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

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Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 15 Aug 2009, 23:44
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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
[Reveal] Spoiler: OA

Last edited by Bunuel on 04 Dec 2012, 02:22, edited 2 times in total.
Renamed the topic and edited the question.
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Re: solve for x? [#permalink] New post 16 Aug 2009, 01:08
I am getting E as an answer if x is -ve.
If x is -ve, we get

0 < -5x < 5

Dividing both sides by -5, we flip both the sides and we land up on

0 > x > -1
ie
-1 < x < 0.

Is that the correct method to solve this problem? Please explain.
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Re: solve for x? [#permalink] New post 16 Aug 2009, 12:54
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!!
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Re: solve for x? [#permalink] New post 16 Aug 2009, 13:10
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

i did it this way

split the inquality into 2

a) /x/-4x<5 ie: -5<x-4x<5 ie: -5<-3x<5 ie: 5/3>x>-5/3....1

b) /x/-4x>0 thus /x/>4x thus eithe x>4x ie: -3x>0 ie: x <0 or -x<4x ie: x>-4x ie: x>0

and i get lost here??
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Re: solve for x? [#permalink] New post 03 Apr 2011, 12:40
0<-5x<5

=> -1<x<0

Answer E.
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Re: solve for x? [#permalink] New post 03 Apr 2011, 17:15
I'm also getting E.

2 cases x > 0 or x < 0

0< -x - 4x < 5

=> 0< -5x < 5

=> x > -1 and x < 0

x - 4x < 5

=> -3x < 5

=> x > -5/3

so x > 0 as x is +ve

So -1 < x < 0

Answer E
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Re: solve for x? [#permalink] New post 14 Jun 2011, 14:22
hi,
apply definition absolute value obtain two possibilites:
A. if x≥0 then 0<|x|-4x<5 go 0<x-4x<5 go 0<-3x<5, go 0>x>-5/3. The intersection is empty
B. if x<0 then 0<|x|-4x<5 go 0<-x-4x<5 go 0<-5x<5 go 0>x>-1. the intersection is -1<x<0

Bye...
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Re: solve for x? [#permalink] New post 14 Jun 2011, 19:24
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Expert's post
puneetj wrote:
Got to the correct answer but took too much time...E


If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

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

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out.
If x = 1/2, |x|-4x is negative so B and C are out.
If x = -4/5, |x|-4x = 4 so D is out and E is the answer.
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Re: solve for x? [#permalink] New post 03 Dec 2012, 20:52
0<|x|-4x<5

A. x<0
Test: x=-5
|-5|-4(-5) = 5 + 20 is not less than 5
FALSE!

B. 0<x<1
Test: x=\frac{1}{4}
\frac{1}{4}-4(\frac{1}{4})=-\frac{3}{4} is not greater than 0
FALSE!


C. -3/5<x<1
x<1 as tested with B
FALSE!

D. -3/5<x<0
E. -1<x<0

We see that D and E are almost the same except for E. covers -3/5 unlike D.
Let x=-3/5
|-\frac{3}{5}|-4(-\frac{3}{5})=\frac{15}{5}=3

Answer: E
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Re: solve for x? [#permalink] New post 10 May 2013, 07:39
VeritasPrepKarishma wrote:
puneetj wrote:
Got to the correct answer but took too much time...E


If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

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

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out.
If x = 1/2, |x|-4x is negative so B and C are out.
If x = -4/5, |x|-4x = 4 so D is out and E is the answer.



I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 10 May 2013, 22:46
Expert's post
yezz wrote:
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


|x|-4x>0 = |x|>4x =\frac{x}{|x|}<1 --> x<0. Again, |x|-4x<5 = -x-4x<5 = -5x<5-->x>-1.
E.
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Re: solve for x? [#permalink] New post 11 May 2013, 03:33
Expert's post
yezz wrote:
VeritasPrepKarishma wrote:
puneetj wrote:
Got to the correct answer but took too much time...E


If you get messed up in mods, such a question can be done in under a minute by trying out some values. Now, I am no fan of plugging in numbers, especially not in DS questions, but such questions are perfect for plugging in if you are not comfortable with algebra. Why? Because they have asked for the range of x. If there is even one value in the given range that doesn't satisfy the inequality, it is not the answer and if there is even one value outside the given range that does satisfy the inequality, it is not the answer.

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

Say, consider option A. If x = -1, |x|-4x = 5 which doesn't satisfy the inequality so A is out.
If x = 1/2, |x|-4x is negative so B and C are out.
If x = -4/5, |x|-4x = 4 so D is out and E is the answer.



I believe the choice of -4/5 to execlude D is wrong -4/5 is not in the range of -3/5<x<0 ????? accordingly i think both D and E could solve as the right range in my opinion is -5/3 < x < 0??? am i right or wrong plz advise!


Focus on
"and if there is even one value outside the given range that does satisfy the inequality, it is not the answer."
given above.

-4/5 is a value which satisfies 0 < |x|-4x < 5 since |-4/5|-4(-4/5) = 4.
Since -4/5 does not lie in the range -3/5<x<0 so (D) cannot be the answer. The correct range needs to cover all possible values of x.
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 11 May 2013, 05:31
@Karishma ... U r absolutely right , been away for years from GMAT ... E is the perfect answer
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 12 May 2013, 06:44
we ve got 3 critical values that are ( 0 from modulus , -5/3& -1 from /x/ = 5+4x) , draw on the number line and test values

.....-5/3........-1...........0....................

only -1<x<0 is the range where all values of x satisfy the compound inequality 0</x/-4x<5
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 01 Jul 2013, 14:08
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

There are two options here - plugging in values given to us in the answer choices or simplifying the inequality.

0<|x|-4x<5

x>0: 0<x-4x<5 0<-3x<5 0<x<-5/3 -5/3<x<0 INVALID as x does not fall within the range of x>0
OR
x<0: 0<(-x)-4x<5 0<-5x<5 0<x<-1 -1<x<0 VALID as x falls within the range of x<0

There is only one valid solution: -1<x<0.
(E)
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 29 Jan 2014, 07:05
Would be happy to hear some comments on whether this approach is correct

|x|-4x>0

So we have two cases

If x>0 then x-4x>0
-3x>0
x<0, this contradicts and hence is not a valid solution

If x<0 then -5x>0
x<0, this solution is valid

So we get that -1<x<0 replacing in the original inequality

E
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] New post 29 Jan 2014, 20:03
Expert's post
jlgdr wrote:
Would be happy to hear some comments on whether this approach is correct

|x|-4x>0

So we have two cases

If x>0 then x-4x>0
-3x>0
x<0, this contradicts and hence is not a valid solution

If x<0 then -5x>0
x<0, this solution is valid

So we get that -1<x<0 replacing in the original inequality

E


Knowing only x < 0, how do you choose between (A), (D) and (E)?
You need to consider |x| - 4x < 5 too
When x < 0, -x -4x < 5
-5x < 5
x > -1
That's how you get -1 < x < 0

Or work on the whole inequality in one go
0 < |x| - 4x < 5
When x < 0,
0< -x - 4x < 5
0 < -5x < 5
0 < -x < 1
0 > x > -1

which is the same as -1 < x < 0
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Re: Solve for x: 0<|x|-4x<5 = ?   [#permalink] 29 Jan 2014, 20:03
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