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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]  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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Kudos [?]: 62455 [1] , given: 9455

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

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.

Hope it's clear.
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Concentration: Strategy, Technology
GMAT Date: 08-01-2013
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Kudos [?]: 159 [0], given: 29

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

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.

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]  01 Jun 2013, 02:57
1
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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

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.

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.
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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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Re: If -1 < x < 0, which of the following must be true? [#permalink]  15 Sep 2015, 03:03
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If -1 < x < 0, which of the following must be true?   [#permalink] 15 Sep 2015, 03:03
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