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If x is positive which of the following could be the correct

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If x is positive which of the following could be the correct [#permalink] New post 12 Aug 2008, 09:45
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If x is positive, which of the following could be the correct ordering of 1/x , 2x and x^2?

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

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

3. 2x < x^2 <1/x


I got that 1 is possible but from 2 and 3 another one is also possible according to the answer. Can someone please explain
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 10:01
I with you on that one. #2 and #3 don't seem possible to be in the right order. It's safe to say we're dealing with x as a positive fraction.
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 10:40
OA -- 1 and 2 are possible. See attached. This is a gmatprep question
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 10:58
x^2 < 1/x < 2x

Tell me if this works

multiply everything by x

x^3 < 1 < 2x^2

We know that if x is any fraction, x^3 will be less than 1 so we shouldn't be all that concerned with x^3 < 1...Now

1 < 2x^2

\frac{1}{2} < x^2

\sqrt{\frac{1}{2}} < x

\frac{1}{\sqrt{2}} < x

So, we have the final

\frac{1}{\sqrt{2}} < x < 1

and #2 can also be true
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:00
mba9now wrote:
If x is positive, which of the following could be the correct ordering of 1/x , 2x and x^2?

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

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

3. 2x < x^2 <1/x


I got that 1 is possible but from 2 and 3 another one is also possible according to the answer. Can someone please explain


x=1/2 I is possible (every body agrees with this)

2)
x^2 < 1/x < 2x
--> x^2-1/x<0 and 1/x-2x<0
x^3-1<0 and 2x*x-1>0 (x is positive)
(x-1)*(x2+1)<0 and x*x>1/2
(because x is postiive)
--> x<1 and x> 1/sqrt(2)

So its possible for any value > 1/sqrt(2) and <1


I and II possible.
3)

2x < x^2 <1/x

x^2-2x>0 and x^2-1/x<0
x*(x-2)>0 and x3-1<0
you know that x>0 (positive)
x-2>0 and x-1<0
x>2 and x<1 not possible at all.


only I and II possible.
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:02
Suresh, It looks like we agree with each other...again :-D
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:10
jallenmorris wrote:
Suresh, It looks like we agree with each other...again :-D


I will be very happy If my score agrees with your score.... in future.. :lol: :lol:
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:15
You're going to do great! I predict 720 - 750 for you.

x2suresh wrote:
jallenmorris wrote:
Suresh, It looks like we agree with each other...again :-D


I will be very happy If my score agrees with your score.... in future.. :lol: :lol:

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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:40
jallenmorris wrote:
You're going to do great! I predict 720 - 750 for you.

x2suresh wrote:
jallenmorris wrote:
Suresh, It looks like we agree with each other...again :-D


I will be very happy If my score agrees with your score.... in future.. :lol: :lol:


Thats!! encouraging... Will try to beat that.. :lol:
RC sucks for me.. ( I need your help to improve the same)
I need to work more on RC and CR.. (Just ordered GMAT CR POWERSCORE BIBLE)
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Last edited by x2suresh on 12 Aug 2008, 12:06, edited 1 time in total.
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 11:53
The powerscore bible is awesome!

What part of RC seems to be the issue? I've never had an issue with RC (read too many cases in law school!). I'll help you where I can.
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Re: DS: Variable x [#permalink] New post 12 Aug 2008, 16:23
jallenmorris wrote:
The powerscore bible is awesome!

What part of RC seems to be the issue? I've never had an issue with RC (read too many cases in law school!). I'll help you where I can.


How to increase reading speed? I am very slow at reading and understanding passages....
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Re: DS: Variable x   [#permalink] 12 Aug 2008, 16:23
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