Question

一个计算器有一个平方键，会把当前显示的数替换成它的平方。例如，如果显示 $3$ ，按下平方键后显示 $9$ 。如果显示的是 $2$ ，要按多少次平方键才能得到大于 $500$ 的显示数？

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 $500?$

$4$

$5$

$8$

$9$

$250$

答案：A

知识点：指数

难度评级：1030

解答：

重复按键得到 $2 \to 4 \to 16 \to 256 \to 65536$ 。

因为 $256 \lt 500 \lt 65536$ ，显示数第一次超过 $500$ 是第四次按键。

所以正确答案是 A。

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 第 19 题

答案：A

难度评级：1030

解答：

其他年份的第 19 题