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Solve for x: 0<|x|-4x<5 = ?

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Math Revolution GMAT Instructor
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Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

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New post 07 Dec 2015, 00:55
Forget conventional ways of solving math questions. In PS, IVY approach is the easiest and quickest way to find the answer.


Solve for x: 0<|x|-4x<5 = ?

A. x<0
B. 0<x<1
C. -3/5<x<1
D. -3/5<x<0
E. -1<x<0


For x>=0 :
0<x-4x<5 ---> 0<-3x<5 ---> -5/3 < x < 0. It doesn't fit to the condition x>=0.

For x<0
0<-x-4x<5 ---> 0<-5x<5 ---> -1 < x < 0.
So the answer is E.
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Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

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New post 19 Apr 2016, 22:20
Hi there..

i am still a bit confused.. in this question..
i Agree that we have two ways to consider the value of x.

when x>0 the equation becomes: 0<-3x<5 and finally making it to 0>x>-5/3
as x has to be greater than zero. this does not qualify.

when x<0

0<|x|-4x<5.. will become 0<x+4x<5 (as if x is negative but it is in MOD and also -4(-x) will become 4x)
I am a bit confused on this can some one please help me with this.

TIA..
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Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

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New post 19 Apr 2016, 22:48
vibhavdwivedi wrote:
Hi there..

i am still a bit confused.. in this question..
i Agree that we have two ways to consider the value of x.

when x>0 the equation becomes: 0<-3x<5 and finally making it to 0>x>-5/3
as x has to be greater than zero. this does not qualify.

when x<0

0<|x|-4x<5.. will become 0<x+4x<5 (as if x is negative but it is in MOD and also -4(-x) will become 4x)
I am a bit confused on this can some one please help me with this.

TIA..



How do you figure this: "0<|x|-4x<5.. will become 0<x+4x<5"?

If x is negative, |x| = -x by definition.

So you get 0 < -x - 4x < 5

You cannot change the sign of -4x. You only substitute |x| by -x.

From this step, I guess you do not fully understand the absolute value definition. You should check out this post:
http://www.veritasprep.com/blog/2014/06 ... -the-gmat/
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Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

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New post 06 Oct 2018, 08:01
rohansherry wrote:
IMO E:

5 + 4x > |x|
5 + 4x > x first cndtn
5 > - 3x
x>-5/3

or

5 + 4x > -x
x > -1


using

4x < |x|
or 4x < x
x<0

or 4x < -x
x<0

thus range lies between -1 to 0

correct me if i m wrong!!





hey i wish to know why havent you changed the sign of the inequality when you opened the mod with a negative sign that is x<0
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Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

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New post 06 Oct 2018, 08:15
VeritasKarishma wrote:
vibhavdwivedi wrote:
Hi there..

i am still a bit confused.. in this question..
i Agree that we have two ways to consider the value of x.

when x>0 the equation becomes: 0<-3x<5 and finally making it to 0>x>-5/3
as x has to be greater than zero. this does not qualify.

when x<0

0<|x|-4x<5.. will become 0<x+4x<5 (as if x is negative but it is in MOD and also -4(-x) will become 4x)
I am a bit confused on this can some one please help me with this.

TIA..



How do you figure this: "0<|x|-4x<5.. will become 0<x+4x<5"?

If x is negative, |x| = -x by definition.

So you get 0 < -x - 4x < 5

You cannot change the sign of -4x. You only substitute |x| by -x.

From this step, I guess you do not fully understand the absolute value definition. You should check out this post:
http://www.veritasprep.com/blog/2014/06 ... -the-gmat/




hi. in the part highlighted above, why havent you changed the sign of inequality when mod is opened with a negative value. i am a bit confued here. plz explain.
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Re: Solve for x: 0<|x|-4x<5 = ? &nbs [#permalink] 06 Oct 2018, 08:15

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