Question

A calculator has a reciprocal key that replaces the number currently displayed with its reciprocal. For example, if the display shows $4$ and the key is pressed, the display becomes $.25.$ If $32$ is currently displayed, what is the fewest number of times the reciprocal key must be pressed so that the display again reads $32?$

$1$

$2$

$3$

$4$

$5$

Solution:

Pressing the key once changes $32$ to its reciprocal $\frac{1}{32}.$

Pressing it a second time takes the reciprocal again, returning to $\frac{1}{1/32} = 32.$ So $2$ presses are enough.

Thus, the correct answer is B .

1989 AMC 8 Problem 18

Solution:

Problem 18 in Other Years