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# integers and inequalities

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Joined: 22 Nov 2007
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Kudos [?]: 80 [0], given: 0

integers and inequalities [#permalink]  09 Mar 2008, 09:35
If x is positive, which of the following could be the correct ordering
of 1/x; 2x and x^2

I. x^2 < 2x < 1/x

II.
x^2 < 1/x < 2x

III
2x < x^2 < 1/x

I only
II only
III only
I and II only
I, II, III

fast method is required
CEO
Joined: 29 Aug 2007
Posts: 2528
Followers: 41

Kudos [?]: 365 [0], given: 19

Re: integers and inequalities [#permalink]  09 Mar 2008, 11:14
marcodonzelli wrote:
If x is positive, which of the following could be the correct ordering of 1/x, 2x and x^2

I. x^2 < 2x < 1/x
II. x^2 < 1/x < 2x
III. 2x < x^2 < 1/x

I only
II only
III only
I and II only
I, II, III

fast method is required

do not see any other method:
I. x^2 < 2x < 1/x is true if x = 0.5
II. x^2 < 1/x < 2x is true if x > 0.75
III. 2x < x^2 < 1/x is not true for any +ve value.
so D.
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Last edited by GMAT TIGER on 09 Mar 2008, 11:34, edited 1 time in total.
Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
Schools: Wharton'11 HBS'12
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Kudos [?]: 135 [0], given: 2

Re: integers and inequalities [#permalink]  09 Mar 2008, 11:21
dont know a fast method but 1 is the only one i get
CEO
Joined: 29 Aug 2007
Posts: 2528
Followers: 41

Kudos [?]: 365 [0], given: 19

Re: integers and inequalities [#permalink]  09 Mar 2008, 11:35
marcodonzelli wrote:
If x is positive, which of the following could be the correct ordering
of 1/x; 2x and x^2

I. x^2 < 2x < 1/x

II.
x^2 < 1/x < 2x

III
2x < x^2 < 1/x

I only
II only
III only
I and II only
I, II, III

fast method is required

i wonder why the format is cleared?

do not see any other method:
I. x^2 < 2x < 1/x is true if x = 0.5
II. x^2 < 1/x < 2x is true if x > 0.75
III. 2x < x^2 < 1/x is not true for any +ve value.

so D.
_________________
Current Student
Joined: 28 Dec 2004
Posts: 3437
Location: New York City
Schools: Wharton'11 HBS'12
Followers: 11

Kudos [?]: 135 [0], given: 2

Re: integers and inequalities [#permalink]  09 Mar 2008, 11:51
ouch..sunday is not going good for me ..grrr..so chalk down sunday as a day for me to take gmat..wait..gmats are not offered on sundays..woo hoo..

yes agree with D..somehow I didnt read the equality signs properly..

GMAT TIGER wrote:
marcodonzelli wrote:
If x is positive, which of the following could be the correct ordering
of 1/x; 2x and x^2

I. x^2 < 2x < 1/x

II.
x^2 < 1/x < 2x

III
2x < x^2 < 1/x

I only
II only
III only
I and II only
I, II, III

fast method is required

i wonder why the format is cleared?

do not see any other method:
I. x^2 < 2x < 1/x is true if x = 0.5
II. x^2 < 1/x < 2x is true if x > 0.75
III. 2x < x^2 < 1/x is not true for any +ve value.

so D.
Re: integers and inequalities   [#permalink] 09 Mar 2008, 11:51
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# integers and inequalities

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