GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 19 Feb 2019, 07:05

### 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

## Events & Promotions

###### Events & Promotions in February
PrevNext
SuMoTuWeThFrSa
272829303112
3456789
10111213141516
17181920212223
242526272812
Open Detailed Calendar
• ### Free GMAT Prep Hour

February 20, 2019

February 20, 2019

08:00 PM EST

09:00 PM EST

Strategies and techniques for approaching featured GMAT topics. Wednesday, February 20th at 8 PM EST

February 21, 2019

February 21, 2019

10:00 PM PST

11:00 PM PST

Kick off your 2019 GMAT prep with a free 7-day boot camp that includes free online lessons, webinars, and a full GMAT course access. Limited for the first 99 registrants! Feb. 21st until the 27th.

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

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor
Joined: 16 Aug 2015
Posts: 6966
GMAT 1: 760 Q51 V42
GPA: 3.82
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

06 Dec 2015, 23:55
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.
_________________

MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy.
"Only \$149 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Intern
Joined: 02 Mar 2015
Posts: 24
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

19 Apr 2016, 21:20
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)

TIA..
Veritas Prep GMAT Instructor
Joined: 16 Oct 2010
Posts: 8883
Location: Pune, India
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

19 Apr 2016, 21:48
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)

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/
_________________

Karishma
Veritas Prep GMAT Instructor

Intern
Joined: 30 Apr 2017
Posts: 6
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

06 Oct 2018, 07:01
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
Intern
Joined: 30 Apr 2017
Posts: 6
Re: Solve for x: 0<|x|-4x<5 = ?  [#permalink]

### Show Tags

06 Oct 2018, 07:15
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)

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.
Re: Solve for x: 0<|x|-4x<5 = ?   [#permalink] 06 Oct 2018, 07:15

Go to page   Previous    1   2   [ 25 posts ]

Display posts from previous: Sort by