x/|x|<x. which of the following must be true about x ?

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Re: x/|x|<x. which of the following must be true about x ? [#permalink]

12 May 2013, 09:11

The question ( must be true about x) asks about x not the solution of the inequality , thus we solve inequality and we see from answer choices if x always is inside our solution of the inequality

x-/x/*x < 0 , i.e x (1-/x/) <0 holds true in 2 cases

a) x+ve and /x/>1 , i.e. x+ve in the range x<-1 ( this is equivalent to x>1) or x>1 thus in this case x is always >1

b) x-ve and /x/<1 , i.e. x-ve and -1<x<1 ( from /x/<1) but since x is always -ve in this assumption therefore the range becomes -1<x<0

now we have 2 ranges that is x>1 and -1<x<0 now we check each answer choice vs. those ranges , x>-1 is always true ( must be true about x) in those ranges

Thus B is the answer
Hope this helps

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Re: PS - Inequality [#permalink]

13 May 2013, 11:28

Vijo wrote:

christoph wrote:

x/|x|<x. which of the following must be true about x ?

a) x>1
b) x>-1
c) |x|<1
d) |x|=1
e) |x|^2>1

this is a question of the GMATCLUB collection 2. i got a different solution and i just dont know why.

The answer should be A.

x/|x| <x
=> dividing both sides by x
=> 1/|x|<1

thus either x>1 or x<-1 only then 1/|x| will be less than 1.
Thus A.

Wrong , you can not divide x this way, bcos its sign is not known.

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Re: x/|x|<x. which of the following must be true about x ? [#permalink]

25 May 2013, 23:47

I think x>1 holds true always but not x>-1
0<x<1 comes under the range x>-1 and it does not satisfy the equation.

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Re: x/|x|<x. which of the following must be true about x ? [#permalink]

26 May 2013, 04:00

pradeepkamp wrote:

I think x>1 holds true always but not x>-1
0<x<1 comes under the range x>-1 and it does not satisfy the equation.

That is incorrect.

Go through Bunuel's Solution.

if-x-0-and-x-x-x-which-of-the-following-must-be-true-143572.html
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All that is equal and not --> inequalities-basics-154285.html

Re: x/|x|<x. which of the following must be true about x ? [#permalink] 26 May 2013, 04:00

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x/|x|<x. which of the following must be true about x ?

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x/|x|<x. which of the following must be true about x ?

x/|x|<x. which of the following must be true about x ?

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