• NEW! FREE Beat The GMAT Quizzes
Hundreds of Questions Highly Detailed Reporting Expert Explanations
• 7 CATs FREE!
If you earn 100 Forum Points

Engage in the Beat The GMAT forums to earn
100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote If |x-6|=2x, then x=? tagged by: Max@Math Revolution This topic has 5 expert replies and 0 member replies GMAT/MBA Expert If |x-6|=2x, then x=? Timer 00:00 Your Answer A B C D E Global Stats Difficult [Math Revolution GMAT math practice question] If |x-6|=2x, then x=? A. -6 B. -4 C. 0 D. 2 E. 6 _________________ Math Revolution Finish GMAT Quant Section with 10 minutes to spare. The one-and-only Worldâ€™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
Email to : info@mathrevolution.com

GMAT/MBA Expert

GMAT Instructor
Joined
25 May 2010
Posted:
15380 messages
Followed by:
1872 members
Upvotes:
13060
GMAT Score:
790
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

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

A. -6
B. -4
C. 0
D. 2
E. 6
We can PLUG IN THE ANSWERS, which represent the value of x.
Since an absolute value cannot be equal to a negative value, the correct answer cannot be A or B.

D: x=2
If we plug x=2 into |x-6|=2x, we get:
|2-6| = 2*2
|-4| = 4
4 = 4.
Success!

The correct answer is D.

_________________
Mitch Hunt
Private Tutor for the GMAT and GRE
GMATGuruNY@gmail.com

If you find one of my posts helpful, please take a moment to click on the "UPVOTE" icon.

Available for tutoring in NYC and long-distance.
For more information, please email me at GMATGuruNY@gmail.com.
Student Review #1
Student Review #2
Student Review #3

Free GMAT Practice Test How can you improve your test score if you don't know your baseline score? Take a free online practice exam. Get started on achieving your dream score today! Sign up now.

GMAT/MBA Expert

GMAT Instructor
Joined
08 Dec 2008
Posted:
13033 messages
Followed by:
1251 members
Upvotes:
5254
GMAT Score:
770
Max@Math Revolution 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

_________________
Brent Hanneson â€“ Creator of GMATPrepNow.com
Use my video course along with

Sign up for free Question of the Day emails
And check out all of these free resources

GMAT Prep Now's comprehensive video course can be used in conjunction with Beat The GMATâ€™s FREE 60-Day Study Guide and reach your target score in 2 months!

GMAT/MBA Expert

GMAT Instructor
Joined
09 Oct 2010
Posted:
1449 messages
Followed by:
32 members
Upvotes:
59
Max@Math Revolution wrote:
[Math Revolution GMAT math practice question]

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

A. -6
B. -4
C. 0
D. 2
E. 6
$$?\,\,\,:\,\,\,\,x\,\,\,{\rm{such}}\,\,{\rm{that}}\,\,\,\,\left| {x - 6} \right| = 2x\,\,\,\,\,\left( {{\rm{Note}}\,\,{\rm{that}}\,\,\,2x \ge 0\,\,,\,\,{\rm{hence}}\,\,x \ge 0} \right)$$
$$\left| {x - 6} \right| = 2x\,\,\,\,\,\,\,\mathop \Rightarrow \limits^{{\rm{squaring}}} \,\,\,\,\,\,\,{\left( {x - 6} \right)^2} = {\left( {2x} \right)^2}\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,3{x^2} + 12x - 36 = 0$$
$$3{x^2} + 12x - 36 = 0\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,{x^2} + 4x - 12 = 0\,\,\,\,\,\,\mathop \Rightarrow \limits_{{\rm{product}}\,\, = \,\, - 12}^{{\rm{sum}}\,\, = \,\, - 4} \,\,\,\,\,x = - 6\,\,\,{\rm{or}}\,\,\,x = 2$$
$${\rm{Testing}}\,\,{\rm{each}}\,\,{\rm{potential}}\,\,{\rm{root}}\,\,{\rm{in}}\,\,{\rm{the}}\,\,{\rm{original}}\,\,{\rm{equation}}\,\,\,\left( * \right)\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,? = x = 2\,\,\,$$

(*) Important: as mentioned in the very beginning, -6 doesnÂ´t need to be tested. Someone (correctly) may argue that 2 does not need, too (otherwise no alternative choice could be chosen).
Anyway, we want to remind you that, whenever an equation is squared - or put to any positive even power - roots may be "created" and, because of that, the "final checking" is an important procedure.

This solution follows the notations and rationale taught in the GMATH method.

Regards,
Fabio.

_________________
Fabio Skilnik :: GMATH method creator ( Math for the GMAT)
English-speakers :: https://www.gmath.net
Portuguese-speakers :: https://www.gmath.com.br

GMAT/MBA Expert

GMAT Instructor
Joined
25 Apr 2015
Posted:
2950 messages
Followed by:
19 members
Upvotes:
43
Max@Math Revolution 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
scott@targettestprep.com

See why Target Test Prep is rated 5 out of 5 stars on BEAT the GMAT. Read our reviews

GMAT/MBA Expert

Legendary Member
Joined
24 Jul 2015
Posted:
2481 messages
Followed by:
32 members
Upvotes:
19
GMAT Score:
=>

|x-6|=2x
=> x-6 = Â±2x
=> -6 = -x Â±2x
=> -6 = x or -6 = -3x
=> x = -6 or x = 2
However, 2x = |x-6| â‰¥ 0.
Thus, we have the unique solution x=2.

Therefore, the answer is D.
Answer: D

_________________

Math Revolution
Finish GMAT Quant Section with 10 minutes to spare.
The one-and-only Worldâ€™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 Email to : info@mathrevolution.com • 5-Day Free Trial 5-day free, full-access trial TTP Quant Available with Beat the GMAT members only code • Free Veritas GMAT Class Experience Lesson 1 Live Free Available with Beat the GMAT members only code • FREE GMAT Exam Know how you'd score today for$0

Available with Beat the GMAT members only code

• 1 Hour Free
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions
25 Video lessons and 6 Webinars for FREE

Available with Beat the GMAT members only code

• Free Practice Test & Review
How would you score if you took the GMAT

Available with Beat the GMAT members only code

• Award-winning private GMAT tutoring
Register now and save up to \$200

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

Top First Responders*

1 Brent@GMATPrepNow 40 first replies
2 Ian Stewart 40 first replies
3 Scott@TargetTestPrep 39 first replies
4 Jay@ManhattanReview 28 first replies
5 GMATGuruNY 25 first replies
* Only counts replies to topics started in last 30 days
See More Top Beat The GMAT Members

Most Active Experts

1 Scott@TargetTestPrep

Target Test Prep

159 posts
2 Max@Math Revolution

Math Revolution

90 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

58 posts
4 Ian Stewart

GMATiX Teacher

49 posts
5 GMATGuruNY

The Princeton Review Teacher

38 posts
See More Top Beat The GMAT Experts