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

It is currently 19 Nov 2018, 10:20

Close

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
Your Progress

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.

Close

Request Expert Reply

Confirm Cancel
Events & Promotions in November
PrevNext
SuMoTuWeThFrSa
28293031123
45678910
11121314151617
18192021222324
2526272829301
Open Detailed Calendar
  • How to QUICKLY Solve GMAT Questions - GMAT Club Chat

     November 20, 2018

     November 20, 2018

     09:00 AM PST

     10:00 AM PST

    The reward for signing up with the registration form and attending the chat is: 6 free examPAL quizzes to practice your new skills after the chat.
  • The winning strategy for 700+ on the GMAT

     November 20, 2018

     November 20, 2018

     06:00 PM EST

     07:00 PM EST

    What people who reach the high 700's do differently? We're going to share insights, tips and strategies from data we collected on over 50,000 students who used examPAL.

If |x-6|=2x, then x=?

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

Hide Tags

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6526
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 25 Oct 2018, 00:22
00:00
A
B
C
D
E

Difficulty:

  15% (low)

Question Stats:

76% (00:54) correct 24% (00:49) wrong based on 66 sessions

HideShow timer Statistics

[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)

_________________

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

Math Expert
User avatar
V
Joined: 02 Aug 2009
Posts: 7038
Re: If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 25 Oct 2018, 04:28
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)


2x is positive so x is positive...
|x-6|=2x
I...
x-6=2x....x=-6 but x>0, so wrong
II..
x-6=-2x....3x=6...x=2.. correct

D
_________________

1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


GMAT online Tutor

CEO
CEO
User avatar
D
Joined: 11 Sep 2015
Posts: 3125
Location: Canada
Re: If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 25 Oct 2018, 05:04
2
Top Contributor
1
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)


There are 3 steps to solving equations involving ABSOLUTE VALUE:
1. Apply the rule that says: If |x| = k, then x = k or x = -k
2. Solve the resulting equations
3. Plug solutions into original equation to check for extraneous roots

Step 1: x - 6 = 2x or x - 6 = -2x

case a: x - 6 = 2x
Step 2: Solve to get x = -6
Step 3: Plug solution into original equation to get: |(-6) - 6| = 2(-6)
Evaluate to get: |-12| = -12 DOESN'T WORK

case b: x - 6 = -2x
Step 2: Solve to get x = 2
Step 3: Plug solution into original equation to get: |(2) - 6| = 2(2)
Evaluate to get: |-4| = 4 WORK!

Answer: D

Cheers,
Brent
_________________

Test confidently with gmatprepnow.com
Image

Board of Directors
User avatar
P
Status: QA & VA Forum Moderator
Joined: 11 Jun 2011
Posts: 4228
Location: India
GPA: 3.5
WE: Business Development (Commercial Banking)
GMAT ToolKit User Premium Member
If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 25 Oct 2018, 06:22
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)


PLUGGIN IN THE OPTIONS

(A) LHS = 12; RHS = -12 (Not equall)
(B) LHS = 10 ; RHS = -8 (Not equall)
(C) LHS = 6 ; RHS = 0 (Not equall)
(D) LHS = 4 RHS = 4 (Possible)
(E) LHS = 0 ; RHS = 12 (Not equall)

Thus, Answer must be (D)
_________________

Thanks and Regards

Abhishek....

PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS

How to use Search Function in GMAT Club | Rules for Posting in QA forum | Writing Mathematical Formulas |Rules for Posting in VA forum | Request Expert's Reply ( VA Forum Only )

Target Test Prep Representative
User avatar
P
Status: Founder & CEO
Affiliations: Target Test Prep
Joined: 14 Oct 2015
Posts: 4170
Location: United States (CA)
Re: If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 28 Oct 2018, 17:27
MathRevolution wrote:
[Math Revolution GMAT math practice question]

If \(|x-6|=2x\), then \(x=?\)

\(A. -6\)
\(B. -4\)
\(C. 0\)
\(D. 2\)
\(E. 6\)


As with any absolute value equation, we must consider two cases:

Case 1. We solve for x when (x - 6) is positive:

x - 6 = 2x

-6 = x

Since 2(-6) = -12, and since |x - 6| cannot be -12, then -6 is not a possible value for x.

Case 2. We solve for x when (x - 6) is negative:

-(x - 6) = 2x

-x + 6 = 2x

6 = 3x

2 = x

Answer: D
_________________

Scott Woodbury-Stewart
Founder and CEO

GMAT Quant Self-Study Course
500+ lessons 3000+ practice problems 800+ HD solutions

Math Revolution GMAT Instructor
User avatar
V
Joined: 16 Aug 2015
Posts: 6526
GMAT 1: 760 Q51 V42
GPA: 3.82
Premium Member
Re: If |x-6|=2x, then x=?  [#permalink]

Show Tags

New post 28 Oct 2018, 18:18
=>

\(|x-6|=2x\)
\(=> x-6 = ±2x\)
\(=> -6 = -x ±2x\)
\(=> -6 = x\) or \(-6 = -3x\)
\(=> x = -6\) or \(x = 2\)
However, \(2x = |x-6| ≥ 0.\)
Thus, we have the unique solution \(x=2.\)


Therefore, the answer is D.
Answer: D
_________________

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 $99 for 3 month Online Course"
"Free Resources-30 day online access & Diagnostic Test"
"Unlimited Access to over 120 free video lessons - try it yourself"

GMAT Club Bot
Re: If |x-6|=2x, then x=? &nbs [#permalink] 28 Oct 2018, 18:18
Display posts from previous: Sort by

If |x-6|=2x, then x=?

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


Copyright

GMAT Club MBA Forum Home| About| Terms and Conditions and Privacy Policy| GMAT Club Rules| Contact| Sitemap

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

Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.