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

 It is currently 20 Jan 2019, 01:10

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

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

Events & Promotions

Events & Promotions in January
PrevNext
SuMoTuWeThFrSa
303112345
6789101112
13141516171819
20212223242526
272829303112
Open Detailed Calendar
• FREE Quant Workshop by e-GMAT!

January 20, 2019

January 20, 2019

07:00 AM PST

07:00 AM PST

Get personalized insights on how to achieve your Target Quant Score.
• GMAT Club Tests are Free & Open for Martin Luther King Jr.'s Birthday!

January 21, 2019

January 21, 2019

10:00 PM PST

11:00 PM PST

Mark your calendars - All GMAT Club Tests are free and open January 21st for celebrate Martin Luther King Jr.'s Birthday.

Is x > x ^3 ?

Author Message
TAGS:

Hide Tags

Director
Joined: 07 Jun 2004
Posts: 599
Location: PA
Is x > x ^3 ?  [#permalink]

Show Tags

28 Jan 2011, 04:59
2
3
00:00

Difficulty:

75% (hard)

Question Stats:

54% (02:13) correct 46% (02:15) wrong based on 226 sessions

HideShow timer Statistics

Is x > x ^3 ?

(1) x < 0
(2) x^2 - x^3 > 2
Math Expert
Joined: 02 Sep 2009
Posts: 52294

Show Tags

28 Jan 2011, 05:54
1
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.

_________________
Manager
Joined: 19 Dec 2010
Posts: 100

Show Tags

17 Mar 2011, 21:49
1
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.
Retired Moderator
Joined: 16 Nov 2010
Posts: 1420
Location: United States (IN)
Concentration: Strategy, Technology

Show Tags

17 Mar 2011, 23:02
(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
Joined: 09 Jun 2012
Posts: 29

Show Tags

05 Mar 2013, 05:49
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.

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?
Math Expert
Joined: 02 Sep 2009
Posts: 52294

Show Tags

06 Mar 2013, 01:55
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.

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,
_________________
Intern
Joined: 09 Jun 2012
Posts: 29

Show Tags

Updated on: 07 Mar 2013, 05:28
Bunuel wrote:

Check here:

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.)

Originally posted by Jaisri on 06 Mar 2013, 23:08.
Last edited by Jaisri on 07 Mar 2013, 05:28, edited 1 time in total.
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: Is x > x ^3 ?  [#permalink]

Show Tags

Updated on: 08 Mar 2013, 06:57
3
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.
_________________

Originally posted by mau5 on 07 Mar 2013, 01:03.
Last edited by mau5 on 08 Mar 2013, 06:57, edited 2 times in total.
Intern
Joined: 09 Jun 2012
Posts: 29
Re: Is x > x ^3 ?  [#permalink]

Show Tags

08 Mar 2013, 05:43
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?
Verbal Forum Moderator
Joined: 10 Oct 2012
Posts: 611
Re: Is x > x ^3 ?  [#permalink]

Show Tags

08 Mar 2013, 06:56
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.
_________________
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8795
Location: Pune, India
Re: Is x > x ^3 ?  [#permalink]

Show Tags

09 Oct 2014, 20:50
2
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.

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

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 09 Jul 2014
Posts: 29
Re: Is x > x ^3 ?  [#permalink]

Show Tags

10 Oct 2014, 04:37
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??
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2726
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: Is x > x ^3 ?  [#permalink]

Show Tags

04 Feb 2016, 09:08
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

_________________

Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6815
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Is x > x ^3 ?  [#permalink]

Show Tags

04 Feb 2016, 17:41
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.
"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"

VP
Joined: 05 Mar 2015
Posts: 1003
Re: Is x > x ^3 ?  [#permalink]

Show Tags

02 Mar 2016, 10:16
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,

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
Non-Human User
Joined: 09 Sep 2013
Posts: 9451
Re: Is x > x ^3 ?  [#permalink]

Show Tags

27 Aug 2018, 10:29
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.
_________________
Re: Is x > x ^3 ? &nbs [#permalink] 27 Aug 2018, 10:29
Display posts from previous: Sort by