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

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30 Jul 2008, 18:25
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

. 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

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Manager
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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
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30 Jul 2008, 20:22
nikhil...pls give expln

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Manager
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30 Jul 2008, 20:38

X>-1/50 means that we have a bigger value thn 50 in the denominator.

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Senior Manager
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31 Jul 2008, 00:34
I agree on D. Is it really C?

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SVP
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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 .... ?

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Manager
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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.

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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) x<-50
(B) x<-10
(C) -1<x<-1/2
(D) -1/50<x<0
(E) x>1/50

provided : |1/x| > 50 => x< 1/50 or -1<x< -1/50

also given that x<0 =>
from above two condns x<0 and -1<x<-0.02 => -1<x< -0.02 => (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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