MathDB
Repeating Decimals in a Base

Source: 2019 AMC 12A #11 / AMC 10A #18

February 8, 2019
AMC 10AMC 12AMC2019 AMC 12A2019 AMC 10A2019 AMC

Problem Statement

For some positive integer kk, the repeating base-kk representation of the (base-ten) fraction 751\frac{7}{51} is 0.23‾k=0.232323...k0.\overline{23}_k = 0.232323..._k. What is kk?
<spanclass=′latex−bold′>(A)</span>13<spanclass=′latex−bold′>(B)</span>14<spanclass=′latex−bold′>(C)</span>15<spanclass=′latex−bold′>(D)</span>16<spanclass=′latex−bold′>(E)</span>17<span class='latex-bold'>(A) </span> 13 \qquad<span class='latex-bold'>(B) </span> 14 \qquad<span class='latex-bold'>(C) </span> 15 \qquad<span class='latex-bold'>(D) </span> 16 \qquad<span class='latex-bold'>(E) </span> 17
Back to ProblemsView on AoPS