GMAT Question of the Day - Daily to your Mailbox; hard ones only

It is currently 24 Apr 2019, 05:26

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

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: 503
Location: Kolkata,India
Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post Updated on: 19 Apr 2017, 11:54
1
6
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

56% (02:02) correct 44% (02:08) wrong based on 233 sessions

HideShow timer Statistics

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

(1) x < 0

(2) n < 0

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

Originally posted by tejal777 on 27 Sep 2009, 22:29.
Last edited by Bunuel on 19 Apr 2017, 11:54, edited 2 times in total.
Edited the question
Most Helpful Expert Reply
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54493
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 26 Jan 2012, 11:31
2
3
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.
_________________
General Discussion
Director
Director
User avatar
Joined: 01 Apr 2008
Posts: 752
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 28 Sep 2009, 00:38
4
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.
Senior Manager
Senior Manager
avatar
Joined: 12 Oct 2008
Posts: 429
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: 752
Name: Ronak Amin
Schools: IIM Lucknow (IPMX) - Class of 2014
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: 152
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: 1099
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
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
Manager
Manager
avatar
B
Joined: 31 Mar 2013
Posts: 63
Location: India
GPA: 3.02
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 14 Sep 2013, 04:24
1
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 \(x^{n-n-1}<x^{n+1-n}\)?
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54493
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.
_________________
SVP
SVP
User avatar
Joined: 06 Sep 2013
Posts: 1661
Concentration: Finance
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: 676
Location: India
GPA: 3.21
WE: Business Development (Other)
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.”
Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 7245
GMAT 1: 760 Q51 V42
GPA: 3.82
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.
"Only $149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"
Manager
Manager
User avatar
G
Joined: 01 Jun 2015
Posts: 212
Location: India
Concentration: Strategy, International Business
GMAT 1: 620 Q48 V26
GMAT ToolKit User
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
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 54493
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 29 Mar 2017, 03:37
Intern
Intern
User avatar
B
Joined: 19 Mar 2015
Posts: 16
Location: India
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
Director
Director
User avatar
D
Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 723
Location: India
Concentration: General Management, Entrepreneurship
GPA: 3.8
WE: Engineering (Energy and Utilities)
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 22 Aug 2017, 06:39
tejal777 wrote:
Is \(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)?

(1) x < 0

(2) n < 0


DS:
\(\frac{x^n}{x^{n+1}}>\frac{x^{n+1}}{x^n}\)
\(\frac{1}{x}>\frac{x[}{fraction]\)

Statement 1 : x<0
-1<x<0, \([fraction]1/x}>\frac{x[}{fraction]\)
x = -1, \([fraction]1/x}=\frac{x[}{fraction]\)
x<-1, \([fraction]1/x}<[fraction]x[/fraction]\)
NOT SUFFICIENT

Statement 2: n<0 has no significance
NOT SUFFICIENT

Answer E
_________________
CAT 2017 (98.95) & 2018 (98.91) : 99th percentiler
UPSC Aspirants : Get my app UPSC Important News Reader from Play store.

MBA Social Network : WebMaggu


Appreciate by Clicking +1 Kudos ( Lets be more generous friends.)



What I believe is : "Nothing is Impossible, Even Impossible says I'm Possible" : "Stay Hungry, Stay Foolish".
Non-Human User
User avatar
Joined: 09 Sep 2013
Posts: 10619
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?  [#permalink]

Show Tags

New post 21 Apr 2019, 06:23
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 Club Bot
Re: Is x^n/x^(n+1) > x^(n+1)/x^n?   [#permalink] 21 Apr 2019, 06:23
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  


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne

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®.