Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 23 May 2017, 07:24

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.

Close

Request Expert Reply

Confirm Cancel

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x^n/x^(n+1) > x^(n+1)/x^n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:

Hide Tags

Director
Director
User avatar
Joined: 25 Oct 2008
Posts: 601
Location: Kolkata,India
Followers: 15

Kudos [?]: 899 [0], given: 100

Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 27 Sep 2009, 22:29
4
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  85% (hard)

Question Stats:

53% (02:29) correct 47% (01:33) wrong based on 298 sessions

HideShow timer Statistics

Is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)?

(1) x < 0

(2) n < 0
[Reveal] Spoiler: OA

_________________

http://gmatclub.com/forum/countdown-beginshas-ended-85483-40.html#p649902


Last edited by Bunuel on 19 Apr 2017, 11:54, edited 2 times in total.
Edited the question
2 KUDOS received
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 882
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 30

Kudos [?]: 703 [2] , given: 18

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 28 Sep 2009, 00:38
2
This post received
KUDOS
The expression can be rephrased as : Is 1/x > x ?
stmt 1. The expression is true for x < 0 except x=-1. But there is no restriction on x. So insuff.
stmt 2. Value of n does not matter.

combining , still the same question, can x be -1 ( and also be < 0 )?
Hence E.
Director
Director
avatar
Joined: 12 Oct 2008
Posts: 547
Followers: 3

Kudos [?]: 481 [0], given: 2

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 01 Oct 2009, 04:25
can you please explain it in detail?

Economist wrote:
The expression can be rephrased as : Is 1/x > x ?
stmt 1. The expression is true for x < 0 except x=-1. But there is no restriction on x. So insuff.
stmt 2. Value of n does not matter.

combining , still the same question, can x be -1 ( and also be < 0 )?
Hence E.
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 882
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Followers: 30

Kudos [?]: 703 [0], given: 18

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 01 Oct 2009, 06:28
x^(n+1) = x^n.x

Now, while reducing the given inequality we need to take care of the inequality sign. ONLY if a -ve value is multiplied/divided on BOTH sides of the equation we need to reverse the inequality.

But, in this case we are not multiplying or dividing each side. We are just canceling out the same factor(-ve or +ve) from each side. So the inequality will remain the same.

In other words, x^n/x^n = 1, regardless of the sign of x^n. So, basically we are just multiplying each side by 1 :)
Manager
Manager
avatar
Joined: 05 Jul 2009
Posts: 182
Followers: 1

Kudos [?]: 51 [0], given: 5

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 23 Oct 2009, 16:26
Economist wrote:
The expression can be rephrased as : Is 1/x > x ?
stmt 1. The expression is true for x < 0 except x=-1. But there is no restriction on x. So insuff.
stmt 2. Value of n does not matter.

combining , still the same question, can x be -1 ( and also be < 0 )?
Hence E.


Is it only for x= -1 or for the range -1<x<0?
Retired Moderator
User avatar
Status: 2000 posts! I don't know whether I should feel great or sad about it! LOL
Joined: 04 Oct 2009
Posts: 1672
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 103

Kudos [?]: 992 [0], given: 109

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 26 Jan 2012, 07:17
+1 E

When we simplify the original inequality, using exponents theory, we get 1/x > x.

So both statements are insufficient.
_________________

"Life’s battle doesn’t always go to stronger or faster men; but sooner or later the man who wins is the one who thinks he can."

My Integrated Reasoning Logbook / Diary: http://gmatclub.com/forum/my-ir-logbook-diary-133264.html

GMAT Club Premium Membership - big benefits and savings

Expert Post
2 KUDOS received
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38821
Followers: 7716

Kudos [?]: 105860 [2] , given: 11593

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 26 Jan 2012, 11:31
2
This post received
KUDOS
Expert's post
3
This post was
BOOKMARKED
Ranges in above solutions are not correct.

Is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)?

First of all realistic GMAT question would mention that \(x\neq{0}\).

Anyway: is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)? --> is \(x^{n-n-1}>x^{n+1-n}\)? --> is \(\frac{1}{x}>x\)? --> is \(\frac{1}{x}-x>0\)? --> is \(\frac{1-x^2}{x}>0\)? --> is \(\frac{(1-x)(1+x)}{x}>0\)? So the question basically asks is \(x<-1\) or \(0<x<1\). (For more on this check: i-have-been-trying-to-understand-inequalities-by-reading-110917.html or range-for-variable-x-in-a-given-inequality-109468.html) Also noitce that the value of n is irrelevant to answer the question.

(1) x < 0. Not sufficient.

(2) n < 0. Not sufficient.

(1)+(2) Still can not answer the question. Not sufficient.

Answer: E.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

1 KUDOS received
Manager
Manager
avatar
B
Joined: 31 Mar 2013
Posts: 72
Location: India
GMAT 1: 770 Q51 V41
GPA: 3.02
Followers: 1

Kudos [?]: 27 [1] , given: 109

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 14 Sep 2013, 04:24
1
This post received
KUDOS
Bunuel wrote:
Ranges in above solutions are not correct.

Is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)?

First of all realistic GMAT question would mention that \(x\neq{0}\).

Anyway: is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)? --> is \(x^{n-n-1}<x^{n+1-n}\)? --> is \(\frac{1}{x}<x\)? --> is \(x-\frac{1}{x}>0\)? --> is \(\frac{x^2-1}{x}>0\)? --> is \(\frac{(x-1)(x+1)}{x}>0\)? So the question basically asks is \(-1<x<0\) or \(x>1\). (For more on this check: i-have-been-trying-to-understand-inequalities-by-reading-110917.html or range-for-variable-x-in-a-given-inequality-109468.html) Also noitce that the value of n is irrelevant to answer the question.

(1) x < 0. Not sufficient.

(2) n < 0. Not sufficient.

(1)+(2) Still can not answer the question. Not sufficient.

Answer: E.


Why have we flipped the inequality sign here? \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)? --> is \(x^{n-n-1}<x^{n+1-n}\)?
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38821
Followers: 7716

Kudos [?]: 105860 [0], given: 11593

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 15 Sep 2013, 09:28
emailmkarthik wrote:
Bunuel wrote:
Ranges in above solutions are not correct.

Is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)?

First of all realistic GMAT question would mention that \(x\neq{0}\).

Anyway: is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)? --> is \(x^{n-n-1}<x^{n+1-n}\)? --> is \(\frac{1}{x}<x\)? --> is \(x-\frac{1}{x}>0\)? --> is \(\frac{x^2-1}{x}>0\)? --> is \(\frac{(x-1)(x+1)}{x}>0\)? So the question basically asks is \(-1<x<0\) or \(x>1\). (For more on this check: i-have-been-trying-to-understand-inequalities-by-reading-110917.html or range-for-variable-x-in-a-given-inequality-109468.html) Also noitce that the value of n is irrelevant to answer the question.

(1) x < 0. Not sufficient.

(2) n < 0. Not sufficient.

(1)+(2) Still can not answer the question. Not sufficient.

Answer: E.


Why have we flipped the inequality sign here? \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)? --> is \(x^{n-n-1}<x^{n+1-n}\)?


It was a typo edited. Thank you. +1.
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Current Student
User avatar
Joined: 06 Sep 2013
Posts: 2005
Concentration: Finance
Followers: 68

Kudos [?]: 643 [0], given: 355

GMAT ToolKit User
Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 01 Jan 2014, 12:41
tejal777 wrote:
Is x^n/x^(n+1)>x^(n+1)/x^n?

(1) x < 0

(2) n < 0


The correct answer is E

From question stem we can simplify and get is 1/x > x?

1/x - x > 0 --> Using key points is x<-1 or 0<x<1?

Statement 1

x<0 not sufficient

Statement 2

I don't care about 'n' at this point

Statements 1 and 2 together

I still don't have enough info

Hence E

Hope it helps
Cheers!

J :)
Director
Director
User avatar
Joined: 25 Apr 2012
Posts: 727
Location: India
GPA: 3.21
WE: Business Development (Other)
Followers: 44

Kudos [?]: 742 [0], given: 723

Premium Member Reviews Badge
Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 03 Jan 2014, 03:57
tejal777 wrote:
Is x^n/x^(n+1)>x^(n+1)/x^n?

(1) x < 0

(2) n < 0


Sol: Given question can be rephrased as is 1/x>x ------> (1-x^2)/x>0

Given x<0, let x=-2 then the above equation holds true but if x= -1/2 then the equation doesn't hold true
(1-1/4)/-1/2 ------>3/4/-1/2---->-6/4 or -3/2 which is less than 0
Ans Statement A is not sufficient

A and D ruled out

St2: given n<0 -----> There is no use for it. Hence B ruled out
With both statements we still don't have anything new.

Hence Ans E
_________________


“If you can't fly then run, if you can't run then walk, if you can't walk then crawl, but whatever you do you have to keep moving forward.”

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 15397
Followers: 648

Kudos [?]: 204 [0], given: 0

Premium Member
Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 03 Sep 2015, 00:24
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________

GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources

Expert Post
Math Revolution GMAT Instructor
User avatar
G
Joined: 16 Aug 2015
Posts: 3280
GPA: 3.82
Followers: 237

Kudos [?]: 2015 [0], given: 0

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 04 Sep 2015, 04:49
Forget conventional ways of solving math questions. In DS, Variable approach is

the easiest and quickest way to find the answer without actually solving the

problem. Remember equal number of variables and equations ensures a solution.



Is x^n/x^(n+1)>x^(n+1)/x^n?

(1) x < 0

(2) n < 0

==>transforming the original condition and the question by variable approach method, we have x^n/x^(n+1)>x^(n+1)/x^n? --> 1/x>x?. multiplying x^2 to both sides (since multiplying square values maintain the direction of the inequality sign), x>x^3? , x^3-x>0?, x(x-1)(x+1)>0? gives us -1<x<0 or 1<x?. Using both 1) and 2), the range of que doesn't include the range of con. Therefore E is the answer.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
Find a 10% off coupon code for GMAT Club members.
“Receive 5 Math Questions & Solutions Daily”
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Manager
Manager
User avatar
S
Joined: 01 Jun 2015
Posts: 110
Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
Followers: 0

Kudos [?]: 20 [0], given: 84

GMAT ToolKit User CAT Tests
Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 29 Mar 2017, 03:23
Is
/frac{x^n}{x^n+1} > /frac{x^n+1}{x^n}

1) x<0
2) n<0
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38821
Followers: 7716

Kudos [?]: 105860 [0], given: 11593

Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 29 Mar 2017, 03:37
techiesam wrote:
Is
/frac{x^n}{x^n+1} > /frac{x^n+1}{x^n}

1) x<0
2) n<0


Merging topics. Please follow the rules when posting a question: https://gmatclub.com/forum/rules-for-po ... 33935.html Pay attention to rule 3.

Also, you might find Writing Mathematical Formulas on the Forum post helpful: https://gmatclub.com/forum/rules-for-po ... l#p1096628
_________________

New to the Math Forum?
Please read this: All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

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?
Extra-hard Quant Tests with Brilliant Analytics

Intern
Intern
User avatar
B
Joined: 19 Mar 2015
Posts: 15
Location: India
Followers: 0

Kudos [?]: 2 [0], given: 1

CAT Tests
Re: Is x^n/x^(n+1) > x^(n+1)/x^n? [#permalink]

Show Tags

New post 21 Apr 2017, 03:44
Is x^n/x^(n+1) > x^(n+1)/x^n?

(1) x < 0

(2) n < 0

x^n/x^(n+1) > x^(n+1)/x^n ==> x^2n > x^2(n+1)
ie X^2 < 1 , therefor the range of X is(-1, 1)

So statement 1 & 2 are not enough to get the sollution
so Ans> E
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?   [#permalink] 21 Apr 2017, 03:44
    Similar topics Author Replies Last post
Similar
Topics:
1 Is a > b? banksy 4 24 Apr 2016, 04:27
5 Experts publish their posts in the topic Is a > 10? Creeper300 4 11 Nov 2010, 08:37
Is a > b ? prab 1 21 Oct 2010, 02:25
2 Experts publish their posts in the topic Is r > s ? agnok 6 24 Jul 2016, 08:02
1 Experts publish their posts in the topic Is a > b ? Maude 5 04 Sep 2015, 04:45
Display posts from previous: Sort by

Is x^n/x^(n+1) > x^(n+1)/x^n?

  new topic post reply Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| 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®.