Question 4
The repeating decimals $0.abab\overline{ab}$ and $0.abcabc\overline{abc}$ satisfy $$
0.abab\overline{ab} + 0.abcabc\overline{abc} = \frac{33}{37},
$$ where $a,$ $b,$ and $c$ are (not necessarily distinct) digits. Find the three-digit number $abc.$
0.abab\overline{ab} + 0.abcabc\overline{abc} = \frac{33}{37},
$$ where $a,$ $b,$ and $c$ are (not necessarily distinct) digits. Find the three-digit number $abc.$