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

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SVP
Joined: 05 Jul 2006
Posts: 1747
Solve for x: 0<|x|-4x<5 = ? [#permalink]

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16 Aug 2009, 00:44
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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, 03:22, edited 2 times in total.
Renamed the topic and edited the question.
Manager
Joined: 28 Jul 2009
Posts: 124
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business

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16 Aug 2009, 02:08
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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
Joined: 27 May 2009
Posts: 268

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16 Aug 2009, 13:54
3
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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
Joined: 05 Jul 2006
Posts: 1747

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16 Aug 2009, 14:10
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
Joined: 01 Feb 2011
Posts: 755

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03 Apr 2011, 13:40
0<-5x<5

=> -1<x<0

SVP
Joined: 16 Nov 2010
Posts: 1664
Location: United States (IN)
Concentration: Strategy, Technology

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03 Apr 2011, 18:15
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
Joined: 14 Jun 2011
Posts: 2

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14 Jun 2011, 15:22
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...
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 7440
Location: Pune, India

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14 Jun 2011, 20:24
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews Senior Manager Joined: 13 Aug 2012 Posts: 464 Concentration: Marketing, Finance GPA: 3.23 Re: solve for x? [#permalink] ### Show Tags 03 Dec 2012, 21:52 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: 1747 Re: solve for x? [#permalink] ### Show Tags 10 May 2013, 08:39 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: 629 Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] ### Show Tags 10 May 2013, 23:46 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: 7440 Location: Pune, India Re: solve for x? [#permalink] ### Show Tags 11 May 2013, 04:33 1 This post received KUDOS 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 Get started with Veritas Prep GMAT On Demand for$199

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SVP
Joined: 05 Jul 2006
Posts: 1747
Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]

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11 May 2013, 06:31
@Karishma ... U r absolutely right , been away for years from GMAT ... E is the perfect answer
SVP
Joined: 05 Jul 2006
Posts: 1747
Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]

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12 May 2013, 07:44
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
Senior Manager
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Posts: 469
Re: Solve for x: 0<|x|-4x<5 = ? [#permalink]

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01 Jul 2013, 15:08
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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

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

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29 Jan 2014, 08:05
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]

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29 Jan 2014, 21:03
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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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Get started with Veritas Prep GMAT On Demand for $199 Veritas Prep Reviews GMAT Club Legend Joined: 09 Sep 2013 Posts: 15960 Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] ### Show Tags 25 Apr 2015, 05:45 Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email. _________________ Intern Joined: 07 Aug 2012 Posts: 4 Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] ### Show Tags 25 Apr 2015, 21:50 Hey, So I had a doubt. For the equaltiy: 0<|x|-4x<5 if I try and solve it algebraically, i first take x<0 In that case won't this equality be: 0<-x-4(-x)<5. I can't just substitute mod x with -x and leave the other x be can I? Please help! Thanks! Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 7440 Location: Pune, India Re: Solve for x: 0<|x|-4x<5 = ? [#permalink] ### Show Tags 26 Apr 2015, 21:49 1 This post received KUDOS Expert's post 1 This post was BOOKMARKED natashakumar91 wrote: Hey, So I had a doubt. For the equaltiy: 0<|x|-4x<5 if I try and solve it algebraically, i first take x<0 In that case won't this equality be: 0<-x-4(-x)<5. I can't just substitute mod x with -x and leave the other x be can I? Please help! Thanks! Say you have an inequality: 4x < 5 and you know that x must be negative. How will you solve the inequality? Will you say that the inequality becomes -4x < 5? No. You are given that 4x < 5. Without changing the inequality, you can write this as x < 5/4. x needs to be negative. All negative values will be less than 5/4. Why do you substitute -x in place of |x|? You cannot solve an equation/inequality with |x| in it. You need to remove the absolute value sign. You know that |x| = x if x is positive and |x| = -x if x is negative. Since you know that x is negative, you can write -x in place of |x| without changing the inequality. If you change the simple x to -x in the inequality, the inequality changes. Check out this post for a more detailed explanation: http://www.veritasprep.com/blog/2014/06 ... -the-gmat/ _________________ Karishma Veritas Prep | GMAT Instructor My Blog Get started with Veritas Prep GMAT On Demand for$199

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Re: Solve for x: 0<|x|-4x<5 = ?   [#permalink] 26 Apr 2015, 21:49

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

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