1968 AMC 12 第 8 题

Question

一个正数本应乘以

6

，却误被除以

6

。以正确结果为基准，所产生的百分误差取最接近的整数为：

A positive number is mistakenly divided by

6

instead of being multiplied by

6.

Based on the correct answer, the error thus committed, to the nearest percent, is:

100

97

83

17

3

设该数为

N

，比较

\frac{N}{6}

与

6N

Let the number be

N

and compare

\frac{N}{6}

with

6N

用绝对误差除以正确结果

Divide the absolute error by the correct result

正确结果为

6N

，误算结果为

\frac{N}{6}

。以正确结果为基准，误差为

\frac{6N-\frac{N}{6}}{6N}=\frac{35}{36}\approx97.2\%

。

因此，正确答案是 B。

The correct result is

6N,

while the mistaken result is

\frac{N}{6}.

Relative to the correct result, the error is

\frac{6N-\frac{N}{6}}{6N}=\frac{35}{36}\approx97.2\%.

Therefore, the correct answer is B.

其他年份的第 8 题