Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

It is currently 22 May 2017, 15:27

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

Is x^2 greater than x ?

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

Hide Tags

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: 1672
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 103

Kudos [?]: 991 [0], given: 109

Is x^2 greater than x ? [#permalink]

Show Tags

New post 20 Jun 2012, 10:44
00:00
A
B
C
D
E

Difficulty:

  95% (hard)

Question Stats:

38% (02:18) correct 62% (01:18) wrong based on 60 sessions

HideShow timer Statistics

Is x^2 greater than x ?

(1) x^2 > x^3.
(2) x^2 > x^4.

I already solved it, but I tried to solve it by also the following method, and I don't know in which part I am wrong.

(1) \(x^2 > x^3\).
\(x^2 - x^3 > 0\)
\(x^2 * (1-x) > 0\)
So, we get: x= 0 and x = 1

-----(+)------0----(-)-------1------(+)------

Therefore, the intervals are x<0 and x>1

However, if we solve it in this way:
\(x^2 > x^3\)
We divide both sides by \(x^2\):
\(1 > x\)
The interval is not the same.

Please, tell me in which part of my first way I am wrong.
Thanks!
[Reveal] Spoiler: OA

_________________

"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

Kellogg MMM ThreadMaster
User avatar
B
Joined: 29 Mar 2012
Posts: 324
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 30

Kudos [?]: 439 [0], given: 23

GMAT ToolKit User
Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 20 Jun 2012, 12:32
metallicafan wrote:
\(x^2 > x^3\).
\(x^2 - x^3 > 0\)
\(x^2 * (1-x) > 0\)
So, we get: x= 0 and x = 1

-----(+)------0----(-)-------1------(+)------


Hi,

When you say,
\(x^2 (1-x) > 0\)
if \(x\neq 0\) then,\(x^2 >0\) for any real value of x.
thus, inequality reduces to \(1-x>0\)
or \(x < 1\)

Also, to use the number line method, you should change the coefficient of x as positive (for simplicity)
\(x^2 (x-1) < 0\) (multiply by -1 and reverse the sign)
now, use the number line;
-----(-)-----1---(+)---------

Please go through the following post:
Solving inequalities

Regards,
Kellogg MMM ThreadMaster
User avatar
B
Joined: 29 Mar 2012
Posts: 324
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 30

Kudos [?]: 439 [0], given: 23

GMAT ToolKit User
Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 20 Jun 2012, 12:41
Hi,

Is \(x^2>x\)?
or \(x^2-x>0\)?
or \(x(x-1)>0\)?
or x<0 or x>1?

Detailed solution:
Using (1),
\(x^2>x^3\)
or \(x^2(1-x)>0\)
or x < 1, for x = 0.5
\(x^2=0.25<x\)
but for x=-1,
\(x^2=1>x\). Thus, Insufficient.

Using (2),
\(x^2>x^4\)
or \(x^2(1-x^2)>0\)
or \(x^2(1-x)(1+x)>0\)
or \(x^2(x-1)(1+x)<0\) (multiplied by -1)
-(+)-------(-1)---(-)-----(+1)-----(+)------
or -1<x<1
Again, for x = 0.5
\(x^2=0.25<x\)
but for x=-0.5,
\(x^2=0.25>x\). Thus, Insufficient.

Even after using (1) & (2), we have -1 < x <1, Insufficient.

Answer is (E),

Regards,
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: 1672
Location: Peru
Schools: Harvard, Stanford, Wharton, MIT & HKS (Government)
WE 1: Economic research
WE 2: Banking
WE 3: Government: Foreign Trade and SMEs
Followers: 103

Kudos [?]: 991 [0], given: 109

Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 20 Jun 2012, 13:32
Thank you both!

It seems that I just memorized the method and didn't analyze it well.

I think that I get it now. And also I think that I have found another way that also can be helpful to you. Please, confirm if I am Ok. Please, Bunuel, take a look too.


(1) \(x^2 > x^3\).
\(x^2 - x^3 > 0\)
\(x^2 * (1-x) > 0\)
So, we get: x= 0 and x = 1

If \(x>1\) -----> \(x^2 * (1-x) < 0\)
If \(0<x<1\) -----> \(x^2 * (1-x) > 0\)
If \(x<0\) -----> \(x^2 * (1-x) > 0\)

So, we get:

-----(+)------0----(+)-------1------(-)------

Therefore, the solution is x < 1.

The same solution using this method:
\(x^2 > x^3\)
We divide by \(x^2\)
\(1 > x\)
\(x < 1\).

What do you think?
_________________

"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

Kellogg MMM ThreadMaster
User avatar
B
Joined: 29 Mar 2012
Posts: 324
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 30

Kudos [?]: 439 [0], given: 23

GMAT ToolKit User
Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 20 Jun 2012, 13:43
metallicafan wrote:
If \(x>1\) -----> \(x^2 * (1-x) < 0\)
If \(0<x<1\) -----> \(x^2 * (1-x) > 0\)
If \(x<0\) -----> \(x^2 * (1-x) > 0\)

Hi,

As you can see, the sign only depends on 1-x, so, even powers can be ignored here.

Regards,
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105764 [0], given: 11581

Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 21 Jun 2012, 01:03
Expert's post
1
This post was
BOOKMARKED
Is x^2 greater than x ?

Question: is \(x^2>x\)? --> is \(x(x-1)>0\)? is \(x<0\) or \(x>1\)?

(1) x^2 > x^3. Now, from this statement we know that \(x\neq{0}\), so \(x^2>0\) and we can safely reduce by it to get \(1>x\) (\(x<1\)). So, finally we have that given inequality holds true for \(x<0\) and \(0<x<1\) (remember we should exclude 0 from the range, since if \(x=0\) then the given inequality doesn't hold true). Not sufficient.

(2) x^2 > x^4. Apply the same logic here: we know that \(x\neq{0}\), so \(x^2>0\) and we can safely reduce by it to get \(1>x^2\) (\(x^2<1\)) --> \(-1<x<1\). So, finally we have that given inequality holds true for \(-1<x<0\) and \(0<x<1\) (remember we should exclude 0 from the range, since if \(x=0\) then the given inequality doesn't hold true). Not sufficient.Not sufficient.

(1)+(2) Intersection of the ranges from (1) and (2) gives: \(-1<x<0\) and \(0<x<1\), so we can still have an YES answer (consider \(x=-0.5\)) as well as a NO answer (consider \(x=0.5\)).

Answer: E.

Hope it's clear.
_________________

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

Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105764 [0], given: 11581

Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 21 Jun 2012, 01:07
cyberjadugar wrote:
Hi,

Is \(x^2>x\)?
or \(x^2-x>0\)?
or \(x(x-1)>0\)?
or x<0 or x>1?

Detailed solution:
Using (1),
\(x^2>x^3\)
or \(x^2(1-x)>0\)
or x < 1, for x = 0.5
\(x^2=0.25<x\)
but for x=-1,
\(x^2=1>x\). Thus, Insufficient.

Using (2),
\(x^2>x^4\)
or \(x^2(1-x^2)>0\)
or \(x^2(1-x)(1+x)>0\)
or \(x^2(x-1)(1+x)<0\) (multiplied by -1)
-(+)-------(-1)---(-)-----(+1)-----(+)------
or -1<x<1
Again, for x = 0.5
\(x^2=0.25<x\)
but for x=-0.5,
\(x^2=0.25>x\). Thus, Insufficient.

Even after using (1) & (2), we have -1 < x <1, Insufficient.

Answer is (E),

Regards,


The red parts are not correct. You should exclude zero, from all the ranges, since if \(x=0\), then neither of statements hold true.

Hope it's clear.
_________________

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

Kellogg MMM ThreadMaster
User avatar
B
Joined: 29 Mar 2012
Posts: 324
Location: India
GMAT 1: 640 Q50 V26
GMAT 2: 660 Q50 V28
GMAT 3: 730 Q50 V38
Followers: 30

Kudos [?]: 439 [0], given: 23

GMAT ToolKit User
Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 21 Jun 2012, 01:14
Hi,

Thanks for pointing it out! :-D

Regards,
Bunuel wrote:
cyberjadugar wrote:
Hi,

Is \(x^2>x\)?
or \(x^2-x>0\)?
or \(x(x-1)>0\)?
or x<0 or x>1?

Detailed solution:
Using (1),
\(x^2>x^3\)
or \(x^2(1-x)>0\)
or x < 1, for x = 0.5
\(x^2=0.25<x\)
but for x=-1,
\(x^2=1>x\). Thus, Insufficient.

Using (2),
\(x^2>x^4\)
or \(x^2(1-x^2)>0\)
or \(x^2(1-x)(1+x)>0\)
or \(x^2(x-1)(1+x)<0\) (multiplied by -1)
-(+)-------(-1)---(-)-----(+1)-----(+)------
or -1<x<1
Again, for x = 0.5
\(x^2=0.25<x\)
but for x=-0.5,
\(x^2=0.25>x\). Thus, Insufficient.

Even after using (1) & (2), we have -1 < x <1, Insufficient.

Answer is (E),

Regards,


The red parts are not correct. You should exclude zero, from all the ranges, since if \(x=0\), then neither of statements hold true.

Hope it's clear.
Intern
Intern
avatar
B
Joined: 11 Jan 2015
Posts: 25
Followers: 0

Kudos [?]: 4 [0], given: 11

GMAT ToolKit User CAT Tests
Is x² greater than x? [#permalink]

Show Tags

New post 30 Dec 2016, 06:27
Is \(x^2\) greater than \(x\)?

(1) \(x^2\) is greater than \(x^3\).
(2) \(x^2\) is greater than \(x^4\).



OA:
[Reveal] Spoiler:
E

Last edited by paddy41 on 30 Dec 2016, 06:38, edited 1 time in total.
Intern
Intern
avatar
B
Joined: 11 Jan 2015
Posts: 25
Followers: 0

Kudos [?]: 4 [0], given: 11

GMAT ToolKit User CAT Tests
Re: Is x² greater than x? [#permalink]

Show Tags

New post 30 Dec 2016, 06:36
Quote:
Explanation: \(x^2\) is greater than x for all numbers except for those values of x between 0 and 1. Thus, we need to know whether or not x falls in that range.

Statement (1) is insucient. To simplify,divide both sides by \(x^2\), resulting in 1 > x. If that's true, x could be between 0 and 1, but it could also be less than 0.

Statement (2) is also insucient. Again, simplify by dividing by \(x^2\), which gives you 1 > \(x^2\). Thus, x could be any number between -1 and 1. Again, it could be between 0 and 1, but it could also be between -1 and 0.

Taken together, it's still insucient. Both statements allow for the possibility that x is between 0 and 1, but both statements also make it possible that x is between -1 and 0. Choice (E) is correct.

Just one question about the highlighted part of the explanation: It is clear that \(x^2\) is always positive. However, is the division by \(x^2\) a valid inequality operation without knowing whether x is positive or negative?
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105764 [0], given: 11581

Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 30 Dec 2016, 08:18
Expert Post
Math Expert
User avatar
P
Joined: 02 Sep 2009
Posts: 38798
Followers: 7713

Kudos [?]: 105764 [0], given: 11581

Re: Is x^2 greater than x ? [#permalink]

Show Tags

New post 30 Dec 2016, 08:20
paddy41 wrote:
Quote:
Explanation: \(x^2\) is greater than x for all numbers except for those values of x between 0 and 1. Thus, we need to know whether or not x falls in that range.

Statement (1) is insucient. To simplify,divide both sides by \(x^2\), resulting in 1 > x. If that's true, x could be between 0 and 1, but it could also be less than 0.

Statement (2) is also insucient. Again, simplify by dividing by \(x^2\), which gives you 1 > \(x^2\). Thus, x could be any number between -1 and 1. Again, it could be between 0 and 1, but it could also be between -1 and 0.

Taken together, it's still insucient. Both statements allow for the possibility that x is between 0 and 1, but both statements also make it possible that x is between -1 and 0. Choice (E) is correct.

Just one question about the highlighted part of the explanation: It is clear that \(x^2\) is always positive. However, is the division by \(x^2\) a valid inequality operation without knowing whether x is positive or negative?


When dividing/multiplying an inequality by a variable we need to know its sign. If it's positive we should keep the sign and if its negative we should flip the sign. That's the rule. We know that x^2 is positive, so we can safely multiply/divide an inequality by it (so in this case it does not matter whether x itself is positive or negative).
_________________

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

Re: Is x^2 greater than x ?   [#permalink] 30 Dec 2016, 08:20
    Similar topics Author Replies Last post
Similar
Topics:
7 Experts publish their posts in the topic Is x^2 greater than x-y? steilbergauf 3 12 Jun 2015, 17:57
14 Experts publish their posts in the topic Is x^2 greater than x ? Bunuel 17 26 Sep 2016, 11:50
8 Experts publish their posts in the topic Is x^2 greater than x ? carcass 7 12 Mar 2016, 18:39
Is x^2 greater than x? 1) x^2 is greater than 1 2) x is siddhans 5 29 Oct 2011, 22:04
10 Experts publish their posts in the topic Is x^2 greater than x? jscott319 19 18 Jul 2016, 04:51
Display posts from previous: Sort by

Is x^2 greater than x ?

  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®.