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 1828
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 19

Kudos [?]: 812 [0], given: 193

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 17 Jul 2014, 17:52
bankerboy30 wrote:
How do we know so is equal the numbers are -1,0,1. I know there consecutive but why not 2,3,4?


Expanding x^3 - x gives the values -1, 0, 1 besides x. Those are derived as shown in my above post

(x+2)(x+3)(x+4) \neq{x^3 - x}
_________________

Kindly press "+1 Kudos" to appreciate :)

Manager
Manager
avatar
Joined: 26 Feb 2015
Posts: 64
Followers: 0

Kudos [?]: 1 [0], given: 11

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 02 Mar 2015, 12:11
Bunuel wrote:
bankerboy30 wrote:
How do we know so is equal the numbers are -1,0,1. I know there consecutive but why not 2,3,4?



As x^3-x=(x-a)(x-b)(x-c) is true for ALL x-es than it must be true for x=0, x=1 and x=-1 too. Substituting these values you get the values of a, b, and c.


I still dont understand this logic. Are we simply looking for any value of X that makes the entire equation 0? What do you specifically mean by "as x^3.... is true for all x-es" - I really dont understand this.
Expert Post
1 KUDOS received
EMPOWERgmat Instructor
User avatar
Status: GMAT Assassin/Co-Founder
Affiliations: EMPOWERgmat
Joined: 19 Dec 2014
Posts: 1387
Location: United States (CA)
GMAT 1: 800 Q51 V49
GRE 1: 340 Q170 V170
Followers: 53

Kudos [?]: 340 [1] , given: 32

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x - [#permalink] New post 02 Mar 2015, 18:18
1
This post received
KUDOS
Expert's post
Hi erikvm,

This is a "layered" concept and it's easy to get "lost" in this prompt because you're used to solving for the final values in most Quant questions.

Here, the 3 "final" numbers are (X - A), (X - B) and (X - C), but the question is NOT asking for any of the 3 final numbers...it's asking for a "piece" of one of them....the value of B.

To answer it, you have to ignore the A, B and C for a moment and go back to the prior "term"

X^3 - X

This can be factored down into 3 pieces. Here's how...

X^3 - X

First, factor out an X...

(X)(X^2 - 1)

Next, reverse-FOIL the other term....
(X)(X+1)(X-1)

Since we're multiplying 3 terms, it doesn't matter what the order is. I'm going to put them in order from least to greatest...

(X-1)(X)(X+1)

Now, looking at THIS, you can figure out what A, B and C are. Since A>B>C, then....

A = +1
B = 0
C = -1

Final Answer:
[Reveal] Spoiler:
C


GMAT assassins aren't born, they're made,
Rich
_________________

Rich Cohen
Rich.C@empowergmat.com
http://www.empowergmat.com

EMPOWERgmat GMAT Club Page, Study Plans, & Discounts
http://gmatclub.com/blog/courses/empowergmat-discount/?fl=menu

Image

Re: If a, b, and c are constants, a > b > c, and x^3 - x = (x -   [#permalink] 02 Mar 2015, 18:18
    Similar topics Author Replies Last post
Similar
Topics:
5 Experts publish their posts in the topic In the equation x^2+bx+c=0, b and c are constants, and x is idinuv 1 06 Mar 2014, 20:26
4 If b, c, and d are constants and x^2 + bx + c = (x + Galiya 3 05 Aug 2011, 05:16
13 Experts publish their posts in the topic If a, b, and c are constants, a > b > c, and x^3-x=(x-a)(x-b jpr200012 17 26 Jul 2010, 11:01
X/|X| <X>1 B) X>-1 C) |X|<1> 1 shoonya 14 07 Aug 2007, 17:45
If x^a = y^b > z^c, is x = y > z? I. a = b > c II. sgrover 5 23 Jun 2006, 16:00
Display posts from previous: Sort by

If a, b, and c are constants, a > b > c, and x^3 - x = (x -

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.