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

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Intern
Joined: 18 Jul 2008
Posts: 34
If x is positive which of the following could be the correct [#permalink]

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12 Aug 2008, 10:45
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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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SVP
Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks

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12 Aug 2008, 11:01
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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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings Intern Joined: 18 Jul 2008 Posts: 34 Re: DS: Variable x [#permalink] ### Show Tags 12 Aug 2008, 11:40 OA -- 1 and 2 are possible. See attached. This is a gmatprep question Attachments DS-variable x.doc [54 KiB] Downloaded 124 times  To download please login or register as a user SVP Joined: 30 Apr 2008 Posts: 1841 Location: Oklahoma City Schools: Hard Knocks Re: DS: Variable x [#permalink] ### Show Tags 12 Aug 2008, 11:58 x^2 < 1/x < 2x Tell me if this works multiply everything by x $$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$$ and #2 can also be true _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

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SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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12 Aug 2008, 12:00
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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SVP
Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks

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12 Aug 2008, 12:02
Suresh, It looks like we agree with each other...again
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J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$. GMAT Club Premium Membership - big benefits and savings SVP Joined: 07 Nov 2007 Posts: 1738 Location: New York Re: DS: Variable x [#permalink] ### Show Tags 12 Aug 2008, 12:10 jallenmorris wrote: Suresh, It looks like we agree with each other...again I will be very happy If my score agrees with your score.... in future.. _________________ Your attitude determines your altitude Smiling wins more friends than frowning SVP Joined: 30 Apr 2008 Posts: 1841 Location: Oklahoma City Schools: Hard Knocks Re: DS: Variable x [#permalink] ### Show Tags 12 Aug 2008, 12:15 You're going to do great! I predict 720 - 750 for you. x2suresh wrote: jallenmorris wrote: Suresh, It looks like we agree with each other...again I will be very happy If my score agrees with your score.... in future.. _________________ ------------------------------------ J Allen Morris **I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a$$.

GMAT Club Premium Membership - big benefits and savings

SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

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Updated on: 12 Aug 2008, 13:06
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

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

Thats!! encouraging... Will try to beat that..
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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Originally posted by x2suresh on 12 Aug 2008, 12:40.
Last edited by x2suresh on 12 Aug 2008, 13:06, edited 1 time in total.
SVP
Joined: 30 Apr 2008
Posts: 1841
Location: Oklahoma City
Schools: Hard Knocks

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12 Aug 2008, 12:53
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.
_________________

------------------------------------
J Allen Morris
**I'm pretty sure I'm right, but then again, I'm just a guy with his head up his a.

GMAT Club Premium Membership - big benefits and savings

SVP
Joined: 07 Nov 2007
Posts: 1738
Location: New York

### Show Tags

12 Aug 2008, 17:23
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....

--== Message from GMAT Club Team ==--

This is not a quality discussion. It has been retired.

If you would like to discuss this question please re-post it in the respective forum. Thank you!

To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.

_________________

Smiling wins more friends than frowning

Re: DS: Variable x   [#permalink] 12 Aug 2008, 17:23
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