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

 It is currently 06 Dec 2019, 09:07 ### 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

#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0

Author Message
TAGS:

### Hide Tags

Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

4
15 00:00

Difficulty:   75% (hard)

Question Stats: 50% (01:55) correct 50% (02:00) wrong based on 270 sessions

### HideShow timer Statistics

[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

_________________
Manager  G
Joined: 30 Jan 2017
Posts: 80
Location: India
Schools: ISB '19
GMAT 1: 630 Q47 V29 GMAT 2: 660 Q47 V34 GMAT 3: 730 Q49 V40 GPA: 3.9
Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

4
3
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

You can write the inequality as:

-6 < |2x-|x|| < 6

Case 1:
If x >= 0 ; |x| = x
|2x-|x|| becomes 2x - x = x

-6 < x < 6
But as x>=0 we only take the values as 0 < x < 6

Case 2:
If x < 0 ; |x| = -x
|2x-|x|| becomes 2x + x = 3x

-6 < 3x < 6
-2 < x < 2
But as x < 0 we only take the values as -2 < x < 0

Combining the results of Case 1 and 2
-2 < x < 6
##### General Discussion
Math Expert V
Joined: 02 Sep 2009
Posts: 59587
Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

2
MathRevolution wrote:
[GMAT math practice question]

Which of the following inequalities is equal to |2x-|x||<6?

A. -2<x<0
B. 0<x<6
C. -2<x<6
D. -2<x<2
E. -6<x<6

Similar question: https://gmatclub.com/forum/which-of-the ... 47913.html
_________________
Manager  G
Joined: 07 Jun 2017
Posts: 160
Location: India
Concentration: Technology, General Management
GMAT 1: 660 Q46 V38 GPA: 3.6
WE: Information Technology (Computer Software)
Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

the maximum range provided in the answer is -6, -2, 2, 0 and 6
check for this range

-6, gives us that |-12-|-6||<6
|-12-6| <6
18<6 not true
Eliminate E

next value given in the answer series is -2
Holds good, so left value in the number line should be 2

Now check for right value by putting 6
Holds good so the range should be -2 to 6

So clearly answer should be C
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8235
GMAT 1: 760 Q51 V42 GPA: 3.82
Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

=>

We should split real number of x into two cases x ≥ 0 and x < 0.

Case 1: x ≥ 0
|2x-|x||<6 ⬄ | 2x – x | < 6 ⬄ |x| < 6 ⬄ -6<x<6.
From the assumption of the case, x ≥ 0, we have 0 ≤ x < 6.

Case 2: x < 0
|2x-|x||<6 ⬄ | 2x + x | < 6 ⬄ |3x| < 6 ⬄ |x| < 2 ⬄ -2<x<2.
From the assumption of the case, x < 0, we have -2<x<0.

Thus, we have -2 < x < 6.

_________________
BSchool Forum Moderator P
Joined: 05 Jul 2017
Posts: 507
Location: India
GMAT 1: 700 Q49 V36 GPA: 4
Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]

### Show Tags

Bunuel - Can you help me understand where did I go wrong?
Attachments IMG_20190209_164506.jpg [ 1.7 MiB | Viewed 692 times ]

_________________ Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0   [#permalink] 09 Feb 2019, 04:24
Display posts from previous: Sort by

# Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  