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 it's 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 $\frac{2}{5}$ is larger.

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1986 AJHSME Problems/Problem 2

Problem

Solution

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