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

It is currently 08 Feb 2016, 11:49
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 > 0 ?

  Question banks Downloads My Bookmarks Reviews Important topics  
Author Message
TAGS:
Senior Manager
Senior Manager
User avatar
Joined: 13 Aug 2012
Posts: 464
Concentration: Marketing, Finance
GMAT 1: Q V0
GPA: 3.23
Followers: 19

Kudos [?]: 320 [0], given: 11

GMAT ToolKit User
Re: Is x > 0 ? [#permalink] New post 15 Jan 2013, 06:22
rxs0005 wrote:
Is x > 0 ?
(1) x < x^2
(2) x < x^3


1. x < x^2
Test x = 2: 2 < 4 OK!
Test x = -1: -1 < 1 OK!
Test x = -1/4: -1/4 < -1/16 OK!
INSUFFICIENT!

2. x < x^3
Test x = 2: 2 < 8 OK!
Test x = -1: -1 = -1 NOT OK!
Test x = -1/4: -1/4 < -1/64 OK!
INSUFFICIENT!

Together: When x is negative fraction or x is greater than 2, both inequalities work!

Answer: E
_________________

Impossible is nothing to God.

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8177
Followers: 416

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: Is x > 0 ? [#permalink] New post 08 Jul 2014, 00:22
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

GMAT Club Legend
GMAT Club Legend
User avatar
Joined: 09 Sep 2013
Posts: 8177
Followers: 416

Kudos [?]: 111 [0], given: 0

Top 10 in overall
Re: Is x > 0 ? [#permalink] New post 12 Nov 2015, 00:45
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

Manager
Manager
avatar
Joined: 07 Feb 2015
Posts: 84
Followers: 1

Kudos [?]: 6 [0], given: 28

Is x > 0? [#permalink] New post 03 Dec 2015, 18:08
Is x > 0?

(1) \(x < x^2\)

(2) \(x < x^3\)

[Reveal] Spoiler:
Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).
Math Forum Moderator
avatar
Joined: 20 Mar 2014
Posts: 2223
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 68

Kudos [?]: 832 [0], given: 615

Re: Is x > 0? [#permalink] New post 03 Dec 2015, 18:17
gmatser1 wrote:
Is x > 0?

(1) \(x < x^2\)

(2) \(x < x^3\)

[Reveal] Spoiler:
Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).


Question asks if x>0 ?

Per statement 1, x^2>x --> x^2-x>0 ---> x(x-1)>0 ---> either x<0 or x>1. Not sufficient to answer the question asked.

Per statement 2, x^3>x ---> x^3-x>0 ---> x(x+1)(x-1)>0 ---> either -1<x<0 or x> 1. Again, not sufficient to answer the question asked.

Combining the 2 statements, you get the ranges for x as -1<x<0 or x>1. Again, still not a definitive answer to the question asked.

E is the correct answer.
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Intern
Intern
avatar
Joined: 30 Sep 2015
Posts: 4
Followers: 0

Kudos [?]: 0 [0], given: 5

Top 10 in overall CAT Tests
Re: Is x > 0? [#permalink] New post 03 Dec 2015, 21:37
Engr2012 wrote:
gmatser1 wrote:
Is x > 0?

either x<0


what is the rationale for inverting the inequality sign?
Expert Post
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 31286
Followers: 5348

Kudos [?]: 62176 [0], given: 9444

Re: Is x > 0 ? [#permalink] New post 03 Dec 2015, 22:43
Expert's post
gmatser1 wrote:
Is x > 0?

(1) \(x < x^2\)

(2) \(x < x^3\)

[Reveal] Spoiler:
Explanation: Statement (1) is insufficient. If \(x < x^3\), x could be negative: \(x^2\) will always be positive, so for any negative value of x, \(x^2\) will be greater. x could also be positive and greater than 1: for any such value, \(x^2\) will be larger. If x is positive and less than 1, \(x^2\) is smaller. Long story short: according to (1), x must be negative or greater than 1. That isn’t enough information.

Statement (2) is also insufficient. x must be between –1 and 0, or greater than 1. If x is a negative fraction, \(x^3\) is a larger number: a negative fraction closer to zero. If x is a positive number greater than 1, \(x^3\) is greater still.

Taken together, it’s still not enough information to determine whether x is positive. x could be between –1 and 0, or it could be greater than 1. The correct choice is (E).


Merging topics.

Please refer to the discussion on previous 2 pages.
_________________

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

Math Forum Moderator
avatar
Joined: 20 Mar 2014
Posts: 2223
GMAT 1: 650 Q49 V30
GMAT 2: 690 Q49 V34
GMAT 3: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Followers: 68

Kudos [?]: 832 [0], given: 615

Re: Is x > 0 ? [#permalink] New post 04 Dec 2015, 03:39
AS7x wrote:
Engr2012 wrote:
gmatser1 wrote:
Is x > 0?

either x<0


what is the rationale for inverting the inequality sign?


What step in particular are you talking about ? I don't see any inversion of the inequality sign!
_________________

Thursday with Ron updated list as of July 1st, 2015: http://gmatclub.com/forum/consolidated-thursday-with-ron-list-for-all-the-sections-201006.html#p1544515
Rules for Posting in Quant Forums: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html
Writing Mathematical Formulae in your posts: http://gmatclub.com/forum/rules-for-posting-please-read-this-before-posting-133935.html#p1096628
GMATCLUB Math Book: http://gmatclub.com/forum/gmat-math-book-in-downloadable-pdf-format-130609.html
Everything Related to Inequalities: http://gmatclub.com/forum/inequalities-made-easy-206653.html#p1582891
Debrief, 650 to 750: http://gmatclub.com/forum/650-to-750-a-10-month-journey-to-the-score-203190.html

Re: Is x > 0 ?   [#permalink] 04 Dec 2015, 03:39

Go to page   Previous    1   2   [ 28 posts ] 

    Similar topics Author Replies Last post
Similar
Topics:
4 Experts publish their posts in the topic If x ≠ 0, is xy > 0? Bunuel 8 19 Jun 2015, 00:58
4 Experts publish their posts in the topic If x > 0, is √x > x ? Bunuel 5 16 Feb 2015, 05:48
2 Experts publish their posts in the topic Is 5 > x > 0 ? GMATD11 9 28 Feb 2011, 23:18
9 Experts publish their posts in the topic If x > 0, is x/y > x ? amitgovin 14 08 Oct 2009, 12:27
2 Is x > 0.05? LM 9 23 Jun 2007, 01:50
Display posts from previous: Sort by

Is x > 0 ?

  Question banks Downloads My Bookmarks Reviews Important topics  


cron

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®.