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Is x between 0 and 1?

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Is x between 0 and 1? [#permalink] New post 06 Feb 2014, 00:16
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Difficulty:

  15% (low)

Question Stats:

76% (01:41) correct 24% (00:36) wrong based on 115 sessions
The Official Guide For GMAT® Quantitative Review, 2ND Edition

Is x between 0 and 1?

(1) x^2 is less than x.
(2) x^3 is positive.

Data Sufficiency
Question: 76
Category: Arithmetic Arithmetic operations
Page: 158
Difficulty: 600


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Re: Is x between 0 and 1? [#permalink] New post 06 Feb 2014, 00:16
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SOLUTION

Is x between 0 and 1?

(1) x^2 is less than x --> x^2<x --> x(x-1)<0:

Multiples must have opposite signs:
x<0 and x-1>0, or x>1 --> no solution (x cannot be simultaneously less than zero and more than 1);
x>0 and x-1<0, or x<1 --> 0<x<1;

So x(x-1)<0 holds true when 0<x<1. Sufficient.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

(2) x^3 is positive --> x^3>0 just tells us that x is positive. Not sufficient.

Answer: A.
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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.


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Re: Is x between 0 and 1? [#permalink] New post 06 Feb 2014, 10:58
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Is x between 0 and 1?

(1) x^2 is less than x.
(2) x^3 is positive.

St1: x>x^2-----> x(1-x)>0
So either x>0 and 1-x>0 or 1>x and thus 0<x<1 or
x<0 or 1-x<0 or x>1...this is not possible cause we said x<0 so st1 alone is sufficent

St2: x^3 is positive...well there are many options like x=2 and x^3=8 or x=1/2 and x^3=1/8

So ans is A

Difficulty level 600 is okay

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Re: Is x between 0 and 1? [#permalink] New post 07 Feb 2014, 18:12
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Is x between 0 and 1? -> is 0 < x < 1?

(1) x^2 is less than x -> only possible for values between 0 and 1. (if x < 0, x^2 always > x; if x > 1, x^2 always > x).
(2) x^3 is positive -> example: x = 2 or 1/2, Not sufficient.

A.
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Re: Is x between 0 and 1? [#permalink] New post 08 Feb 2014, 04:55
Expert's post
SOLUTION

Is x between 0 and 1?

(1) x^2 is less than x --> x^2<x --> x(x-1)<0:

Multiples must have opposite signs:
x<0 and x-1>0, or x>1 --> no solution (x cannot be simultaneously less than zero and more than 1);
x>0 and x-1<0, or x<1 --> 0<x<1;

So x(x-1)<0 holds true when 0<x<1. Sufficient.

For alternate approach check "How to solve quadratic inequalities": x2-4x-94661.html#p731476

(2) x^3 is positive --> x^3>0 just tells us that x is positive. Not sufficient.

Answer: A.
_________________

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

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Re: Is x between 0 and 1? [#permalink] New post 23 May 2014, 06:45
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Hi Bunuel, Just a small typo here. This is question number 76 on page#189 in OG Quant Review and not 71 as you mention here. thanks
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Re: Is x between 0 and 1? [#permalink] New post 23 May 2014, 09:11
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MensaNumber wrote:
Hi Bunuel, Just a small typo here. This is question number 76 on page#189 in OG Quant Review and not 71 as you mention here. thanks


Edited. Thank you. BTW, the question IS on page 158, the solution is on 189.
_________________

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

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Joined: 29 Oct 2013
Posts: 173
Concentration: Finance
GMAT 1: 750 Q48 V46
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Followers: 3

Kudos [?]: 107 [0], given: 115

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Re: Is x between 0 and 1? [#permalink] New post 23 May 2014, 09:29
Great! yup youre right about the page no.
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Re: Is x between 0 and 1?   [#permalink] 23 May 2014, 09:29
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