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2019 AMC 10AProblem 18P16-20~4 minPrint
Bases & DigitsFractions & DecimalsQuadraticsUse the answer choices (mod checks, size, form) to eliminate or selectSet up the equation/formula and compute; no special trick needed

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 ?

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Problem © Mathematical Association of America (MAA), American Mathematics Competitions. Reproduced for non-commercial educational use. Solution and commentary are original to this site.