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.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 350,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
04 Nov 2010, 18:49

1

This post received KUDOS

2

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

5% (low)

Question Stats:

85% (01:42) correct
15% (02:01) wrong based on 93 sessions

Is X between 0 and 1 ?

(1) x^2 is less than x (2) x^3 is positive

I am curious how to rephrase Statement 1 using inequalities. I rewrote it as x^2 - x < 0 , which then gives me x(x-1) < 0. If x < 0 and x < 1 then 0>x<1. Wouldnt this statement be insufficient? or am i writing that dual inequality incorrectly?

Re: GMAT Quant Rev 2nd Ed - DS 76 [#permalink]
04 Nov 2010, 18:55

Expert's post

jscott319 wrote:

Is X between 0 and 1 ?

1) x^2 is less than x 2) x^3 is positive

I am curious how to rephrase Statement 1 using inequalities. I rewrote it as x^2 - x < 0 , which then gives me x(x-1) < 0. If x < 0 and x < 1 then 0>x<1. Wouldnt this statement be insufficient? or am i writing that dual inequality incorrectly?

Re: GMAT Quant Rev 2nd Ed - DS 76 [#permalink]
04 Nov 2010, 19:02

Hmm i think i am more confused after reading that the first time through....

I think i am missing the reason why the inequality sign for x < 0 should actually bex > 0. I determined x< 1 because i set the inequality of x - 1 < 0 and after subtracting from both sides give me x < 1 . What is different about x < 0 becoming x > 0 ?

Re: GMAT Quant Rev 2nd Ed - DS 76 [#permalink]
04 Nov 2010, 19:14

1

This post received KUDOS

Expert's post

jscott319 wrote:

Hmm i think i am more confused after reading that the first time through....

I think i am missing the reason why the inequality sign for x < 0 should actually bex > 0. I determined x< 1 because i set the inequality of x - 1 < 0 and after subtracting from both sides give me x < 1 . What is different about x < 0 becoming x > 0 ?

x(x - 1) < 0 is not the same as x <0 and (x - 1)< 0

When I multiply two terms, the result is negative if and only if one of them is negative and the other is positive. When I multiply x with (x - 1), the result x(x - 1) will be negative (less than 0) in two cases:

Case I: x < 0 (x is negative) but (x - 1) > 0 (x - 1 is positive) (x - 1) > 0 implies x > 1 But this is not possible. x cannot be less than 0 and greater than 1 at the same time.

Case II: x > 0 (x is positive) but (x - 1) < 0 (x - 1 is negative) (x - 1) < 0 implies x < 1 This will happen when x lies between 0 and 1. i.e. when 0 < x < 1.

The link gives you the shortcut of solving inequalities of this type. _________________

Re: GMAT Quant Rev 2nd Ed - DS 76 [#permalink]
04 Nov 2010, 19:15

Expert's post

jscott319 wrote:

Is X between 0 and 1 ?

1) x^2 is less than x 2) x^3 is positive

I am curious how to rephrase Statement 1 using inequalities. I rewrote it as x^2 - x < 0 , which then gives me x(x-1) < 0. If x < 0 and x < 1 then 0>x<1. Wouldnt this statement be insufficient? or am i writing that dual inequality incorrectly?

Is x between 0 and 1?

Is 0<x<1?

(1) x^2 is less than x --> x^2<x --> x(x-1)<0:

Multiples must have opposite signs: x<0 and x-1>0, or x>1 --> no solution (x can not be simultaneously less than zero and more than 1); x>0 and x-1<0, or x<1 --> 0<x<1;

Re: GMAT Quant Rev 2nd Ed - DS 76 [#permalink]
04 Nov 2010, 19:27

1

This post received KUDOS

Ok I see it now! I was not taking into consideration the 2 cases that you've just made clear for me. Now I see how x(x-1) < 0 must become 0<x<1 . Thanks guys!

Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
07 Jun 2012, 17:44

I have a question is this. Why have we considered both the options.

x(x-1)<0:

Multiples must have opposite signs: 1. x<0 and x-1>0, or x>1 --> no solution (x can not be simultaneously less than zero and more than 1); 2. x>0 and x-1<0, or x<1 --> 0<x<1;

In the link to the post when we find the roots of the quadratic equation and if we know the sign is "<" we can directly right the roots as "root 1" < x < "root 2". The same way in this case also there are 2 roots 0 and 1 so we can directly write it this way. 0<x<1. Why do we have to consider case 1 also.

Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
08 Jun 2012, 02:33

Expert's post

rggoel9 wrote:

I have a question is this. Why have we considered both the options.

x(x-1)<0:

Multiples must have opposite signs: 1. x<0 and x-1>0, or x>1 --> no solution (x can not be simultaneously less than zero and more than 1); 2. x>0 and x-1<0, or x<1 --> 0<x<1;

In the link to the post when we find the roots of the quadratic equation and if we know the sign is "<" we can directly right the roots as "root 1" < x < "root 2". The same way in this case also there are 2 roots 0 and 1 so we can directly write it this way. 0<x<1. Why do we have to consider case 1 also.

Rahul

These are just two different approaches. _________________

Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
08 Jun 2012, 21:14

Hi Bunuel, Am I right in construing when I say that x(x-1)<0, which means the roots are 0, 1 and since it is "<" the solution must lie between 0 and 1 and hence, 0<x<1. Please confirm.

Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
09 Jun 2012, 01:56

Expert's post

pavanpuneet wrote:

Hi Bunuel, Am I right in construing when I say that x(x-1)<0, which means the roots are 0, 1 and since it is "<" the solution must lie between 0 and 1 and hence, 0<x<1. Please confirm.

Re: Is X between 0 and 1? [#permalink]
01 Mar 2013, 04:07

Expert's post

irfankool wrote:

Is X between 0 and 1? 1. x^2 is less than x. 2. x^3 is positive

From F.S 1, we have x^2<x

or x*(x-1)<0 . This is possible only if they have different signs. Thus, either x<0 AND (x-1)>0[ This is not possible as x can't be more than 1 and yet be negative] or x>0 AND (x-1)<0. This gives us that 0<x<1. Sufficient.

From F.S 2, we know that x^3 >0. Thus, cancelling out x^2 from both sides, we have x>0. Insufficient.

Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is [#permalink]
05 Nov 2014, 14:17

Could someone please explain why it's not possible:

x^2 < x try x=1/2 => 1/4 < 1/2 Yes, 0 < x < 1 try x=-1 => 1 > -1 No, x < 0 < 1

Why can x be only positive in this case since it can be negative and squared? It is not implied in"0 < x <1" that x must be a positive number? The question asks whether x is between 0 and 1, in case 1 x can be -1 and still satisfy the equation...

EDIT: Sorry, I realized that statement 1 must be correct in itself... _________________

GMATPrep 1: 410 Q26 V20 (20 and 19 incorrect) GMATPrep 2: 620 Q44 V32 (12 and 14 incorrect) GMATPrep 3: 690 Q48 V37 (12 and 12 incorrect)

Most important lessons learned so far: 1) Your first prep is NOT indicative of your true level. 2) First 10 questions ARE important (notice that between preps 2 and 3 I had only 2 less incorrect questions on Quant, but a 70 point total score difference)

gmatclubot

Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is
[#permalink]
05 Nov 2014, 14:17

I´ve done an interview at Accepted.com quite a while ago and if any of you are interested, here is the link . I´m through my preparation of my second...

It’s here. Internship season. The key is on searching and applying for the jobs that you feel confident working on, not doing something out of pressure. Rotman has...