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If X > X / |X| , Which of the following gives solution set of integer

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If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:19
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A
B
C
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If X > X / |X| , Which of the following gives solution set of integer X?
A. X > 1
B. X > -1
C. |X| < 1
D. |X| = 1
E.|X|^2 > 1

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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:25
x > \(\frac{x}{|x|}\)
If x>0 then x > \(\frac{x}{|x|}\) = x > \(\frac{x}{x}\) or x>1.
Satisfies.

If x<0 then x > \(\frac{x}{|x|}\) = x > \(\frac{x}{-x}\) or x>-1. Since no integer exists between -1 and 0. This is invalid.

Hence x>1.

A is the answer.
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:25
x/|x| = 1 when x>0
= -1 when x<0
So x>x/|x| has a solution set of -1<x<0 and x>1. But since here we need only integer solutions X>1 is the correct answer as no integer lies between -1 and 0
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:28
I think option (A) is the correct answer here. Please find solution attached!

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GLadi+
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:32
x can be greater than x/|x| only when -1<x<0 . This is best matched by option C. Hence C is the Answer
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:37
If X > X / |X| , Which of the following gives solution set of integer X?.
A. X > 1
B. X > -1
C. |X| < 1
D. |X| = 1
E.|X|^2 > 1
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IMO A
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:54
X > X / |X|

when x is +ve , x>1
when x is -ve , x>-1

Thus ans A.
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Re: If X > X / |X| , Which of the following gives solution set of integer  [#permalink]

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New post 13 Oct 2018, 09:54
X > X / |X| , Which of the following gives solution set of integer X?.
Given X > X / |X| ==> for this to be true X should always be greater than 1 , Consider X = 2
2 > 2 /2 { |2| = 2} ==> True
when X = -2 , -2 > -2/2 ==> -2> -1 ==> which is False
A. X > 1 ===> OA
B. X > -1
C. |X| < 1
D. |X| = 1
E.|X|^2 > 1
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Re: If X > X / |X| , Which of the following gives solution set of integer   [#permalink] 13 Oct 2018, 09:54
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If X > X / |X| , Which of the following gives solution set of integer

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