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Is x > x^2 ? (1) x is greater than x^3 (2) x is greater t

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Is x > x^2 ? (1) x is greater than x^3 (2) x is greater t [#permalink] New post 04 Feb 2012, 08:23
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Question Stats:

57% (02:16) correct 42% (01:28) wrong based on 38 sessions
Is x > x^2 ?

(1) x is greater than x^3

(2) x is greater than x^4


hi can you solve this Agebraically instead of picking numbers
[Reveal] Spoiler: OA

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Last edited by Bunuel on 04 Feb 2012, 08:30, edited 1 time in total.
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Re: x > x^2 [#permalink] New post 04 Feb 2012, 08:58
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Expert's post
rxs0005 wrote:
B

what I have been realizing ( i feel its wrong now ) is that

x ( x - 1 ) < 0 Means

either x< 0 or x - 1 < 0 or x < 1

so x < 0 or x < 1 how did u get 0 < x < 1 ?


x(x-1)<0 --> roots are x=0 and x=1 --> "<" sign indicates that the solution lies between the roots: 0<x<1:
Attachment:
1.gif
1.gif [ 891 Bytes | Viewed 978 times ]


If it were: x(x-1)>0 --> the same roots: x=0 and x=1 --> ">" sign indicates that the solution lies to the left of the smaller root and to the right of the larger root: x<0 or x>1:
Attachment:
2.gif
2.gif [ 997 Bytes | Viewed 979 times ]


Follow the links in my previous post for more on this subject.

Hope it helps.
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Re: x > x^2 [#permalink] New post 04 Feb 2012, 08:29
Expert's post
rxs0005 wrote:
hi can you solve this Agebraically instead of picking numbers

Is x > x^2 ?

S1 x is greater than x^3

S2 x is greater than x^4


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

(1) x > x^3 --> x*(x^2-1)<0 --> (x+1)*x*(x-1)<0 --> 0<x<1 or x<-1. Not sufficient.

(2) x > x^4 --> 0<x<1 (only in this range x will be more than x^4). Sufficient.

Answer: B.

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Check this for more on solving this kind of inequalities:
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everything-is-less-than-zero-108884.html?hilit=extreme#p868863
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Hope it helps.
_________________

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?
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Director
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Re: x > x^2 [#permalink] New post 04 Feb 2012, 08:30
thanks B

nice to have u back
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Director
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Re: x > x^2 [#permalink] New post 04 Feb 2012, 08:39
B

what I have been realizing ( i feel its wrong now ) is that

x ( x - 1 ) < 0 Means

either x< 0 or x - 1 < 0 or x < 1

so x < 0 or x < 1 how did u get 0 < x < 1 ?
_________________

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Re: Is x > x^2 ? (1) x is greater than x^3 (2) x is greater t [#permalink] New post 23 Feb 2014, 04:57
Expert's post
Re: Is x > x^2 ? (1) x is greater than x^3 (2) x is greater t   [#permalink] 23 Feb 2014, 04:57
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