1987 AMC 12 第 5 题
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所有题目均经美国数学协会（MAA）官方合法授权使用。
5.
一名学生记录了一组测量值的精确百分比频数分布，如下表所示。然而，学生忘记标明测量值的总数 。 的最小可能值是多少？
| 测量值 | 百分比频数 |
|---|---|
A student recorded the exact percentage frequency distribution for a set of measurements, as shown below. However, the student neglected to indicate the total number of measurements. What is the smallest possible value of
| measured value | percent frequency |
|---|---|
答案：B
小提示：
将每个非零百分比写成总数的最简分数
Express each nonzero percentage as a reduced fraction of the total
大提示：
由此得到的每个频数都必须是整数
Every resulting frequency must be a whole number
解答：
由于 ，总数 必须能被 整除。取 时，各频数为 ，均为整数。因此，最小可能总数为 。
所以正确答案是 B。
Since the total must be divisible by Taking gives frequencies all whole numbers. Thus the smallest possible total is
Therefore the correct answer is B.
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