2008 AMC 12B 第 6 题

Question

邮差 Pete 有一个计步器来记录步数。计步器最多显示

99999

步，下一步会翻转为

00000

。Pete 计划计算自己一年的里程。一月

1

日，Pete 将计步器设为

00000

。一年中，计步器从

99999

翻到

00000

共四十四次。十二月

31

日，计步器显示

50000

。Pete 每英里走

1800

步。下列哪一项最接近 Pete 这一年走过的英里数？

Postman Pete has a pedometer to count his steps. The pedometer records up to

99999

steps, then flips over to

00000

on the next step. Pete plans to determine his mileage for a year. On January

1

Pete sets the pedometer to

00000.

During the year, the pedometer flips from

99999

to

00000

forty-four times. On December

31

the pedometer reads

50000.

Pete takes

1800

steps per mile. Which of the following is closest to the number of miles Pete walked during the year?

2500

3000

3500

4000

4500

答案：A

知识点：位值估算单位换算

难度评级：1350

小提示：

计步器每翻转一次代表

100000

步；再加上最后显示的

50000

。

Each flip of the pedometer represents

100000

steps; add the final reading of

50000

大提示：

将总步数除以

1800

，换算成英里。

Divide the total number of steps by

1800

to convert to miles

解答：

每次翻转表示

100000

步，所以这一年的总步数为

\begin{aligned} &44 \cdot 100000 \\ &\quad {}+ 50000 = 4{,}450{,}000 \end{aligned}\text{。}

每英里

1800

步，所以里程为

\dfrac{4{,}450{,}000}{1800} \approx 2472

，最接近

2500

。

因此，正确答案是 A。

Each flip counts

100000

steps, so the year’s steps total

\begin{aligned} &44 \cdot 100000 \\ &\quad {}+ 50000 = 4{,}450{,}000. \end{aligned}

At

1800

steps per mile, the mileage is

\dfrac{4{,}450{,}000}{1800} \approx 2472,

which is closest to

2500.

Thus, the correct answer is A.

2008 AMC 12B 第 6 题

答案：A

难度评级：1350

小提示：

大提示：

解答：

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