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

It is currently 29 Jul 2014, 08:56

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:
Manager
Manager
avatar
Joined: 10 Feb 2011
Posts: 116
Followers: 1

Kudos [?]: 20 [0], given: 10

Is x < 0 ? [#permalink] New post 01 Mar 2011, 09:51
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

35% (00:00) correct 65% (00:52) wrong based on 17 sessions
Is x < 0 ?

(1) x^3 < x^2
(2) x^3 < x^4
[Reveal] Spoiler: OA
Director
Director
avatar
Status: Matriculating
Affiliations: Chicago Booth Class of 2015
Joined: 03 Feb 2011
Posts: 932
Followers: 11

Kudos [?]: 182 [0], given: 123

Reviews Badge
Re: Is x < 0 ? (1) x3 < x2 (2) x3 < x4 [#permalink] New post 01 Mar 2011, 09:58
banksy wrote:
Is x < 0 ?
(1) x^3 < x^2
(2) x^3 < x^4


1) Insufficient. x < 0 or 0< x < 1
2) Insufficient. x < 0 or x > 1

1) + 2) Sufficient.

if 0 < x < 1 then x^4 < x^3 < x^2
if x < 0 then x^3 is negative and x^2 and x^4 are positive.

C
Manager
Manager
avatar
Joined: 14 Dec 2010
Posts: 220
Location: India
Concentration: Technology, Entrepreneurship
GMAT 1: 680 Q44 V39
Followers: 2

Kudos [?]: 18 [0], given: 5

GMAT Tests User
Re: Is x < 0 ? (1) x3 < x2 (2) x3 < x4 [#permalink] New post 01 Mar 2011, 23:20
I agree. C is correct.
Statement 1 tells us that x could be less than 0 or between 0 and 1. So insufficient.
Statement 2 tells us that x could be less than 0 or greater than 1. So insufficient.

Combining 1 and 2, we can deduce that x should be less than 0. So sufficient.
Math Forum Moderator
avatar
Joined: 20 Dec 2010
Posts: 2048
Followers: 126

Kudos [?]: 884 [0], given: 376

GMAT Tests User
Re: Is x < 0 ? (1) x3 < x2 (2) x3 < x4 [#permalink] New post 02 Mar 2011, 00:04
banksy wrote:
Is x < 0 ?
(1) x^3 < x^2
(2) x^3 < x^4


Can someone explain how to find the ranges using the number line approach (+ve and -ve curves); I find these types so tough.

1.
x^3 < x^2
x^3 - x^2 < 0
x^2(x-1) < 0

Roots are; 0 and 1
Now; for a very small value of x; the above equation holds true

So; the ranges are x<0, 0<x<1, x>1

According to the rule; we should consider the -ve curves for "<" sign

so; x<0 and x>1. However, the correct ranges are x<0 or 0<x<1.

How come the positive curve 0<x<1 holds true for "<" sign and x>1 doesn't; How does the rule change for even exponents and odd exponents.

(2) x^3 < x^4

x^3 - x^4 <0
x^3(1-x) < 0
x^3(x-1) > 0 {Multiplying by -ve}

roots 0 and 1

for a big value of x, the above equation holds good
so; the ranges are; x>1, 0<x<1, x<0

Considering +ve curves because the sign here is ">"
x>1
x<0

This looks okay.
_________________

~fluke

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Expert Post
2 KUDOS received
Math Expert
User avatar
Joined: 02 Sep 2009
Posts: 18816
Followers: 3263

Kudos [?]: 22699 [2] , given: 2640

Re: Is x < 0 ? (1) x3 < x2 (2) x3 < x4 [#permalink] New post 02 Mar 2011, 01:44
2
This post received
KUDOS
Expert's post
fluke wrote:
banksy wrote:
Is x < 0 ?
(1) x^3 < x^2
(2) x^3 < x^4


Can someone explain how to find the ranges using the number line approach (+ve and -ve curves); I find these types so tough.

1.
x^3 < x^2
x^3 - x^2 < 0
x^2(x-1) < 0

Roots are; 0 and 1
Now; for a very small value of x; the above equation holds true

So; the ranges are x<0, 0<x<1, x>1

According to the rule; we should consider the -ve curves for "<" sign

so; x<0 and x>1. However, the correct ranges are x<0 or 0<x<1.

How come the positive curve 0<x<1 holds true for "<" sign and x>1 doesn't; How does the rule change for even exponents and odd exponents.

(2) x^3 < x^4

x^3 - x^4 <0
x^3(1-x) < 0
x^3(x-1) > 0 {Multiplying by -ve}

roots 0 and 1

for a big value of x, the above equation holds good
so; the ranges are; x>1, 0<x<1, x<0

Considering +ve curves because the sign here is ">"
x>1
x<0

This looks okay.


You should simplify x^3 < x^2 first. Reduce by x^2 (x^3 < x^2 means that x is not equal to zero so x^2>0) --> x<1, excluding one point x=0.

So you can ignore the even power expressions in the approach you talk (just look whether zero is inclusive or not). For example, solve (x+3)(x+1)(x-1)(x+5)^2<0:

Reduce by (x+5)^2 and note that x doesn't equal to -5'
So we have (x+3)(x+1)(x-1)<0 and x doesn't equal to -5 --> roots -3, -1 and 1. Trying extreme value for x tells that in 4th range (when x>1) the whole expression is positive so it's negative in 3rd and 1st ranges (+-+-): -1<x<1 or x<-3 excluding x=-5 (you can wirte it also as x<-5, or -5<x<-3, or -1<x<1).

If it were: (x+3)(x+1)(x-1)(x+5)^2<=0 then the answer would be: -1<=x<=1 or x<=-3 (so x=-5, as well as the other roots, is included as the whole expression can equal to zero)

Hope its' clear.
_________________

NEW TO MATH FORUM? PLEASE READ THIS: ALL YOU NEED FOR QUANT!!!

PLEASE READ AND FOLLOW: 11 Rules for Posting!!!

RESOURCES: [GMAT MATH BOOK]; 1. Triangles; 2. Polygons; 3. Coordinate Geometry; 4. Factorials; 5. Circles; 6. Number Theory; 7. Remainders; 8. Overlapping Sets; 9. PDF of Math Book; 10. Remainders; 11. GMAT Prep Software Analysis NEW!!!; 12. SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) NEW!!!; 12. Tricky questions from previous years. NEW!!!;

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?
25 extra-hard Quant Tests

Get the best GMAT Prep Resources with GMAT Club Premium Membership

Re: Is x < 0 ? (1) x3 < x2 (2) x3 < x4   [#permalink] 02 Mar 2011, 01:44
    Similar topics Author Replies Last post
Similar
Topics:
9 Experts publish their posts in the topic If xyz < 0, is x < 0 ? Bunuel 6 27 Jun 2014, 09:21
29 Experts publish their posts in the topic If 0<x<y, is y-x < 0.00005 imhimanshu 16 05 Apr 2012, 08:26
2 Experts publish their posts in the topic Is x<0 ? ashiima 10 10 Dec 2011, 16:52
1 Is X < 0 ? mustu 4 01 Jul 2011, 07:06
2 Experts publish their posts in the topic If x≠0, is |x| < 1? SMAbbas 5 19 Oct 2009, 06:10
Display posts from previous: Sort by

Is x < 0 ?

  Question banks Downloads My Bookmarks Reviews Important topics  


GMAT Club MBA Forum Home| About| Privacy Policy| 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®.