1965 AHSME Problems/Problem 15

Problem

The symbol $25_b$ represents a two-digit number in the base $b$ . If the number $52_b$ is double the number $25_b$ , then $b$ is:

$\textbf{(A)}\ 7 \qquad \textbf{(B) }\ 8 \qquad \textbf{(C) }\ 9 \qquad \textbf{(D) }\ 11 \qquad \textbf{(E) }\ 12$

Solution

We begin by converting both $25_b$ and $52_b$ to base $10$ . $25_b = 2b+5$ in base $10$ and $52_b = 5b+2$ base $10$ . The problem tells us that $5b+2 = 4b+10$ , yielding $\boxed{\textbf{(B) }8}$ as our final answer.

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1965 AHSME Problems/Problem 15

Problem

Solution