Question

A calculator has a squaring key that replaces the number currently displayed with its square. For example, if the display reads $3$ and the squaring key is pressed, the display becomes $9.$ If the display reads $2,$ how many times must the squaring key be pressed to produce a displayed number greater than $500?$

$4$

$5$

$8$

$9$

$250$

Solution:

Pressing the key repeatedly gives $2 \to 4 \to 16 \to 256 \to 65536.$

Since $256 \lt 500 \lt 65536,$ the display first exceeds $500$ on the fourth press.

Thus, the correct answer is A .

1987 AMC 8 Problem 19

Solution:

Problem 19 in Other Years