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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$99 for 3 month Online Course
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Last edited by Max@Math Revolution on Fri Oct 12, 2018 7:25 am; edited 1 time in total

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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.

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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 :: https://GMATH.net (Math for the GMAT)
Testimonials :: https://GMATH.net/testimonials.html
Course release PROMO : finish our test drive till 31/Oct with (at least) 60 correct answers out of 92 (12-questions Mock included) to gain a 60% discount!

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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.

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