• 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=0.abcabc........(a repeating infinite decimal), what is tagged by: Max@Math Revolution ##### This topic has 3 expert replies and 0 member replies ### GMAT/MBA Expert ## If x=0.abcabc........(a repeating infinite decimal), what is ## Timer 00:00 ## Your Answer A B C D E ## Global Stats Difficult [Math Revolution GMAT math practice question] If x=0.abcabc........(a repeating infinite decimal), what is the value of a+b+c? 1) 1-x=0.123123123â€¦â€¦. 2) 0.8 < x < 0.9 _________________ 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
Email to : info@mathrevolution.com

Last edited by Max@Math Revolution on Fri Oct 12, 2018 7:25 am; edited 1 time in total

### GMAT/MBA Expert

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

If x=0.abcabc........(a repeating infinite decimal), what is the value of a+b+c?

1) 1-x=0.123123123â€¦â€¦.
2) 0.8 < x < 0.9
$$x = 0.\overline {abc} \,\,\,\,\left( {{\rm{common}}\,\,{\rm{russian}}\,\,{\rm{notation}}} \right)$$
$$? = a + b + c$$
$$\left( 1 \right)\,\,\,1 - x = 0.\overline {123} = {{123} \over {999}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = {{876} \over {999}} = 0.\overline {876} \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 8 + 7 + 6$$
$$\left( 2 \right)\,\,0.8 < x < 0.9\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 0.\overline {801} \,\,\,\,\, \Rightarrow \,\,\,? = 8 + 0 + 1\,\, \hfill \cr \,{\rm{Take}}\,\,x = 0.\overline {802} \,\,\,\,\, \Rightarrow \,\,\,? = 8 + 0 + 2 \hfill \cr} \right.$$

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

If x=0.abcabc........(a repeating infinite decimal), what is the value of a+b+c?

1) 1-x=0.123123123â€¦â€¦.
2) 0.8
$$x = 0.\overline {abc} \,\,\,\,\left( {{\rm{common}}\,\,{\rm{russian}}\,\,{\rm{notation}}} \right)$$
$$? = a + b + c$$
$$\left( 1 \right)\,\,\,1 - x = 0.\overline {123} = {{123} \over {999}}\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,x = {{876} \over {999}} = 0.\overline {876} \,\,\,\,\,\,\,\,\,\, \Rightarrow \,\,\,\,\,\,\,\,? = 8 + 7 + 6$$
$$\left( 2 \right)\,\,0.8 < x < 0.9\,\,\,\,\,\,\left\{ \matrix{ \,{\rm{Take}}\,\,x = 0.\overline {801} \,\,\,\,\, \Rightarrow \,\,\,? = 8 + 0 + 1\,\, \hfill \cr \,{\rm{Take}}\,\,x = 0.\overline {802} \,\,\,\,\, \Rightarrow \,\,\,? = 8 + 0 + 2 \hfill \cr} \right.$$

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

Legendary Member
Joined
24 Jul 2015
Posted:
2232 messages
Followed by:
32 members
19
GMAT Score:
=>
Forget conventional ways of solving math questions. For DS problems, the VA (Variable Approach) method is the quickest and easiest way to find the answer without actually solving the problem. Remember that equal numbers of variables and independent equations ensure a solution.

Since we have 4 variables (x, a, b and c) and 1 equation (x = 0.abcabcâ€¦.), E is most likely to be the answer. However, condition 1) includes 3 hidden equations (matching the values of the decimal places) and allows us to determine the values of all four variables as follows:
x = 1 - 0.123123123â€¦ = 0.876876876â€¦ = 0.abcabcabcabcâ€¦
Thus a = 8, b = 7, c = 6 and a + b + c = 8 + 7 + 6 = 21.
Condition 1) is sufficient.

Condition 2)
If x = 0.811811811â€¦, then a = 8, b = 1, c = 1 and a + b + c = 10.
If x = 0.812812812â€¦, then a = 8, b = 1, c = 2 and a + b + c = 11.
Since we donâ€™t have a unique solution, condition 2) is not sufficient.

_________________

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 • 1 Hour Free BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • 5-Day Free Trial 5-day free, full-access trial TTP Quant 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

• Free Veritas GMAT Class
Experience Lesson 1 Live Free

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

Available with Beat the GMAT members only code

• 5 Day FREE Trial
Study Smarter, Not Harder

Available with Beat the GMAT members only code

• Magoosh
Study with Magoosh GMAT prep

Available with Beat the GMAT members only code

• Free Trial & Practice Exam
BEAT THE GMAT EXCLUSIVE

Available with Beat the GMAT members only code

• Get 300+ Practice Questions

Available with Beat the GMAT members only code

### Top First Responders*

1 Jay@ManhattanReview 74 first replies
2 Brent@GMATPrepNow 66 first replies
3 GMATGuruNY 40 first replies
4 Ian Stewart 25 first replies
5 Scott@TargetTestPrep 15 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

200 posts
2 Max@Math Revolution

Math Revolution

93 posts
3 Brent@GMATPrepNow

GMAT Prep Now Teacher

91 posts
4 Jay@ManhattanReview

Manhattan Review

81 posts
5 GMATGuruNY

The Princeton Review Teacher

61 posts
See More Top Beat The GMAT Experts