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Re: if -1<x<o, which of following must be true? [#permalink]
31 Jan 2013, 05:28

1

This post received KUDOS

Expert's post

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.

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

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. _________________

"Where are my Kudos" ............ Good Question = kudos

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

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

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