# 1986 AJHSME Problems/Problem 2

## Problem

Which of the following numbers has the largest reciprocal? $\text{(A)}\ \frac{1}{3} \qquad \text{(B)}\ \frac{2}{5} \qquad \text{(C)}\ 1 \qquad \text{(D)}\ 5 \qquad \text{(E)}\ 1986$

## Solution

For positive numbers, the larger the number, the smaller its reciprocal. Likewise, smaller numbers have larger reciprocals.

Thus, all we have to do is find the smallest number.

But which one is it? $\frac{1}{3}$? or $\frac{2}{5}$? We see that $\frac{1}{3} = \frac{5}{15}$, and $\frac{2}{5} = \frac{6}{15}$, so obviously $\frac{1}{3}$ is smaller. $\boxed{\text{A}}$

## See Also

 1986 AJHSME (Problems • Answer Key • Resources) Preceded byProblem 1 Followed byProblem 3 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 All AJHSME/AMC 8 Problems and Solutions

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