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

It is currently 22 Aug 2014, 06:23

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#0 and x#1, and if x is replaced by 1/x everywhere in th

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Manager
Manager
avatar
Joined: 02 Dec 2012
Posts: 178
Followers: 2

Kudos [?]: 257 [0], given: 0

If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 27 Dec 2012, 05:45
5
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  25% (medium)

Question Stats:

74% (02:11) correct 26% (02:03) wrong based on 263 sessions
(\frac{x+1}{x-1})^2

If x#0 and x#1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to

A. (\frac{x+1}{x-1})^2

B. (\frac{x-1}{x+1})^2

C. \frac{x^2+1}{1-x^2}

D. \frac{x^2-1}{x^2+1}

E. -(\frac{x-1}{x+1})^2
[Reveal] Spoiler: OA
Expert Post
3 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19048
Followers: 3368

Kudos [?]: 24509 [3] , given: 2680

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 27 Dec 2012, 05:56
3
This post received
KUDOS
Expert's post
1
This post was
BOOKMARKED
(\frac{x+1}{x-1})^2

If x#0 and x#1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to


A. (\frac{x+1}{x-1})^2

B. (\frac{x-1}{x+1})^2

C. \frac{x^2+1}{1-x^2}

D. \frac{x^2-1}{x^2+1}

E. -(\frac{x-1}{x+1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2.

Answer: A.
_________________

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

2 KUDOS received
Manager
Manager
avatar
Joined: 04 Dec 2011
Posts: 81
Schools: Smith '16 (I)
Followers: 0

Kudos [?]: 12 [2] , given: 13

GMAT ToolKit User
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 02 May 2013, 14:38
2
This post received
KUDOS
Bunuel wrote:
[b](\frac{x+1}{x-1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2 .


How did 1-X in the denominator become X-1 in last step?
_________________

Life is very similar to a boxing ring.
Defeat is not final when you fall down…
It is final when you refuse to get up and fight back!

1 Kudos = 1 thanks
Nikhil

3 KUDOS received
Intern
Intern
avatar
Joined: 23 Apr 2013
Posts: 22
Followers: 0

Kudos [?]: 12 [3] , given: 1

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 02 May 2013, 20:57
3
This post received
KUDOS
nikhil007 wrote:
Bunuel wrote:
[b](\frac{x+1}{x-1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2 .


How did 1-X in the denominator become X-1 in last step?


It's not (1-x) that became (x-1).
(1-x)^2 is simply rewritten as (x-1)^2.
Both (1-x)^2 and (x-1)^2 are essentially the same :)
Expert Post
1 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 627
Followers: 41

Kudos [?]: 550 [1] , given: 135

Premium Member
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 02 May 2013, 21:03
1
This post received
KUDOS
Expert's post
nikhil007 wrote:
Bunuel wrote:
[b](\frac{x+1}{x-1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2 .


How did 1-X in the denominator become X-1 in last step?



(1-x)^2 = (x-1)^2. For example, (1-4)^2 = (4-1)^2 = 9.
The negative sign inside the bracket gets taken care of because of the square.
_________________

All that is equal and not-Deep Dive In-equality

Hit and Trial for Integral Solutions

Manager
Manager
avatar
Joined: 29 Mar 2010
Posts: 141
Location: United States
Concentration: Finance, International Business
GMAT 1: 590 Q28 V38
GPA: 2.54
WE: Accounting (Hospitality and Tourism)
Followers: 1

Kudos [?]: 32 [0], given: 12

GMAT ToolKit User
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 30 Jun 2013, 17:47
Does anyone have any similar questions this this one?

I like this problem.

Thanks,
Hunter
_________________

4/28 GMATPrep 42Q 36V 640

Intern
Intern
User avatar
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09-27-2013
Followers: 0

Kudos [?]: 6 [0], given: 55

GMAT ToolKit User
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 25 Jul 2013, 01:48
Bunuel wrote:
(\frac{x+1}{x-1})^2

If x#0 and x#1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to


A. (\frac{x+1}{x-1})^2

B. (\frac{x-1}{x+1})^2

C. \frac{x^2+1}{1-x^2}

D. \frac{x^2-1}{x^2+1}

E. -(\frac{x-1}{x+1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2.

Answer: A.


I don´t get (\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2.. could you please explain your steps in a few words?
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19048
Followers: 3368

Kudos [?]: 24509 [1] , given: 2680

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 25 Jul 2013, 02:12
1
This post received
KUDOS
Expert's post
sv3n wrote:
Bunuel wrote:
(\frac{x+1}{x-1})^2

If x#0 and x#1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to


A. (\frac{x+1}{x-1})^2

B. (\frac{x-1}{x+1})^2

C. \frac{x^2+1}{1-x^2}

D. \frac{x^2-1}{x^2+1}

E. -(\frac{x-1}{x+1})^2

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2.

Answer: A.


I don´t get (\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2.. could you please explain your steps in a few words?


Step by step:

(\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2=(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2.

(\frac{\frac{1+x}{x}}{\frac{1-x}{x}})^2=(\frac{1+x}{x}*\frac{x}{1-x})^2

(\frac{1+x}{x}*\frac{x}{1-x})^2=(\frac{1+x}{1-x})^2

(\frac{1+x}{1-x})^2=(\frac{x+1}{x-1})^2

Can you please tell me which step didn't you understand?
_________________

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
User avatar
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09-27-2013
Followers: 0

Kudos [?]: 6 [0], given: 55

GMAT ToolKit User
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 25 Jul 2013, 04:10
I do not understand the first of these four steps. -.-

I understand that 1/x+1 is the same as 1+x/x, but why have you done it?
I only get it if I see the result and go backwards..
Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 19048
Followers: 3368

Kudos [?]: 24509 [1] , given: 2680

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 25 Jul 2013, 05:59
1
This post received
KUDOS
Expert's post
sv3n wrote:
I do not understand the first of these four steps. -.-

I understand that 1/x+1 is the same as 1+x/x, but why have you done it?
I only get it if I see the result and go backwards..


We want to simplify (\frac{\frac{1}{x}+1}{\frac{1}{x}-1})^2 so this step seemed quite natural to me.
_________________

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
User avatar
Joined: 18 May 2013
Posts: 7
Location: Germany
GMAT Date: 09-27-2013
Followers: 0

Kudos [?]: 6 [0], given: 55

GMAT ToolKit User
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 25 Jul 2013, 06:10
Tried it several times again. I think I got it know.. thanks.
Intern
Intern
avatar
Joined: 27 Dec 2013
Posts: 35
Concentration: Finance, General Management
Schools: ISB '15
Followers: 0

Kudos [?]: 7 [0], given: 29

CAT Tests
Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 10 May 2014, 05:50
Walkabout wrote:
(\frac{x+1}{x-1})^2

If x#0 and x#1, and if x is replaced by 1/x everywhere in the expression above, then the resulting expression is equivalent to

A. (\frac{x+1}{x-1})^2

B. (\frac{x-1}{x+1})^2

C. \frac{x^2+1}{1-x^2}

D. \frac{x^2-1}{x^2+1}

E. -(\frac{x-1}{x+1})^2


We can use a substitution method and process of elimination method to avoid the cumbersome calculations.

Say x = 2

x is replaced by 1/x. So, [(1/x + 1)/(1/x -1)] ^2 = [1+x/1-x] ^2

By substituting 2 we get, [(1+2)/(1-2)] ^2 = 9

Now, substitute x = 2 in the answer choices and an answer choice that gives the final answer as 9 is the correct answer.

Option A gives us 9.

Hence, A is the correct answer.
_________________

Kindly consider for kudos if my post was helpful!

Intern
Intern
avatar
Joined: 21 Apr 2014
Posts: 7
Followers: 0

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

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 10 May 2014, 06:19
nikhil007 wrote:
How did 1-X in the denominator become X-1 in last step?

Rewrite the equation so that x appears as the first term in the equation:

(1-x)^2 = (-x+1)^2

let's now rewrite the equation so that x is positive:

(1-x)^2 = (-x+1)^2 = [ (-1) \cdot (x-1)]^2

the laws of exponents establish that (a \cdot b)^n = a^n \cdot b^n which means that:

(1-x)^2 = (-x+1)^2 = [ (-1) \cdot (x-1)]^2 = (-1)^2 \cdot (x-1)^2

notice that (-1)^2 = -1 \cdot -1 = 1 therefore:

(1-x)^2 = (-x+1)^2 = [ (-1) \cdot (x-1)]^2 = (-1)^2 \cdot (x-1)^2 = 1 \cdot (x-1)^2 = (x-1)^2
Intern
Intern
avatar
Joined: 08 Feb 2014
Posts: 3
Followers: 0

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

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 20 Aug 2014, 13:50
Can't we just multiply the numerator and denominator by x, after substituing in (1/x)?
1 KUDOS received
Director
Director
User avatar
Status: The Best Or Nothing
Joined: 27 Dec 2012
Posts: 812
Location: India
Concentration: General Management, Technology
WE: Information Technology (Computer Software)
Followers: 4

Kudos [?]: 196 [1] , given: 165

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th [#permalink] New post 21 Aug 2014, 00:20
1
This post received
KUDOS
JackSparr0w wrote:
Can't we just multiply the numerator and denominator by x, after substituing in (1/x)?


We require to compute\frac{1}{x} + 1 & \frac{1}{x} - 1 before that

Refer Bunuel's method; done the very best
_________________

Kindly press "+1 Kudos" to appreciate :)

Re: If x#0 and x#1, and if x is replaced by 1/x everywhere in th   [#permalink] 21 Aug 2014, 00:20
    Similar topics Author Replies Last post
Similar
Topics:
1 Experts publish their posts in the topic If x#0, is 1/x + 1/y = 4 ? buguy7 2 31 May 2013, 04:44
17 Experts publish their posts in the topic If y=|x+1|/x and x!=0, is xy>0? Zarrolou 7 16 May 2013, 10:24
7 Experts publish their posts in the topic In the Sequence x0, x1, x2, ..., xn, each term from x1 to xk tonebeeze 9 14 Dec 2010, 16:40
Is x=0 (1) x+1>0 (2) x= -x linau1982 3 23 Oct 2008, 14:45
What is the value of x? 1) x^3-x=0 2) x^2-x=0 I realize the willgoldberg 4 05 Feb 2005, 15:19
Display posts from previous: Sort by

If x#0 and x#1, and if x is replaced by 1/x everywhere in th

  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®.