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

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Manager
Joined: 22 Jul 2006
Posts: 50
If x is positive which of the following could be the correct [#permalink]

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03 Nov 2006, 17:44
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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

(A) None
(B) I only
(C) III only
(D) I and II only
(E) I II and III

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-positive-which-of-the-following-could-be-the-104082.html

Last edited by Sam Kana on 04 Nov 2006, 05:27, edited 1 time in total.
Manager
Joined: 22 Jul 2006
Posts: 50

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03 Nov 2006, 17:46
I know if

x is a fraction (1/2 ..) condition 1 holds true....but I dont get any other number satisfying any of the other two condition...! or my brain has froze...
Intern
Joined: 29 Oct 2006
Posts: 2

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03 Nov 2006, 20:49
Quote:
1. x^2 < 2x < 1/x

can be satisfied by taking x = 1/4
Senior Manager
Joined: 01 Oct 2006
Posts: 495

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04 Nov 2006, 01:56
sst 1 holds true all fractions...
for numbers none of these hold true...
so if x is postive then x must be fraction..
so my pick is one... but what is OA
Manager
Joined: 22 Jul 2006
Posts: 50

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04 Nov 2006, 04:12
OA is 1 and 2..! it is OG test...!
SVP
Joined: 05 Jul 2006
Posts: 1747

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04 Nov 2006, 06:26
if x is positive, which of the following could be the correct order of 1/x, 2x, x^2

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

IF X IS A FRACTION SCENARIO ONE IS RIGHT

X= 1/2

X^2 = 1/4 , 2X= 1 , 1/X = 2

I CANT SEE WHY 2 IS CORRECT
Manager
Joined: 01 Nov 2006
Posts: 70

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04 Nov 2006, 06:41
Just work out the inequalities

2x < 1/x when x < Sqrt(2)/2
x^2 < 1/x when x < 1
x^2 < 2x when x < 2

for x < Sqrt(2)/2 we have x^2 < 2x < 1/x
for sqrt(2)/2 < x < 1 we have x^2 < 1/x < 2x
for 1 < x < 2 we have 1/x < x^2 < 2x
for x > 2 we have 1/x < 2x < x^2

so 1. and 2. both work.

This is a good example of why you don't plug in numbers. You would need to pick a number between Sqrt(2)/2 and 1 to get the right answer.
Manager
Joined: 22 Jul 2006
Posts: 50

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04 Nov 2006, 07:20
that is great...so do u arbitarily pick up one of the conditions and find the intervals?
Director
Joined: 11 Sep 2006
Posts: 514

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04 Nov 2006, 10:10
Make sure you try both a decimal and a fraction when you do these.

for 1; try1/4, then
1/16<1/2<4
for 2, try .9, then
.81<1.11<1.8
_________________

...there ain't no such thing as a free lunch...

Manager
Joined: 01 Nov 2006
Posts: 70

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04 Nov 2006, 11:11
uphillclimb wrote:
Make sure you try both a decimal and a fraction when you do these.

for 1; try1/4, then
1/16<1/2<4
for 2, try .9, then
.81<1.11<1.8

No. Any "decimal" you try is just a fraction anyway. Do not "try" numbers. Do the math - there are far too many numbers to try.
Senior Manager
Joined: 01 Oct 2006
Posts: 495

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04 Nov 2006, 11:29
joeydvivre wrote:
Just work out the inequalities

2x < 1/x when x < Sqrt(2)/2
x^2 < 1/x when x < 1
x^2 < 2x when x < 2

for x < Sqrt(2)/2 we have x^2 < 2x < 1/x
for sqrt(2)/2 < x < 1 we have x^2 < 1/x < 2x
for 1 < x < 2 we have 1/x < x^2 < 2x
for x > 2 we have 1/x < 2x < x^2

so 1. and 2. both work.

This is a good example of why you don't plug in numbers. You would need to pick a number between Sqrt(2)/2 and 1 to get the right answer.

Could you please explain how did you come up with values for various inequalities
Manager
Joined: 01 Nov 2006
Posts: 70

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04 Nov 2006, 11:57
2x < 1/x => (multiply by x) 2x^2 < 1 => (divide by 2) x^2 < 1/2 =>
x < 1/Sqrt(2) => x < Sqrt(2)/2

x^2 < 1/x => x^3 < 1 => x < 1 (taking cube roots)

x^2 < 2x => x < 2 (divide by x)
Manager
Joined: 22 Jul 2006
Posts: 50

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04 Nov 2006, 14:39
Thanks Joey..!
Uphill climb ur suggestion will not work, u should remember any decimal is baiscally a fraction..the key is to choose the right intervals..!
Intern
Joined: 13 Dec 2012
Posts: 3
Re: if x is positive, which of the following could be the [#permalink]

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13 Dec 2012, 23:41
1 holds true all fractions...
for numbers none of these hold true...
so if x is postive then x must be fraction..
so my pick is one... but what is OA
Math Expert
Joined: 02 Sep 2009
Posts: 39738
Re: if x is positive, which of the following could be the [#permalink]

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14 Dec 2012, 02:08
gmatcard wrote:
1 holds true all fractions...
for numbers none of these hold true...
so if x is postive then x must be fraction..
so my pick is one... but what is OA

OA for the question is D.

OPEN DISCUSSION OF THIS QUESTION IS HERE: if-x-is-positive-which-of-the-following-could-be-the-104082.html
_________________
Re: if x is positive, which of the following could be the   [#permalink] 14 Dec 2012, 02:08
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