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

It is currently 20 Oct 2018, 21:00

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 between 0 and 1 ? (1) x^2 is less than x (2) x^3 is

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

Hide Tags

Intern
Intern
avatar
Joined: 31 Aug 2010
Posts: 41
Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 04 Nov 2010, 19:49
2
14
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

78% (00:56) correct 22% (01:05) wrong based on 407 sessions

HideShow timer Statistics

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?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post 04 Nov 2010, 19:55
1
1
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?



\(x(x-1) < 0\) gives you the solution 0 < x < 1.

check out the link below for the explanation:
http://gmatclub.com/forum/inequalities-trick-91482.html#p804990
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!

Intern
Intern
avatar
Joined: 31 Aug 2010
Posts: 41
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post 04 Nov 2010, 20:02
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 be\(x > 0\). 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 \(x > 0\) ?
Veritas Prep GMAT Instructor
User avatar
P
Joined: 16 Oct 2010
Posts: 8399
Location: Pune, India
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post Updated on: 04 Nov 2010, 20:18
1
1
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 be\(x > 0\). 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.
_________________

Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >

GMAT self-study has never been more personalized or more fun. Try ORION Free!


Originally posted by VeritasKarishma on 04 Nov 2010, 20:14.
Last edited by VeritasKarishma on 04 Nov 2010, 20:18, edited 1 time in total.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post 04 Nov 2010, 20:15
1
2
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 \(x<1\) --> \(0<x<1\);

So \(x(x-1)<0\) holds true when \(0<x<1\). Sufficient.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

(2) x^3 is positive --> \(x^3>0\) just tells us that x is positive. Not sufficient.

Answer: A.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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: 31 Aug 2010
Posts: 41
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post 04 Nov 2010, 20:27
1
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!
Director
Director
User avatar
B
Status: No dream is too large, no dreamer is too small
Joined: 14 Jul 2010
Posts: 514
Arithmetic operation  [#permalink]

Show Tags

New post 21 Feb 2011, 11:12
2
is x between 0 and 1?
1. x^2 is less than x
2. x^3 is positive

I answer C considering x could be negative or positive but option 2 ensures x is positive. Please help what is the wrong with me.
_________________

Collections:-
PSof OG solved by GC members: http://gmatclub.com/forum/collection-ps-with-solution-from-gmatclub-110005.html
DS of OG solved by GC members: http://gmatclub.com/forum/collection-ds-with-solution-from-gmatclub-110004.html
100 GMAT PREP Quantitative collection http://gmatclub.com/forum/gmat-prep-problem-collections-114358.html
Collections of work/rate problems with solutions http://gmatclub.com/forum/collections-of-work-rate-problem-with-solutions-118919.html
Mixture problems in a file with best solutions: http://gmatclub.com/forum/mixture-problems-with-best-and-easy-solutions-all-together-124644.html

Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Arithmetic operation  [#permalink]

Show Tags

New post 21 Feb 2011, 11:19
Merging similar topics.

Baten80 wrote:
is x between 0 and 1?
1. x^2 is less than x
2. x^3 is positive

I answer C considering x could be negative or positive but option 2 ensures x is positive. Please help what is the wrong with me.


In (1) as x^2<x then x can not be negative, because if it is then we would have x^2>0>x.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Retired Moderator
avatar
Joined: 20 Dec 2010
Posts: 1835
Re: GMAT Quant Rev 2nd Ed - DS 76  [#permalink]

Show Tags

New post 21 Feb 2011, 11:22
Q: Is 0<x<1?

1.
x^2<x
x^2-x<0
x(x-1)<0

Means;
case I:
x<0 and x-1>0=>x>1
OR
case II:
x>0 and x-1<0=>x<1
case I is impossible. x can't be greater than 1 and less than 0 at the same time.

Thus; only case II is valid and x>0 and x<1
In other words; 0<x<1
Sufficient.

2.x^3 is +ve.
if x=0.1; x^3=.001(a positive value); 0<x<1
if x=2; x^3=8(a positive value); but x>1
Not sufficient.

Ans: "A"
_________________

~fluke

GMAT Club Premium Membership - big benefits and savings

Intern
Intern
avatar
Joined: 07 Jan 2011
Posts: 19
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 07 Jun 2012, 18:44
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.

Rahul
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 08 Jun 2012, 03:33
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.
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Manager
Manager
avatar
Joined: 26 Dec 2011
Posts: 93
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 08 Jun 2012, 22:14
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.
Math Expert
User avatar
V
Joined: 02 Sep 2009
Posts: 50007
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 09 Jun 2012, 02:56
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.


Yes, that's correct: x(x-1)<0 --> 0<x<1.

Explained here: x2-4x-94661.html#p731476
_________________

New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | 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

Verbal Forum Moderator
User avatar
Joined: 10 Oct 2012
Posts: 613
Premium Member
Re: Is X between 0 and 1?  [#permalink]

Show Tags

New post 01 Mar 2013, 05:07
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.

A.
_________________

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

Hit and Trial for Integral Solutions

Manager
Manager
avatar
B
Joined: 07 Feb 2011
Posts: 91
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 26 Mar 2013, 05:08
One of my favorite number property questions. Really good approach and you need to come to inferences fast on this one.
_________________

We appreciate your kudos'

Current Student
avatar
Status: Eagles Become Vultures
Joined: 19 Jun 2014
Posts: 60
Concentration: Finance, Strategy
Schools: LBS '18 (M)
GMAT 1: 710 Q48 V39
GPA: 4
WE: Corporate Finance (Energy and Utilities)
Reviews Badge
Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 05 Nov 2014, 15:17
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...
Intern
Intern
avatar
Joined: 28 May 2016
Posts: 1
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 30 Jul 2016, 10:45
Hi, when I first tackled this problem, I took the square root of both sides so that gave me the equation of x < sqrt(x).

Is it wrong to approach it this way? I now understand this is a positives and negatives problem based on the solutions above...
Board of Directors
User avatar
V
Status: Stepping into my 10 years long dream
Joined: 18 Jul 2015
Posts: 3622
Premium Member Reviews Badge
Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 30 Jul 2016, 10:55
1
nancy77 wrote:
Hi, when I first tackled this problem, I took the square root of both sides so that gave me the equation of x < sqrt(x).

Is it wrong to approach it this way? I now understand this is a positives and negatives problem based on the solutions above...


Even if you take x < sqrt(x), you know that :

1) x has to be positive because sqrt of -ve number is always imaginary.
2) for x to be less than its square root , it has to be less than 1 and greater than 0. because any number greater than 1 would have its square root less than itself.

Thus, your approach is also fine.
_________________

My GMAT Story: From V21 to V40
My MBA Journey: My 10 years long MBA Dream
My Secret Hacks: Best way to use GMATClub | Importance of an Error Log!
Verbal Resources: All SC Resources at one place | All CR Resources at one place
Blog: Subscribe to Question of the Day Blog

GMAT Club Inbuilt Error Log Functionality - View More.
New Visa Forum - Ask all your Visa Related Questions - here.

New! Best Reply Functionality on GMAT Club!



Find a bug in the new email templates and get rewarded with 2 weeks of GMATClub Tests for free

Check our new About Us Page here.

Intern
Intern
avatar
B
Joined: 17 Sep 2016
Posts: 44
GMAT 1: 640 Q44 V35
Need advice on number property  [#permalink]

Show Tags

New post 24 Feb 2017, 06:48
Refer OG 16 quant review
Question no 89

Is x between 0 & 1
1. X square is less than X
2. X cube is positive

Ans please with explanation

Sent from my Lenovo A7020a48 using GMAT Club Forum mobile app
CEO
CEO
User avatar
D
Joined: 12 Sep 2015
Posts: 3021
Location: Canada
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is  [#permalink]

Show Tags

New post 24 Feb 2017, 07:16
Top Contributor
jscott319 wrote:
Is x between 0 and 1 ?

(1) x² is less than x
(2) x³ is positive



Target question: Is x between 0 and 1 ?

Statement 1:x² is less than x
In other words, x² < x
We can apply some inequality rules here.
Since x² must be POSITIVE here, we can take x² < x and divide both sides by x²
We get: 1 < 1/x
Since 1/x is greater than 1, we can conclude that 1/x is positive, which means x is POSITIVE (i.e., x > 0)
Since x is POSITIVE, we can take 1 < 1/x and multiply both sides by x to get: x < 1
When we combine our two inequalities, we get 0 < x < 1
In other words, x IS between 0 and 1
Since we can answer the target question with certainty, statement 1 is SUFFICIENT

Statement 2: x³ is positive
There are several values of x that satisfy statement 2. Here are two:
Case a: x = 1/2 (so, x³ = (1/2)³ = 1/8). In this case, x IS between 0 and 1
Case b: x = 2 (so, x³ = 2³ = 8). In this case, x is NOT between 0 and 1
Since we cannot answer the target question with certainty, statement 2 is NOT SUFFICIENT

Answer: A

RELATED VIDEO FROM OUR COURSE

_________________

Brent Hanneson – GMATPrepNow.com
Image
Sign up for our free Question of the Day emails

GMAT Club Bot
Re: Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is &nbs [#permalink] 24 Feb 2017, 07:16

Go to page    1   2    Next  [ 22 posts ] 

Display posts from previous: Sort by

Is X between 0 and 1 ? (1) x^2 is less than x (2) x^3 is

  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®.