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

It is currently 24 May 2016, 15:23
GMAT Club Tests

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

Is x > x ^3 ?

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

Hide Tags

2 KUDOS received
Director
Director
User avatar
Joined: 07 Jun 2004
Posts: 613
Location: PA
Followers: 3

Kudos [?]: 519 [2] , given: 22

Is x > x ^3 ? [#permalink]

Show Tags

New post 28 Jan 2011, 05:59
2
This post received
KUDOS
3
This post was
BOOKMARKED
00:00
A
B
C
D
E

Difficulty:

  75% (hard)

Question Stats:

51% (02:39) correct 49% (02:43) wrong based on 186 sessions

HideShow timer Statistics

Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2
[Reveal] Spoiler: OA

_________________

If the Q jogged your mind do Kudos me : )

Expert Post
1 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32965
Followers: 5746

Kudos [?]: 70386 [1] , given: 9844

Re: Friday Algebra DS [#permalink]

Show Tags

New post 28 Jan 2011, 06:54
1
This post received
KUDOS
Expert's post
rxs0005 wrote:
Is x > x ^3


S1 x < 0

S2 x^2 - x^3 > 2


Is x> x^3?

Is \(x>x^3\)? --> is \(x^3-x<0\)? --> is \((x+1)x(x-1)<0\)? is \(x<-1\) or \(0<x<1\)

(1) x<0. Not sufficient.

(2) x^2-x^3>2 --> \(x^2(1-x)>2\) --> only true for \(x<-1\) (note that if \(x>1\) then \(x^2(1-x)\) is negative so this range is not good and if \(-1\leq{x}\leq{1}\) then \(x^2(1-x)\leq{2}\) so this range is also not good). Sufficient.

Answer: B.
_________________

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
User avatar
Joined: 19 Dec 2010
Posts: 145
Followers: 2

Kudos [?]: 25 [1] , given: 12

Re: Friday Algebra DS [#permalink]

Show Tags

New post 17 Mar 2011, 22:49
1
This post received
KUDOS
I goofed on this because I tricked myself but this is easy...think about it as always before putting pen to paper..
When is x>x^3?
ONLY when x = negative integer OR a positive fraction.
1) x= -ve, ok but is it a fraction?
Insuff
2) x^2 - x^3 >2
x^2 (x-1)<2
Use gurpreets method to draw the number line. You will see that
Statement is positive for all: x>1 = positive, x>0 = positive
Therefore between 0 and 1 the statement is negative..hence the original statement holds true.
Because X is a positive fraction, B is sufficient.
SVP
SVP
avatar
Joined: 16 Nov 2010
Posts: 1673
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 34

Kudos [?]: 440 [0], given: 36

Premium Member Reviews Badge
Re: Friday Algebra DS [#permalink]

Show Tags

New post 18 Mar 2011, 00:02
(1)

If x is not a fraction, say -2 , then x > x^3

But if x = -1/2, then -1/2 < -1/8


(2) x is not a proper fraction, and is a -ve number

(-3)^2 - (-3)^3 = 9 - (-27) = 36


So 2 is sufficient. Answer B.
_________________

Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 09 Jun 2012
Posts: 31
Followers: 0

Kudos [?]: 15 [0], given: 13

Re: Friday Algebra DS [#permalink]

Show Tags

New post 05 Mar 2013, 06:49
Bunuel wrote:
rxs0005 wrote:
Is x > x ^3

(2) x^2-x^3>2 --> \(x^2(1-x)>2\) --> only true for \(x<-1\) (note that if \(x>1\) then \(x^2(1-x)\) is negative so this range is not good and if \(-1\leq{x}\leq{1}\) then \(x^2(1-x)\leq{2}\) so this range is also not good). Sufficient.

Answer: B.


Hi Bunuel,

For x^2-x^3>2 how did you directly arrive at the intervals <-1 between -1 and 1 and >1. When we deal with (1-x) >2 we get x <-1. But how did you chose the other point 1?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 32965
Followers: 5746

Kudos [?]: 70386 [0], given: 9844

Re: Friday Algebra DS [#permalink]

Show Tags

New post 06 Mar 2013, 02:55
Expert's post
Jaisri wrote:
Bunuel wrote:
rxs0005 wrote:
Is x > x ^3

(2) x^2-x^3>2 --> \(x^2(1-x)>2\) --> only true for \(x<-1\) (note that if \(x>1\) then \(x^2(1-x)\) is negative so this range is not good and if \(-1\leq{x}\leq{1}\) then \(x^2(1-x)\leq{2}\) so this range is also not good). Sufficient.

Answer: B.


Hi Bunuel,

For x^2-x^3>2 how did you directly arrive at the intervals <-1 between -1 and 1 and >1. When we deal with (1-x) >2 we get x <-1. But how did you chose the other point 1?


Check here:
x2-4x-94661.html#p731476,
inequalities-trick-91482.html,
everything-is-less-than-zero-108884.html?hilit=extreme#p868863,
xy-plane-71492.html?hilit=solving%20quadratic#p841486
_________________

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
avatar
Joined: 09 Jun 2012
Posts: 31
Followers: 0

Kudos [?]: 15 [0], given: 13

Re: Friday Algebra DS [#permalink]

Show Tags

New post 07 Mar 2013, 00:08
Bunuel wrote:

Check here:


Hi Bunuel, Thanks for your reply and reference to some wonderful materials around quadratic inequalities.

May I ask you one more question - going back to the basics now. What would be the roots of the eqn we have in hand in this post: x^2 - x^3 >2.
I solved the roots to be 0 and -1 by following the below steps:
x^2(1-x)>2
X^2 implies 0 is a root.
1-x>2 implies x<-1, so -1 is a root.
From your explanations the roots seem to be 1 and -1. Where am I going wrong? (I also saw another post of yours where I was not able to solve the correct roost when x^3 was involved. Please help.)

Last edited by Jaisri on 07 Mar 2013, 06:28, edited 1 time in total.
Expert Post
3 KUDOS received
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 630
Followers: 72

Kudos [?]: 930 [3] , given: 136

Premium Member
Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 07 Mar 2013, 02:03
3
This post received
KUDOS
Expert's post
rxs0005 wrote:
Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2


Nothing to add after Bunuel's explanation. But just writing down how to get the inequality x<-1 from F.S 2 for those who couldn't get it.

F.S 1 clearly not sufficient. Take x= -1,you get a NO for stem, but for -0.5, you get a YES.

F.S 2, states \(x^2-x^3-2>\)0

or\(( x^2-1)-(x^3+1)>0\)

or\((x+1)[(x-1) - (x^2+1-x)]>0\)

\(or (x+1)[-x^2+2x-2]>0\)

or \((x+1)[-(x^2-2x+2)]>0\)

or \(-(x+1)[(x-1)^2+1]>0\)

as\((x-1)^2+1\) will always be positive, thus (x+1) has to be negative.

or x+1<0

or x<-1

Sufficient.

B.
_________________

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

Hit and Trial for Integral Solutions


Last edited by mau5 on 08 Mar 2013, 07:57, edited 2 times in total.
Intern
Intern
avatar
Joined: 09 Jun 2012
Posts: 31
Followers: 0

Kudos [?]: 15 [0], given: 13

Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 08 Mar 2013, 06:43
vinaymimani wrote:
rxs0005 wrote:
Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2


Nothing to add after Bunuel's explanation. But just writing down how to get the inequality x<-1 from F.S 2 for those who couldn't get it.

F.S 1 clearly not sufficient. Take x= -1,you get a NO for stem, but for -0.5, you get a YES.

F.S 2, states \(x^2-x^3-2>\)0

or\(( x^2-1)-(x^3-1)>0\)

or\((x-1)[(x+1) - (x^2+1+x)]>0\)

or\((x-1)(-x^2)\)>0. Thus, (x-1) has to be negative

or x-1<0

or x<-1.

Sufficient.

B.


+1 Kudos. Thanks for showing how to solve this inequality!
There is a minor change though... x-1 >0 gives x<1 and not x <-1. Bunuel seems to have considered -1 and 1 as the roots. Any reasons for that?
Expert Post
Verbal Forum Moderator
Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 630
Followers: 72

Kudos [?]: 930 [0], given: 136

Premium Member
Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 08 Mar 2013, 07:56
Expert's post
Quote:

+1 Kudos. Thanks for showing how to solve this inequality!
There is a minor change though... x-1 >0 gives x<1 and not x <-1. Bunuel seems to have considered -1 and 1 as the roots. Any reasons for that?




thanks for pointing out the mistake. It was a splendidly foolish mistake. Apologies.
_________________

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

Hit and Trial for Integral Solutions

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9612
Followers: 465

Kudos [?]: 120 [0], given: 0

Premium Member
Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 09 Oct 2014, 08:57
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
2 KUDOS received
Veritas Prep GMAT Instructor
User avatar
Joined: 16 Oct 2010
Posts: 6563
Location: Pune, India
Followers: 1788

Kudos [?]: 10745 [2] , given: 210

Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 09 Oct 2014, 21:50
2
This post received
KUDOS
Expert's post
rxs0005 wrote:
Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2


You can either use inequalities here or the big picture approach.

When is x greater than x^3? It is when x < -1 or 0 < x <1.
(Recall that we should know the relations of x, x^2 and x^3 in the ranges 'less than -1', '-1 to 0', '0 to 1' and 'greater than 1')

(1) x < 0
When x is between -1 and 0, x^3 is greater than x. When x < -1, then x is greater than x^3. So this statement alone is not sufficient.

(2) x^2 - x^3 > 2
Now, this is not very easy to handle using inequalities. Without the cube, we would have just taken 2 to the other side and solved the quadratic. But this will be more easily solved using the big picture. Think of a number line.
What does x^2 - x^3 > 2 imply? It means x^2 is greater than x^3 and is 2 units to the right of x^3 on the number line. x^2 is never negative so it must be to the right of 0. Now there are two cases: Either x^2 is between 0 and 1 or it is greater than 1.
If x^2 were between 0 and 1, x would be between -1 and 1 and x^3 would be between 0 and -1. In this case, difference between x^3 and x^2 cannot be greater than 2. Hence this is not possible. So x^2 must be to the right of 1 and hence, x would be greater than 1 or less than -1. If x were greater than 1, x^3 would be greater than x^2 so x cannot be greater than 1. Hence x must be less than -1.
When x is less than -1, then x IS greater than x^3. Sufficient alone.

Answer (B)

Again, spend some time checking out the relations of x, x^2 and x^3 on the number line.
_________________

Karishma
Veritas Prep | GMAT Instructor
My Blog

Get started with Veritas Prep GMAT On Demand for $199

Veritas Prep Reviews

Intern
Intern
avatar
Joined: 09 Jul 2014
Posts: 44
Followers: 0

Kudos [?]: 2 [0], given: 63

Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 10 Oct 2014, 05:37
Bunuel
Is x> x^3?
Is x>x^3? --> is x^3-x<0? --> is (x+1)x(x-1)<0? is x<-1 or 0<x<1

when (x+1)x(x-1)<0,, doesnt it gives us the rage as x>-1 or x<1 ... because ..as you explained in an another question that

Intersection points are the roots of the equation x^2-4x+3=0, which are x_1=1 and x_2=3. "<" sign means in which range of x the graph is below x-axis. Answer is 1<x<3 (between the roots).
From this i understood that "<" sign means roots to the RIGHT of the smaller root and to the LEFT of the bigger root).

I am getting it wrong??
please explain
GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 9612
Followers: 465

Kudos [?]: 120 [0], given: 0

Premium Member
Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 04 Feb 2016, 04:42
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
VP
VP
User avatar
Joined: 08 Jul 2010
Posts: 1190
Location: India
GMAT: INSIGHT
WE: Education (Education)
Followers: 42

Kudos [?]: 952 [0], given: 40

Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 04 Feb 2016, 10:08
Expert's post
rxs0005 wrote:
Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2


Question : Is x > x ^3 ?

for x to be greater than x^3
Case 1: Either x < -1 or
Case 2: 0 < x < 1

Statement 1: x < 0
x may be -0.5 or x may be -2 hence
NOT SUFFICIENT

Statement 2: x^2 - x^3 > 2
For this statement to be true x < -1, (Just try some values to substitute in expression to check acceptable values of x), Hence
SUFFICIENT

Answer: Option B
_________________

Prosper!!!

GMATinsight

Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com
Call us : +91-9999687183 / 9891333772
http://www.GMATinsight.com/testimonials.html


Contact for One-on-One LIVE ONLINE (SKYPE Based) or CLASSROOM Quant/Verbal FREE Demo Class



READ: http://gmatclub.com/forum/620-to-760-getting-reborn-161230.html
Classroom Centre Address:
GMATinsight
107, 1st Floor, Krishna Mall, Sector-12 (Main market), Dwarka, New Delhi-110075

______________________________________________________
Please press the Image if you appreciate this post !!

Expert Post
Math Revolution GMAT Instructor
User avatar
Joined: 16 Aug 2015
Posts: 1185
GPA: 3.82
Followers: 71

Kudos [?]: 548 [0], given: 0

Premium Member
Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 04 Feb 2016, 18:41
Expert's post
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 independent equations ensures a solution.

Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2


When it comes to inequality questions, it is crucial that if range of que includes range of con, that con is sufficient.
When you modify the original condition and the question, they become x^3-x<0?, x(x-1)(x+1)<0? -> x<-1, 0<x<1?. Then, there is 1 variable(x), which should match with the number of equations. So you need 1 more equation. For 1) 1 equation, for 2) 1 equation, which is likey to make D the answer.
For 1), if x<0, the range of que doesn’t include the range of con, which is not sufficient.
For 2), in x^3-x+2<0, (x+1)(x^2-2x+2)<0, x^2-2x+2=(x-1)^2+1 is derived, which is always bigger than 0. Then, x+1<0 -> x<-1, in which the range of que includes the range of con. Thus, it is sufficient and the answer is B.


-> For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
_________________

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.
Unlimited Access to over 120 free video lessons - try it yourself
See our Youtube demo

Manager
Manager
User avatar
Joined: 05 Mar 2015
Posts: 134
Followers: 0

Kudos [?]: 13 [0], given: 21

Re: Is x > x ^3 ? [#permalink]

Show Tags

New post 02 Mar 2016, 11:16
Hi Bunuel,

For x^2-x^3>2 how did you directly arrive at the intervals <-1 between -1 and 1 and >1. When we deal with (1-x) >2 we get x <-1. But how did you chose the other point 1?[/quote]

Check here:
x2-4x-94661.html#p731476,
inequalities-trick-91482.html,
everything-is-less-than-zero-108884.html?hilit=extreme#p868863,
xy-plane-71492.html?hilit=solving%20quadratic#p841486[/quote][/quote]

i could not understand with those links...
as x^2-x^3>2 we can write as X^2(1-X)>2
so roots are 0,1
So range will be x>1 or x<0
or in number line if i plot i get +ve values within 0<x<1(i m plotting with roots 0 and 1 only in consideration)
Plz help.........
secondly plz clear me also that the for selecting different roots is same for different inequality like x^2-x^3>2 and x^2-x^3>0

Thanks
Re: Is x > x ^3 ?   [#permalink] 02 Mar 2016, 11:16
    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic Is (|x|)^x > x|x|^3? amgelcer 3 28 Sep 2013, 08:54
23 Experts publish their posts in the topic If x is positive, is x > 3 rohitgoel15 11 16 Apr 2012, 09:42
Is x^3 > x^2? siddhans 0 21 Jun 2015, 01:48
14 Experts publish their posts in the topic Is x^3 > x^2? thesfactor 21 15 Mar 2011, 03:24
Experts publish their posts in the topic Is x^3 > x^2 ? seekmba 6 16 Aug 2010, 14:18
Display posts from previous: Sort by

Is x > x ^3 ?

  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®.