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Is x > 1? [#permalink]
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01 Nov 2009, 03:56
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Is x > 1? (1) x^3 > x (2) x^2 > x > 0
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Re: is X>1? [#permalink]
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01 Nov 2009, 04:23



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Re: is X>1? [#permalink]
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01 Nov 2009, 04:38
Bunuel wrote: Is \(x>1\)?
(1) \(x^3x>0\) > \(x(x^21)>0\): Two cases: A.\(x>0\), \(x^21>0\) > \(x>0\) and \(x>1\) \(x<1\)> \(x>1\) B. \(x<0\), \(x^21<0\) > \(x<0\) and \(1<x<1\) > \(1<x<0\)
Two ranges \(x>1\) or \(1<x<0\), not sufficient.
(2) \(x>0\), \(x^2>x\) > \(x^2x>0\)> \(x(x1)>0\) > as \(x>0\), \(x1>0\) > \(x>1\). One range \(x>1\). Sufficient.
Answer: B. bingo! and very clear derivation..



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Re: is X>1? [#permalink]
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01 Nov 2009, 05:07
If we put values in option 1, we can consider it sufficient also. x^3>x ==>> (2)^3> 2 ==>> wrong ==>> (2)^3>2===> Correct So x^3>x is true for all values of x greater than 1. Where did I go wrong???
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Re: is X>1? [#permalink]
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01 Nov 2009, 05:24
Hussain15 wrote: If we put values in option 1, we can consider it sufficient also.
x^3>x ==>> (2)^3> 2 ==>> wrong ==>> (2)^3>2===> Correct
So x^3>x is true for all values of x greater than 1.
Where did I go wrong??? Don't forget that 0 is also a possible value. So, x^3>x is true for all values of x greater than 0.



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Re: is X>1? [#permalink]
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01 Nov 2009, 05:27
Hussain15 wrote: If we put values in option 1, we can consider it sufficient also.
x^3>x ==>> (2)^3> 2 ==>> wrong ==>> (2)^3>2===> Correct
So x^3>x is true for all values of x greater than 1.
Where did I go wrong??? consider the values between 1 and 0. x^3>x ==>> (1/2)^3> 1/2



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Re: is X>1? [#permalink]
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01 Nov 2009, 05:33



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Re: is X>1? [#permalink]
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01 Nov 2009, 05:36



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Re: is X>1? [#permalink]
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01 Nov 2009, 05:43
Thanks!!! I got it now. Conclusion: The range of 1 to 1 is the deadly one. 1<x<0 :::Too dangerous 0<x<1 ::: Dangerous but well known due to square powers
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Re: is X>1? [#permalink]
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01 Nov 2009, 05:58
Bunuel wrote: Is \(x>1\)?
(1) \(x^3x>0\) > \(x(x^21)>0\): Two cases: A.\(x>0\), \(x^21>0\) > \(x>0\) and \(x>1\) \(x<1\)> \(x>1\) B. \(x<0\), \(x^21<0\) > \(x<0\) and \(1<x<1\) > \(1<x<0\)
Two ranges \(x>1\) or \(1<x<0\), not sufficient.
(2) \(x>0\), \(x^2>x\) > \(x^2x>0\)> \(x(x1)>0\) > as \(x>0\), \(x1>0\) > \(x>1\). One range \(x>1\). Sufficient.
Answer: B. Hi Bunuel! I have seen already your answers in which you mention the ranges both in inequalities & in modules questions. Can you kindly explain how does it work or refer to some good resource to understand the raging concept.
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Re: is X>1? [#permalink]
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01 Nov 2009, 06:20
Hussain15 wrote: Bunuel wrote: Is \(x>1\)?
(1) \(x^3x>0\) > \(x(x^21)>0\): Two cases: A.\(x>0\), \(x^21>0\) > \(x>0\) and \(x>1\) \(x<1\)> \(x>1\) B. \(x<0\), \(x^21<0\) > \(x<0\) and \(1<x<1\) > \(1<x<0\)
Two ranges \(x>1\) or \(1<x<0\), not sufficient.
(2) \(x>0\), \(x^2>x\) > \(x^2x>0\)> \(x(x1)>0\) > as \(x>0\), \(x1>0\) > \(x>1\). One range \(x>1\). Sufficient.
Answer: B. Hi Bunuel! I have seen already your answers in which you mention the ranges both in inequalities & in modules questions. Can you kindly explain how does it work or refer to some good resource to understand the raging concept. Unfortunately I can not refer to any resources as I studied this staff in school. But I'll try to explain the basics of it if you specify the issue or post question(s).
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Re: is X>1? [#permalink]
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02 Nov 2009, 07:39
@Bunuel
x>0, x^2>x > x^2x>0> x(x1)>0 > as x>0, x1>0 > x>1. One range x>1. Sufficient.
you haven't considered the second half i guess..
x(x1)>0 >x<0, x<1>x<1..
if x = 2 then 2(21)>0..
I think its E..correct me if am wrong..



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Re: is X>1? [#permalink]
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02 Nov 2009, 07:52



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Re: is X>1? [#permalink]
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02 Nov 2009, 08:07
Oh my bad..sloppy work..
Thanks Bunuel...



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Re: Is x > 1? [#permalink]
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05 Apr 2014, 09:12
gmattokyo wrote: Is x > 1?
(1) x^3 > x (2) x^2 > x > 0 sol: st1: x^3 >x (subtracting same value from both sides do not change the sign) x^3x >0 => x(x1) (x+1)>0 <(ve)(1)(+ve)(0)(ve)(1)(+ve)> 1<x<0 or x>1 two sol hence not sufficient st2: x^2 x>0 (also x>0) x(x1)>0 (also x>0) (+ve)(0)(ve)1(+ve) x>1 or x<0 <this can be retired since x>0 which is actual condition therefore x>1 so answer is option B











