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# Is X>1? 1) x^3>x 2) x^2>x>0

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Is X>1? 1) x^3>x 2) x^2>x>0 [#permalink]  19 Mar 2006, 15:39
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Is X>1?
1) x^3>x
2) x^2>x>0

Last edited by Professor on 19 Mar 2006, 19:21, edited 1 time in total.
Manager
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Re: DS [#permalink]  19 Mar 2006, 19:10
Professor wrote:
Q. Is X>1?
1) x3>x
2) x2>x>0

E.

1) x=3 3(3) = 9, 9>x
x=-3 -3(3) = -9, -9<x
INSUFFICIENT

2) x = .5
.5(2) = 1
1>.5>0
INSUFFICIENT

tegether, we still can't get any further.

E it is
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Re: DS [#permalink]  19 Mar 2006, 19:16
kook44 wrote:

2) x = .5
.5(2) = 1
1>.5>0
INSUFFICIENT

tegether, we still can't get any further.

E it is

I belive Prof meant x2 => x^2. If that is true. it should be B.
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1) x^3>x

x^3-x > 0
x(x^2-1)>0
x(x-1)(x+1)>0

The inequality:

-1 < x < 0
x > 1

Insufficient as we do not know which range x falls into.

2) x^2 > x > 0

- We know x must be positive
- We know x^2 must be greater than x, so x cannot be a positive fraction (e.g. 1/2)
- We know x cannot be 1 as well since this will result in x^2 = x

Sufficient.

Ans B
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Re: DS [#permalink]  19 Mar 2006, 19:17
Professor wrote:
Q. Is X>1?
1) x3>x
2) x2>x>0

Prof, I'm taking x3 as x^3 & x2 as x^2.

"D".
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ywilfred wrote:
1) x^3>x

x^3-x > 0
x(x^2-1)>0
x(x-1)(x+1)>0

The inequality:

-1 < x < 0
x > 1

Insufficient as we do not know which range x falls into.

2) x^2 > x > 0

- We know x must be positive
- We know x^2 must be greater than x, so x cannot be a positive fraction (e.g. 1/2)
- We know x cannot be 1 as well since this will result in x^2 = x

Sufficient.

Ans B

Wilfred & girish,

I got how you treated first condition but I have a different view here.

x^3 > x

Without solving it, if we plug & play in this equation, we easily get the range of x i.e. x>1

Reason:
1) For x < 0
x^3 < x, if x = -3, x^3 = -27

2) For 0 < x < 1
x^3 < x, if x = 0.2, x^3 = 0.008

3) For x > 1
x^3 > x, if x = 3, x^3 = 27

The only range that satisfies x^3 > x, is x > 1.

Am I missing something?
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I put it down as insufficient as the questions asks whether we can definitely say that x is always greater than 1. Statement 1 tells us that x does not always has to be 1, it could be -1/2 and still satisfy the inequality given in statement 1.
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Re: DS [#permalink]  19 Mar 2006, 19:30
Professor wrote:
Q. Is X>1?
1) x^3>x
2) x^2>x>0

1) insufficient

2^3 > 2

but also

-1/2 ^ 3 > -1/2

so X could be smaller than 1

2) x>0 and x^2 > 0

sufficient

I would go with B
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ywilfred wrote:
I put it down as insufficient as the questions asks whether we can definitely say that x is always greater than 1. Statement 1 tells us that x does not always has to be 1, it could be -1/2 and still satisfy the inequality given in statement 1.

Yup, got it. Thanks
I got the blunder I made!
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Re: DS [#permalink]  19 Mar 2006, 19:36
thats correct. i updated the question.
vivek123 wrote:
Professor wrote:
Q. Is X>1?
1) x3>x
2) x2>x>0

Prof, I'm taking x3 as x^3 & x2 as x^2.

thanks guys. i donot have OA and OE. i borrowed it from here: http://www.gmatclub.com/phpbb/viewtopic.php?t=27371
Re: DS   [#permalink] 19 Mar 2006, 19:36
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