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

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SVP
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Solve for x: 0<|x|-4x<5 = ? [#permalink]  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.
Manager
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Re: solve for x? [#permalink]  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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Senior Manager
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Re: solve for x? [#permalink]  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!!
SVP
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Re: solve for x? [#permalink]  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??
Director
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Re: solve for x? [#permalink]  03 Apr 2011, 12:40
0<-5x<5

=> -1<x<0

SVP
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Re: solve for x? [#permalink]  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

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Intern
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Re: solve for x? [#permalink]  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

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Re: solve for x? [#permalink]  14 Jun 2011, 19:24
3
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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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Save $100 on Veritas Prep GMAT Courses And Admissions Consulting Enroll now. Pay later. Take advantage of Veritas Prep's flexible payment plan options. Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GMAT 1: Q V0 GPA: 3.23 Followers: 16 Kudos [?]: 216 [0], given: 11 Re: solve for x? [#permalink] 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 _________________ Impossible is nothing to God. SVP Joined: 05 Jul 2006 Posts: 1537 Followers: 5 Kudos [?]: 87 [0], given: 39 Re: solve for x? [#permalink] 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! Verbal Forum Moderator Joined: 10 Oct 2012 Posts: 630 Followers: 47 Kudos [?]: 626 [0], given: 135 Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] 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. _________________ Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 4949 Location: Pune, India Followers: 1184 Kudos [?]: 5639 [0], given: 167 Re: solve for x? [#permalink] 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. _________________ Karishma Veritas Prep | GMAT Instructor My Blog Save$100 on Veritas Prep GMAT Courses And Admissions Consulting
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SVP
Joined: 05 Jul 2006
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]  11 May 2013, 05:31
@Karishma ... U r absolutely right , been away for years from GMAT ... E is the perfect answer
SVP
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]  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]  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.
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Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]  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]  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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# Solve for x: 0<|x|-4x<5 = ?

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