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Repeating Decimal Addition

Source: 2014 AIME II Problem 4

March 27, 2014
modular arithmeticAMCAIME

Problem Statement

The repeating decimals 0.ababab‾0.abab\overline{ab} and 0.abcabcabc‾0.abcabc\overline{abc} satisfy 0.ababab‾+0.abcabcabc‾=3337,0.abab\overline{ab}+0.abcabc\overline{abc}=\frac{33}{37}, where a,ba,b, and cc are (not necessarily distinct) digits. Find the three-digit number abcabc.
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