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# Is |n| < 1 ?

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Math Expert
Joined: 02 Sep 2009
Posts: 44322
Is |n| < 1 ? [#permalink]

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20 Oct 2014, 06:52
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Difficulty:

65% (hard)

Question Stats:

60% (01:19) correct 40% (01:36) wrong based on 359 sessions

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Tough and Tricky questions: Absolute Values.

Is |n| < 1 ?

(1) n^x - n < 0
(2) x^(-1) = -2
[Reveal] Spoiler: OA

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Director
Joined: 25 Apr 2012
Posts: 720
Location: India
GPA: 3.21
Is |n| < 1 ? [#permalink]

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20 Oct 2014, 22:47
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Bunuel wrote:

Tough and Tricky questions: Absolute Values.

Is |n| < 1 ?

(1) n^x - n < 0
(2) x^(-1) = -2

We need to find whether -1<n<1

St 1 says n^x-n <0 or n (n^x-1 -1)<0 We don't know the value of x so not sufficient

St 2 says 1/x=-2 or x=-1/2...So important question what is this got to do with -1<n<1 : not sufficient

Combining we see that $$\sqrt{n}-n<0$$

So we have $$\sqrt{n}(1-\sqrt{n})<0$$

We will have 2 cases

Case 1 $$\sqrt{n}>0$$ and $$1-\sqrt{n}<0$$ or$$\sqrt{n}>1$$ or n^2>1 or n>1 or n<-1

Case 2$$\sqrt{n} <0$$ but it is not possible as the lowest possible value of $$\sqrt{n}=0$$ so we need not consider this case..

Thus ans is C
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Manager
Joined: 05 Jun 2014
Posts: 69
GMAT 1: 630 Q42 V35
Re: Is |n| < 1 ? [#permalink]

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28 Oct 2014, 11:03
If x=-0.5, Then why doesnt n^x become "1/sq.root n"
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Joined: 25 Apr 2012
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Re: Is |n| < 1 ? [#permalink]

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28 Oct 2014, 12:25
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If x=-0.5, Then why doesnt n^x become "1/sq.root n"

Thanks for pointing out
If x=-1/2 then the question becomes 1-n^3/2 <0 or n^3/2>1

n>1^2/3 or n>1

Sufficient

We will only have to consider one case as sqrt n is greater than 0

Ans is C

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Joined: 05 Dec 2015
Posts: 125
Re: Is |n| < 1 ? [#permalink]

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23 Apr 2016, 13:17
Buneul can you post the way to get the solution please? Thank you
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Re: Is |n| < 1 ? [#permalink]

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28 Aug 2016, 10:19
How is this solved when n^(-1/2) is not considered as 1/√n ? Bunuel Can you kindly explain the solution as well?
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Re: Is |n| < 1 ? [#permalink]

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09 Sep 2017, 22:46
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: Is |n| < 1 ?   [#permalink] 09 Sep 2017, 22:46
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