GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 18 Jan 2020, 08:32

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

Retired Moderator
Joined: 05 Jul 2006
Posts: 1375
Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

Updated on: 04 Dec 2012, 03:22
3
34
00:00

Difficulty:

65% (hard)

Question Stats:

60% (02:13) correct 40% (02:18) wrong based on 854 sessions

### HideShow timer Statistics

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

Originally posted by yezz on 16 Aug 2009, 00:44.
Last edited by Bunuel on 04 Dec 2012, 03:22, edited 2 times in total.
Renamed the topic and edited the question.
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9983
Location: Pune, India
Re: solve for x?  [#permalink]

### Show Tags

14 Jun 2011, 20:24
5
6
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.
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
##### General Discussion
Manager
Joined: 28 Jul 2009
Posts: 84
Location: India
Schools: NUS, NTU, SMU, AGSM, Melbourne School of Business
Re: solve for x?  [#permalink]

### Show Tags

16 Aug 2009, 02:08
2
2
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.
Manager
Joined: 27 May 2009
Posts: 156
Re: solve for x?  [#permalink]

### Show Tags

16 Aug 2009, 13:54
4
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!!
Retired Moderator
Joined: 05 Jul 2006
Posts: 1375
Re: solve for x?  [#permalink]

### Show Tags

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: 528
Re: solve for x?  [#permalink]

### Show Tags

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

=> -1<x<0

Retired Moderator
Joined: 16 Nov 2010
Posts: 1222
Location: United States (IN)
Concentration: Strategy, Technology
Re: solve for x?  [#permalink]

### Show Tags

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

_________________
Formula of Life -> Achievement/Potential = k * Happiness (where k is a constant)

GMAT Club Premium Membership - big benefits and savings
Intern
Joined: 14 Jun 2011
Posts: 2
Re: solve for x?  [#permalink]

### Show Tags

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...
Senior Manager
Joined: 13 Aug 2012
Posts: 395
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
$$|-\frac{3}{5}|-4(-\frac{3}{5})=\frac{15}{5}=3$$

Retired Moderator
Joined: 05 Jul 2006
Posts: 1375
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: 578
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: 9983
Location: Pune, India
Re: solve for x?  [#permalink]

### Show Tags

11 May 2013, 04:33
2
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Retired Moderator
Joined: 05 Jul 2006
Posts: 1375
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

11 May 2013, 06:31
@Karishma ... U r absolutely right , been away for years from GMAT ... E is the perfect answer
Retired Moderator
Joined: 05 Jul 2006
Posts: 1375
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

12 May 2013, 07:44
1
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
Joined: 13 May 2013
Posts: 396
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

01 Jul 2013, 15:08
1
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)
SVP
Joined: 06 Sep 2013
Posts: 1527
Concentration: Finance
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

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
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 9983
Location: Pune, India
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

29 Jan 2014, 21:03
2
1
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
_________________
Karishma
Veritas Prep GMAT Instructor

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Intern
Joined: 07 Aug 2012
Posts: 3
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: 9983
Location: Pune, India
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

26 Apr 2015, 21:49
1
1
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

Learn more about how Veritas Prep can help you achieve a great GMAT score by checking out their GMAT Prep Options >
Manager
Joined: 02 Nov 2014
Posts: 181
GMAT Date: 08-04-2015
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

07 Dec 2015, 00:33
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

Soln: We'll consider two cases: x>0 and $$x<0$$ where $$|x|$$ will become $$x$$ and $$-x$$ respectively.
x>0: 0 < x - 4x < 5, or, 0 < -3x < 5, or -5/3 < x < 0 (dividing by -3 and thereby changing the direction of the inequality)
BUT, if $$x>0$$ then x cannot lie in $$-5/3 < x < 0$$. No solution here.

$$x<0: 0 < -x - 4x < 5,$$ or, $$0 < -5x < 5,$$ or $$-1 < x < 0$$ (dividing by -3 and thereby changing the direction of the inequality)
This range is GOOD. Anything in this range will be permissible.

Choice E is the same range: $$-1 < x < 0$$
Re: Solve for x: 0<|x|-4x<5 = ?   [#permalink] 07 Dec 2015, 00:33

Go to page    1   2    Next  [ 26 posts ]

Display posts from previous: Sort by

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

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne