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Reverse numbers in different bases

Source: 1971 AHSME Problem 11

April 19, 2014
modular arithmeticAMC

Problem Statement

The numeral 4747 in base aa represents the same number as 7474 in base bb. Assuming that both bases are positive integers, the least possible value of a+ba+b written as a Roman numeral, is
<spanclass=′latex−bold′>(A)</span>XIII<spanclass=′latex−bold′>(B)</span>XV<spanclass=′latex−bold′>(C)</span>XXI<spanclass=′latex−bold′>(D)</span>XXIV<spanclass=′latex−bold′>(E)</span>XVI<span class='latex-bold'>(A) </span>\mathrm{XIII}\qquad<span class='latex-bold'>(B) </span>\mathrm{XV}\qquad<span class='latex-bold'>(C) </span>\mathrm{XXI}\qquad<span class='latex-bold'>(D) </span>\mathrm{XXIV}\qquad <span class='latex-bold'>(E) </span>\mathrm{XVI}
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