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If -1 < x < 0, which of the following must be true?

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If -1 < x < 0, which of the following must be true? [#permalink] New post 31 Jan 2013, 05:02
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If -1 < x < 0, which of the following must be true?

I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2

A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III
[Reveal] Spoiler: OA

Last edited by Bunuel on 31 Jan 2013, 05:29, edited 2 times in total.
Renamed the topic, edited the question, moved to PS forum and edited OA.
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Re: if -1<x<o, which of following must be true? [#permalink] New post 31 Jan 2013, 05:28
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rakesh20j wrote:
if -1<x<o, which of following must be true?
1) x^3<x^2 2) x^5<1-x 3) x^4<x^2

A. I only B. I and II C. I II and III D. I and III E. II and III


The question should read:

If -1 < x < 0, which of the following must be true?

I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2


A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III

I. x^3 < x^2 --> from -1 < x < 0 it follows that LHS<0<RHS, so this statement is true.

II. x^5 < 1 – x --> x(x^4+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.

III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 0, then x^2 must be less than 1. Hence, this statement is also true.

Answer: E.

Hope it's clear.
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Re: if -1<x<o, which of following must be true? [#permalink] New post 01 Jun 2013, 02:49
Bunuel wrote:
rakesh20j wrote:
if -1<x<o, which of following must be true?
1) x^3<x^2 2) x^5<1-x 3) x^4<x^2

A. I only B. I and II C. I II and III D. I and III E. II and III


The question should read:

If -1 < x < 0, which of the following must be true?

I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2


A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III

I. x^3 < x^2 --> from -1 < x < 0 it follows that LHS<0<RHS, so this statement is true.

II. x^5 < 1 – x --> x(x^4+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.

III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 0, then x^2 must be less than 1. Hence, this statement is also true.

Answer: E.

Hope it's clear.


Bunuel,

Did not understand the colored part. :(

As -1 < x < 0, then X will always be negative and X2 will always be positive, so how to derive that x<1.
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Re: if -1<x<o, which of following must be true? [#permalink] New post 01 Jun 2013, 02:57
Expert's post
targetbschool wrote:
Bunuel wrote:
rakesh20j wrote:
if -1<x<o, which of following must be true?
1) x^3<x^2 2) x^5<1-x 3) x^4<x^2

A. I only B. I and II C. I II and III D. I and III E. II and III


The question should read:

If -1 < x < 0, which of the following must be true?

I. x^3 < x^2
II. x^5 < 1 – x
III. x^4 < x^2


A. I only
B. I and II only
C. II and III only
D. I and III only
E. I, II and III

I. x^3 < x^2 --> from -1 < x < 0 it follows that LHS<0<RHS, so this statement is true.

II. x^5 < 1 – x --> x(x^4+1) < 1 --> negative*positive < 0 < 1, so this statement is also true.

III. x^4 < x^2 --> reduce by x^2 (we can safely do that since from -1 < x < 0 is follows that x^2>0): x^2 < 1. Again, as -1 < x < 0, then x^2 must be less than 1. Hence, this statement is also true.

Answer: E.

Hope it's clear.


Bunuel,

Did not understand the colored part. :(

As -1 < x < 0, then X will always be negative and X2 will always be positive, so how to derive that x<1.


Consider this: x^4 < x^2 holds true if -1<x<0 or 0<x<1.

Therefore, since given that -1<x<0, then x^4 < x^2 must be true.

Hope it's 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.


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Re: If -1 < x < 0, which of the following must be true? [#permalink] New post 25 Jun 2014, 04:01
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Re: If -1 < x < 0, which of the following must be true?   [#permalink] 25 Jun 2014, 04:01
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