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# If x is negative and the absolute value of 1/x is greater

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Current Student
Joined: 11 May 2008
Posts: 552
If x is negative and the absolute value of 1/x is greater [#permalink]

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30 Jul 2008, 18:25
. If x is negative and the absolute value of 1/x is greater than 50, which of the following about x must be true?
(A) x1/50

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Manager
Joined: 14 Jul 2008
Posts: 95
Schools: HBS, Stanford.

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30 Jul 2008, 18:44
I believe it's D.

|1/x| > 50

x is negative, thus..
1/x < -50
1 > -50x
1/-50 < x

therefore x > -1/50.
since x < 0 (given)

(D) -1/50<x<0
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Current Student
Joined: 11 May 2008
Posts: 552

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30 Jul 2008, 20:22
nikhil...pls give expln
Manager
Joined: 27 May 2008
Posts: 139

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30 Jul 2008, 20:38

X>-1/50 means that we have a bigger value thn 50 in the denominator.
Senior Manager
Joined: 09 Oct 2007
Posts: 459

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31 Jul 2008, 00:34
I agree on D. Is it really C?
VP
Joined: 28 Dec 2005
Posts: 1499

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31 Jul 2008, 05:05
how can it be D ? Consider the case where x=-1/49. Then, 1/x = -49, and the absolute value of x is 49, which isnt greater than 50 .... ?
Manager
Joined: 27 May 2008
Posts: 139

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31 Jul 2008, 06:56
arjtryarjtry wrote:
. If x is negative and the absolute value of 1/x is greater than 50, which of the following about x must be true?
(A) x<-50
(B) x<-10
(C) -1<x<-1/2
(D) -1/50<x<0
(E) x>1/50

Here's a way to understand it.

the absolute value of 1/x is greater than 50.

i.e l-1/xl = l1/xl >50

thus the value of x must be such that when it divides 1, we get something above 50. i.e x should be lesser thn .02. Thus, the value of x<1/50 and if x is negative it should be X> -1/50. Only option D suits.
VP
Joined: 17 Jun 2008
Posts: 1322

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03 Aug 2008, 07:29
arjtryarjtry wrote:
. If x is negative and the absolute value of 1/x is greater than 50, which of the following about x must be true?
(A) x1/50

provided : |1/x| > 50 => x
from above two condns x -1 (C) is apt here
Matches the criteria
IMO C

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Re: inequality   [#permalink] 03 Aug 2008, 07:29
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# If x is negative and the absolute value of 1/x is greater

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