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# Is x between 0 & 1? 1. x^2 is less than x 2. x^3 is

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Is x between 0 & 1? 1. x^2 is less than x 2. x^3 is [#permalink]

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25 May 2004, 06:19
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Is x between 0 & 1?
1. x^2 is less than x
2. x^3 is positive
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25 May 2004, 07:29
A) is sufficient
x^2 is always +ve and since it is less than x X has to be +ve and always lies between 0 and 1

B) Just tells us that x is +ve(Insufficient)
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25 May 2004, 16:05
mirhaque wrote:
Is x between 0 & 1?
1. x^2 is less than x
2. x^3 is positive

A
x^2-x<0; x(1-x)>0
hence, either x>0 AND x<1; or x<0 AND x>1
The latter makes no sense so x>0 AND x<1 has to be true!
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27 May 2004, 15:08
(1) Tell us that either -1<x<0 or 0<x<1.

(2) Tell us that x>0

== > so to me both statements are mandatory and we get 0<x<1

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27 May 2004, 20:21
Bundo wrote:
(1) Tell us that either -1<x<0 or 0<x<1.

(2) Tell us that x>0

== > so to me both statements are mandatory and we get 0<x<1

(1) x^2 < x

let x= 1/2 , (1/2)^2 < 1/2
let x = - 1/2 , ( -1/2) ^2 = 1/4. Thus 1/4> - 1/2, which means in order for x^2 < x, x has to be +ve. (1) is sufficient.

(2) simply says x is +ve. X can be 2, 3, 4, or 1/2 or 1/3 0r 1/5 . Squaring any of these numbers can be both greater or less than than original x.

Thus, (1) is sufficient

which means
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28 May 2004, 01:43
You re rigth, I have completely overlooked the fact that -1/2 < 1/4
28 May 2004, 01:43
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