1961 AMC 12 第 18 题

Question

某镇人口在连续四年中的逐年变化依次为：增加

25\%

、增加

25\%

、减少

25\%

、减少

25\%

。这四年的净变化取到最接近的百分数为：

The yearly changes in the population census of a town for four consecutive years are, respectively,

25\%

increase,

25\%

increase,

25\%

decrease,

25\%

decrease. The net change over the four years, to the nearest percent, is:

-12

-1

0

1

12

每次增加用因子

1.25

表示，每次减少用

0.75

表示

Represent each increase by a factor of

1.25

and each decrease by

0.75

比较

1.25^2\cdot0.75^2

与

1

Compare

1.25^2\cdot0.75^2

with

1

最终人口相当于原人口乘以

(1.25)^2(0.75)^2=\frac{225}{256}\approx0.879\text{。}

这表示约减少

12.1\%

，取整后为

12\%

。

所以，正确答案是 A。

The final population is multiplied by

(1.25)^2(0.75)^2=\frac{225}{256}\approx0.879.

This is a decrease of about

12.1\%,

which rounds to

12\%.

Thus, the correct answer is A.

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