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

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Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8665
Location: Pune, India
Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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15 Oct 2018, 02:32
topper97 wrote:
Can't any one or two numbers(that are same) be used in all the three statements? The problem is plugging number in statement II is not satisfying. Pls explain by putting in same numbers in all statements. (I got that Statment 3 is not satisfying)

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You cannot plug in same numbers in each statement and expect to get the answer. The requirement of each statement is different. Hence, we need to find transition points to ensure that we get the answer. This is explained in the link given here: https://gmatclub.com/forum/if-x-is-posi ... l#p1748102
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Karishma
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Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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17 Oct 2018, 04:50
lylya4 wrote:
Vavali wrote:
If x is positive, which of the following could be 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
(e) I, II and III

could be correct ordering

So if we can find any example that satisfy the inequation, that statement will be correct

(I) x = 0.1 => 0.01 < 0.2 < 10
(II) x= 1/2 => 1/4 < 1/2 < 1

(III)
2x < x^2 <=> x ( 2 -x) < 0, x > 0 then x > 2

with x > 2 ==> x^2 < 1/x <=> x^3 < 1 <=> x < 1

So (III) can't happen

Hey I feel that the
The example for part (II) is incorrect. The middle value has been taken as x instead of 1/x

Please correct me if I am wrong.
Thank you.
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Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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15 Nov 2018, 20:46
Hi Bunuel, bb
how can I find more practice questions which are of this type?
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Joined: 02 Sep 2009
Posts: 51121
Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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15 Nov 2018, 22:24
1
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Joined: 24 Apr 2016
Posts: 27
Re: If x is positive, which of the following could be correct ordering of  [#permalink]

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01 Dec 2018, 08:16
Bunuel wrote:
imhimanshu wrote:
Hi Bunnel,

Could you please provide a reasoning to the below text... how did you find the range...Pls help

The reasoning is that in these ranges x (2x), 1/x and x^2 are ordered differently:

For $$x>2$$ --> $$x^2$$ has the largest value. Since no option offers this we know that $$x$$ cannot be more that 2;
For $$1<x<2$$ --> $$2x$$ has the largest value, then comes $$x^2$$. Since no option offers this we know that $$x$$ cannot be from this range either;

So, we are left with last range: $$0<x<1$$. In this case $$x^2$$ has the least value. Options, I and II offer this, so we should concentrate on them and test the values of x from 0 to 1.

Hope it's clear.

How do you know right off the bat that these ranges are ordered differently? Is this something one should remember?
Re: If x is positive, which of the following could be correct ordering of &nbs [#permalink] 01 Dec 2018, 08:16

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