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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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13 Oct 2018, 10:19
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35% (01:17) correct 65% (01:27) wrong based on 80 sessions

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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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13 Oct 2018, 10:25
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.

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

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13 Oct 2018, 10:25
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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13 Oct 2018, 10:28
I think option (A) is the correct answer here. Please find solution attached!

Regards,
Attachments

Q4_5.jpeg [ 86.95 KiB | Viewed 818 times ]

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

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13 Oct 2018, 10:32
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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13 Oct 2018, 10:37
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
___________

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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13 Oct 2018, 10:54
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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13 Oct 2018, 10:54
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
Re: If X > X / |X| , Which of the following gives solution set of integer   [#permalink] 13 Oct 2018, 10:54
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