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(|x| - 1)/(x - 1) =?

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(|x| - 1)/(x - 1) =?  [#permalink]

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New post 13 Jan 2016, 23:36
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(|x| - 1)/(x - 1) =?

(1) x < 0
(2) |x| = -x
Most Helpful Expert Reply
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Joined: 02 Aug 2009
Posts: 7764
Re: (|x| - 1)/(x - 1) =?  [#permalink]

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New post 14 Jan 2016, 00:08
5
4
fattty wrote:
(|x| - 1)/(x - 1) =?

(1) x < 0
(2) |x| = -x


Hi,
if we look at the eq..
(|x| - 1)/(x - 1) ..

the value depends on :-
1) if x is 0 or +ive, ans is 1, irrespective of value of x..
2) if x is -ive, the value of denominator and numerator changes, and the equations value will depend on value of x..

lets see the statements now..
(1) x < 0
here x is negative , so the value depends on value of x.. insuff

(2) |x| = -x
again value of x is -ive.. insuff..

combined .nothing new.. insuff
E..

just for knowledge...
Why x is -ive in statement 2..
|x| = -x..
The LHS is positive because it is absolute mod, so RHS will also be positive..
RHS=-x... now -x will become positive only when x is -ive

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Posts: 56251
Re: (|x| - 1)/(x - 1) =?  [#permalink]

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New post 13 Jul 2017, 03:37
Director
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Affiliations: IIT Dhanbad
Joined: 13 Mar 2017
Posts: 731
Location: India
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Re: (|x| - 1)/(x - 1) =?  [#permalink]

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New post 13 Jul 2017, 04:10
fattty wrote:
(|x| - 1)/(x - 1) =?

(1) x < 0
(2) |x| = -x



Given : Nothing
DS : (|x| - 1)/(x - 1) =?

Option 1: x < 0 ,
So, |x| = -x
(|x| - 1)/(x - 1) = (-x-1)/(x-1)
NOT SUFFICIENT

Option 2: |x| = -x
(|x| - 1)/(x - 1) = (-x-1)/(x-1)
NOT SUFFICIENT

Answer E

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Re: (|x| - 1)/(x - 1) =?  [#permalink]

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New post 17 Sep 2018, 07:39
chetan2u what is mod of 0? Is it zero or undefined?
If its undefined, why do we say that |x| >=0. I think i am getting confused between 2 things.
Please advise
Thanks in advance
Siddharth
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Re: (|x| - 1)/(x - 1) =?  [#permalink]

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New post 17 Sep 2018, 08:06
Sidbendale1 wrote:
chetan2u what is mod of 0? Is it zero or undefined?
If its undefined, why do we say that |x| >=0. I think i am getting confused between 2 things.
Please advise
Thanks in advance
Siddharth



Siddharth,

|0|=0, it is not undefined..
Modulus just removes the negative sign
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Posts: 1
(|x| - 1)/(x - 1) =?  [#permalink]

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New post 14 Nov 2018, 09:45
chetan2u wrote:
fattty wrote:
(|x| - 1)/(x - 1) =?

(1) x < 0
(2) |x| = -x


Hi,
if we look at the eq..
(|x| - 1)/(x - 1) ..

the value depends on :-
1) if x is 0 or +ive, ans is 1, irrespective of value of x..
2) if x is -ive, the value of denominator and numerator changes, and the equations value will depend on value of x..

lets see the statements now..
(1) x < 0
here x is negative , so the value depends on value of x.. insuff

(2) |x| = -x
again value of x is -ive.. insuff..

combined .nothing new.. insuff
E..

just for knowledge...
Why x is -ive in statement 2..
|x| = -x..
The LHS is positive because it is absolute mod, so RHS will also be positive..
RHS=-x... now -x will become positive only when x is -ive




Firstly this statement isn't correct: "1) if x is 0 or +ive, ans is 1, irrespective of value of x.."
If x is equal to 1 then ans is 0.
Secondly shouldn't 0 be the only solution for this: |x| = -x since |x| can never be negative.
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(|x| - 1)/(x - 1) =?   [#permalink] 14 Nov 2018, 09:45
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