text: GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video
  
   It is currently 31 May 2020, 15:09
  
  ### 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
  
  # Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0
  
  Author Message
  TAGS:
  
  ### Hide Tags
  
  Math Revolution GMAT Instructor
  Joined: 16 Aug 2015
  Posts: 9006
  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
  
  04 Oct 2017, 00:45
  4
  15
  00:00
  
  Difficulty:
  
  75% (hard)
  
  Question Stats:
  
  50% (01:56) correct 50% (02:00) wrong based on 278 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
  
  _________________
  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 \$79 for 1 month Online Course"
  "Free Resources-30 day online access & Diagnostic Test"
  "Unlimited Access to over 120 free video lessons - try it yourself"
  Manager
  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
  
  04 Oct 2017, 01:31
  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
  Joined: 02 Sep 2009
  Posts: 64250
  Re: Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0  [#permalink]
  
  ### Show Tags
  
  04 Oct 2017, 00:47
  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
  Joined: 07 Jun 2017
  Posts: 158
  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
  
  04 Oct 2017, 02:44
  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
  Joined: 16 Aug 2015
  Posts: 9006
  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
  
  06 Oct 2017, 01:42
  =>
  
  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.
  
  _________________
  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 \$79 for 1 month Online Course"
  "Free Resources-30 day online access & Diagnostic Test"
  "Unlimited Access to over 120 free video lessons - try it yourself"
  BSchool Forum Moderator
  Joined: 05 Jul 2017
  Posts: 499
  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
  
  09 Feb 2019, 03:24
  Bunuel - Can you help me understand where did I go wrong?
  Attachments
  
  IMG_20190209_164506.jpg [ 1.7 MiB | Viewed 774 times ]
  
  _________________
  Which of the following inequalities is equal to |2x-|x||<6? A. -2<x<0   [#permalink] 09 Feb 2019, 03:24
metadata: {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0}