|
Author |
Message |
|
TAGS:
|
|
|
Senior Manager
Status: ready to boMBArd
Joined: 31 Oct 2010
Posts: 493
Location: India
Concentration: Entrepreneurship, Strategy
GMAT 1: 710 Q48 V40
WE: Project Management (Manufacturing)
Followers: 10
Kudos [?]:
31
[0], given: 67
|
Which of the following represents the complete range of x [#permalink]
 08 Feb 2011, 09:29
Question Stats:
54% (02:45) correct
45% (01:36) wrong based on 15 sessions
Which of the following represents the complete range of x over which x^3 – 4x^5 < 0? A. 0 < |x| < ½ B. |x| > ½ C. –½ < x < 0 or ½ < x D. x < –½ or 0 < x < ½ E. x < –½ or x > 0
_________________
My GMAT debrief: from-620-to-710-my-gmat-journey-114437.html
|
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9564
[9] , given: 826
|
Re: Everything is Less Than Zero [#permalink]
08 Feb 2011, 09:41
9
This post received
KUDOS
|
|
|
|
|
|
Senior Manager
Joined: 08 Nov 2010
Posts: 435
WE 1: Business Development
Followers: 6
Kudos [?]:
25
[0], given: 161
|
Re: Everything is Less Than Zero [#permalink]
09 Feb 2011, 23:41
Thanks Bunuel. +1 A question - what is the best way u use to know if the "good" area is above or below? i mean - what was the best way for u to know that its between -1/2 to 0 i used numbers ex. 1/4 but it consumes time! is there any better technique? thanks.
_________________
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9564
[3] , given: 826
|
Re: Everything is Less Than Zero [#permalink]
10 Feb 2011, 03:28
3
This post received
KUDOS
144144 wrote: Thanks Bunuel. +1
A question - what is the best way u use to know if the "good" area is above or below?
i mean - what was the best way for u to know that its between -1/2 to 0
i used numbers ex. 1/4 but it consumes time! is there any better technique?
thanks. Check the link in my previous post. There are beautiful explanations by gurpreetsingh and Karishma. General idea is as follows: We have: (1+2x)*x^3*(1-2x)<0 --> roots are -1/2, 0, and 1/2 (equate the expressions to zero to get the roots and list them in ascending order), this gives us 4 ranges: x<-\frac{1}{2}, -\frac{1}{2}<x<0, 0<x<\frac{1}{2} and x>\frac{1}{2} --> now, test some extreme value: for example if x is very large number than first two terms ((1+2x) and x) will be positive but the third term will be negative which gives the negative product, so when x>\frac{1}{2} the expression is negative. Now the trick: as in the 4th range expression is negative then in 3rd it'll be positive, in 2nd it'l be negative again and finally in 1st it'll be positive: + - + -. So, the ranges when the expression is negative are: -\frac{1}{2}<x<0 (2nd range) or x>\frac{1}{2} (4th range). Hope its clear.
_________________
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
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. NEW!!!
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. NEW!!!
What are GMAT Club Tests?
25 extra-hard Quant Tests
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
SVP
Joined: 16 Nov 2010
Posts: 1721
Location: United States (IN)
Concentration: Strategy, Technology
Followers: 26
Kudos [?]:
228
[0], given: 34
|
Re: Everything is Less Than Zero [#permalink]
13 Feb 2011, 21:31
Hi Bunuel I'm getting D as answer : x^3(1-2x)(1+2x) < 0 -ve --- -1/2---- +ve--- 0----- -ve-----1/2--- +veCould you please explain where I'm wrong ? Regards, Subhash
_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)
Find out what's new at GMAT Club - latest features and updates
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3109
Location: Pune, India
Followers: 569
Kudos [?]:
2006
[3] , given: 92
|
Re: Everything is Less Than Zero [#permalink]
13 Feb 2011, 22:05
3
This post received
KUDOS
subhashghosh wrote: Hi Bunuel
I'm getting D as answer :
x^3(1-2x)(1+2x) < 0
-ve --- -1/2---- +ve--- 0----- -ve-----1/2--- +ve
Could you please explain where I'm wrong ?
Regards,
Subhash Even though your question is directed to Bunuel, I will give a quick explanation. The concept of the rightmost section being positive is applicable when every term is positive in the rightmost region. This is the case whenever the expressions involved are of the form (x - a) or (ax - b) etc. When you have a term such as (1-2x), the rightmost region becomes negative. So either, as Bunuel mentioned, check for an extreme value of x or convert (1-2x) to (2x - 1) and flip the sign to >.
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Senior Manager
Joined: 08 Nov 2010
Posts: 435
WE 1: Business Development
Followers: 6
Kudos [?]:
25
[0], given: 161
|
Re: Everything is Less Than Zero [#permalink]
15 Feb 2011, 14:33
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9564
[0], given: 826
|
Re: Everything is Less Than Zero [#permalink]
02 Mar 2011, 18:04
|
|
|
|
|
|
Director
Status: Admitted
Affiliations: Chicago Booth
Joined: 03 Feb 2011
Posts: 947
Followers: 10
Kudos [?]:
143
[0], given: 123
|
Re: Everything is Less Than Zero [#permalink]
02 Mar 2011, 18:40
Karishma I flipped the sign before. So I got x^3(2x-1)(2x-1) > 0 2 cases - both +ve or both -ve case 1 ------- x > 0 and |x| > 1/2. Hence x > 1/2 case 2 ------ x < 0 and 4x^2 - 1 < 0 x < 0 and -1/2 < x < 1/2 Taking the most restrictive value- -1/2 < x < 0 I hope this is correct. Btw this is 750 level in 2 mins. VeritasPrepKarishma wrote: subhashghosh wrote: Hi Bunuel
I'm getting D as answer :
x^3(1-2x)(1+2x) < 0
-ve --- -1/2---- +ve--- 0----- -ve-----1/2--- +ve
Could you please explain where I'm wrong ?
Regards,
Subhash Even though your question is directed to Bunuel, I will give a quick explanation. The concept of the rightmost section being positive is applicable when every term is positive in the rightmost region. This is the case whenever the expressions involved are of the form (x - a) or (ax - b) etc. When you have a term such as (1-2x), the rightmost region becomes negative. So either, as Bunuel mentioned, check for an extreme value of x or convert (1-2x) to (2x - 1) and flip the sign to >. |
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3109
Location: Pune, India
Followers: 569
Kudos [?]:
2006
[1] , given: 92
|
Re: Everything is Less Than Zero [#permalink]
02 Mar 2011, 19:12
1
This post received
KUDOS
gmat1220 wrote: Karishma
I flipped the sign before. So I got x^3(2x-1)(2x-1) > 0
2 cases - both +ve or both -ve
case 1
-------
x > 0 and |x| > 1/2. Hence x > 1/2
case 2
------
x < 0 and 4x^2 - 1 < 0
x < 0 and -1/2 < x < 1/2
Taking the most restrictive value-
-1/2 < x < 0
I hope this is correct. Btw this is 750 level in 2 mins.
Yes, it is correct... and since you know what you are doing, you will need to work very hard to fall short of time on GMAT.
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9564
[0], given: 826
|
Re: Everything is Less Than Zero [#permalink]
04 Mar 2011, 02:52
|
|
|
|
|
|
SVP
Joined: 01 Sep 2010
Posts: 1745
Followers: 55
Kudos [?]:
568
[0], given: 467
|
Which of the following represents the complete range of x ov [#permalink]
02 Mar 2012, 11:45
Which of the following represents the complete range of x over which x^3 – 4x^5 < 0? (A) 0 < |x| < ½ (B) |x| > ½ (C) –½ < x < 0 or ½ < x (D) x < –½ or 0 < x < ½ (E) x < –½ or x > 0
_________________
KUDOS is the good manner to help the entire community.
|
|
|
|
|
|
GMAT Club team member
Joined: 02 Sep 2009
Posts: 11534
Followers: 1795
Kudos [?]:
9564
[0], given: 826
|
Re: Which of the following represents the complete range of x ov [#permalink]
02 Mar 2012, 11:53
|
|
|
|
|
|
Manager
Joined: 16 Feb 2012
Posts: 213
Concentration: Finance, Economics
Followers: 4
Kudos [?]:
17
[0], given: 93
|
Re: Everything is Less Than Zero [#permalink]
11 Jun 2012, 05:42
VeritasPrepKarishma wrote: gmat1220 wrote: Karishma
I flipped the sign before. So I got x^3(2x-1)(2x-1) > 0
2 cases - both +ve or both -ve
case 1
-------
x > 0 and |x| > 1/2. Hence x > 1/2
case 2
------
x < 0 and 4x^2 - 1 < 0
x < 0 and -1/2 < x < 1/2
Taking the most restrictive value-
-1/2 < x < 0
I hope this is correct. Btw this is 750 level in 2 mins.
Yes, it is correct... and since you know what you are doing, you will need to work very hard to fall short of time on GMAT. Thanks for the explanation. It's very useful to know to solve any problem with different approaches...
_________________
Kudos if you like the post!
Failing to plan is planning to fail.
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3109
Location: Pune, India
Followers: 569
Kudos [?]:
2006
[1] , given: 92
|
Re: Everything is Less Than Zero [#permalink]
20 Jun 2012, 22:42
1
This post received
KUDOS
gmatpapa wrote: Which of the following represents the complete range of x over which x^3 - 4x^5 < 0?
(A) 0 < |x| < ½
(B) |x| > ½
(C) –½ < x < 0 or ½ < x
(D) x < –½ or 0 < x < ½
(E) x < –½ or x > 0 Responding to a pm: The problem is the same here. How do you solve this inequality: (1+2x)*x^3*(1-2x)<0Again, there are 2 ways - The long algebraic method: When is (1+2x)*x^3*(1-2x) negative? When only one of the terms is negative or all 3 are negative. There will be too many cases to consider so this is painful. The number line method: Multiply both sides of (1+2x)*x^3*(1-2x)<0 by -1 to get (2x + 1)*x^3*(2x - 1)>0Take out 2 common to get 2(x + 1/2)*x^3*2(x - 1/2)>0 [because you want each term to be of the form (x + a) or (x - a)] Now plot them on the number line and get the regions where this inequality holds. Basically, you need to go through this entire post: inequalities-trick-91482.html
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Intern
Joined: 08 May 2012
Posts: 8
Followers: 0
Kudos [?]:
0
[0], given: 14
|
Re: Which of the following represents the complete range of x [#permalink]
21 Jun 2012, 19:11
thankyou, actually after your reply to the other thread this one i got very easily.
Also the lnk is best for summary as well that you posted.
|
|
|
|
|
|
Director
Status: Final Lap Up!!!
Affiliations: NYK Line
Joined: 21 Sep 2012
Posts: 906
Location: India
GMAT Date: 05-29-2013
GPA: 3.2
WE: Engineering (Transportation)
Followers: 12
Kudos [?]:
83
[1] , given: 55
|
Re: Which of the following represents the complete range of x [#permalink]
01 Nov 2012, 16:06
1
This post received
KUDOS
Bunuel
Thanx a trillion for your post on solving inequalities using graph
You know i paid over 300$ to test prep institutes but got nothing out of it.......when i asked such basic question the tutor got frustrated and insulted me.....But hats off to you... MAx wat will i give 1 kudo......
Wat an expeirence it has been with GMAt club
Thanx a lot Bunuel
Trillion kudos to you and Hats off to you for addressing problems with patience..............I cant express myself how satisfied i am feeling.
|
|
|
|
|
|
Intern
Joined: 27 Nov 2010
Posts: 2
Followers: 0
Kudos [?]:
1
[0], given: 2
|
Re: Which of the following represents the complete range of x [#permalink]
15 Nov 2012, 13:58
Hi All,
Could I conclude that for this case i.e (1+2x)*x^3*(1-2x)<0
even if one of the terms <0, that does not necessarily mean that the entire product of the 3 terms <0.
Cause like if the eq was (1+2x)*x^3*(1-2x)= 0 ....I could have safely concluded that
However in this case for the entire product <0.. either 1 terms or 2 terms or even all 3 terms can be - ve.
|
|
|
|
|
|
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 3109
Location: Pune, India
Followers: 569
Kudos [?]:
2006
[1] , given: 92
|
Re: Which of the following represents the complete range of x [#permalink]
15 Nov 2012, 19:03
1
This post received
KUDOS
lesnin wrote: Hi All,
Could I conclude that for this case i.e (1+2x)*x^3*(1-2x)<0
even if one of the terms <0, that does not necessarily mean that the entire product of the 3 terms <0.
Cause like if the eq was (1+2x)*x^3*(1-2x)= 0 ....I could have safely concluded that
However in this case for the entire product <0.. either 1 terms or 2 terms or even all 3 terms can be - ve. When you have product of two or more terms, the product will be negative only when odd number of terms are negative i.e. either only one term is negative and rest are positive or only 3 terms are negative and rest are positive or only 5 terms are negative and rest are positive. (-)(+)(+) = (-) (-)(-)(+) = (+) (-)(-)(-) = (-)
_________________
Karishma
Veritas Prep | GMAT Instructor
My Blog
Save 10% on Veritas Prep GMAT Courses And Admissions Consulting
Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options.
Veritas Prep Reviews
|
|
|
|
|
|
Senior Manager
Joined: 13 Aug 2012
Posts: 468
Followers: 12
Kudos [?]:
75
[0], given: 11
|
Re: Which of the following represents the complete range of x [#permalink]
06 Dec 2012, 04:15
Using the amazing technique:
x^3(1-4x^2)<0
x^3(1-2x)(1+2x)<0
+ (-1/2) - (0) + (1/2) -
If less than 0, select (-) curves.
Answer: -1/2 < x < 0 or 1/2 < x ==> C
|
|
|
|
|
|
|
Re: Which of the following represents the complete range of x
[#permalink]
06 Dec 2012, 04:15
|
|
|
|
|
|
|
|
|
|
|
close
