2021 JMC 10 Problems/Problem 9

Problem

In Malachar, the number system is identical to ours, but all real numbers are written with digits in reverse order. A citizen in Malachar writes $15\cdot 73.$ What does this Malacharian write as the answer?

$\textbf{(A) } 1095 \qquad\textbf{(B) } 1887 \qquad\textbf{(C) } 3723 \qquad\textbf{(D) } 5901 \qquad\textbf{(E) } 7881$

Solution

Let $e$ denote our number system and $m$ denote the Malacharian number system. Note that $15_m \cdot 73_m = 51_e \cdot 37_e = 1887_e = 7881_m,$ so $7881$ is the desired answer.

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2021 JMC 10 Problems/Problem 9

Problem

Solution