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

Oldest

Best Reply

Author

Message

TAGS:

Intern

Joined: 31 Jan 2013

Posts: 2

Followers: 0

Kudos [?]: 0 [0], given: 2

If -1 < x < 0, which of the following must be true? [#permalink]

31 Jan 2013, 06:02

00:00

Question Stats:

53% (01:44) correct

46% (00:48) wrong

based on 8 sessions

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, 06:29, edited 2 times in total.

Renamed the topic, edited the question, moved to PS forum and edited OA.

GMAT Club team member

Joined: 02 Sep 2009

Posts: 11506

Followers: 1791

Kudos [?]: 9526 [0], given: 826

Re: if -1<x<o, which of following must be true? [#permalink]

31 Jan 2013, 06:28

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.
_________________

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

Re: if -1<x<o, which of following must be true? [#permalink] 31 Jan 2013, 06:28

		Similar topics	Author	Replies	Last post
Similar Topics:		If 0<x<1, which of the following must be true? 1.	2times	14	20 Aug 2006, 18:05
		x<y and z>0 which of the following must be true?	Capthan	2	20 Mar 2008, 07:11
		If b<1 and 2x-b=0 which of the following must be true?	redbeanaddict	1	10 Oct 2008, 21:25
	1	If -1< x <0 or x >1 then which of the following must be true	Joy111	1	25 May 2012, 07:56
	8	If x#0 and x/\|x\|<x, which of the following must be true?	Marcab	25	04 Dec 2012, 04:38

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

Main navigation

GMAT Resources

Partners

MBA Resources

GMAT ® is a registered trademark of the Graduate Management Admission Council ® (GMAC ®). GMAT Club's website has not been reviewed or endorsed by GMAC.

GMAT Courses

Admissions Consulting

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

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

Main navigation

GMAT Resources

Partners

MBA Resources