Question

某一年中，汽油价格在一月上涨 $20\%$ ，二月下跌 $20\%$ ，三月上涨 $25\%$ ，四月下跌 $x\%$ 。四月底的汽油价格与一月初相同。四舍五入到最接近的整数， $x$ 是多少？

In a certain year the price of gasoline rose by $20\%$ during January, fell by $20\%$ during February, rose by $25\%$ during March, and fell by $x\%$ during April. The price of gasoline at the end of April was the same as it had been at the beginning of January. To the nearest integer, what is $x?$

$12$

$17$

$20$

$25$

$35$

答案：B

知识点：百分数

难度评级：1330

解答：

一月至三月后，价格变为原价的 $1.2 \cdot 0.8 \cdot 1.25 = 1.2$ 倍。

要回到原价，四月必须乘以 $\dfrac{1}{1.2}$ ，也就是下降 $1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%$ 。四舍五入后， $x = 17$ 。

所以正确答案是 B。

After January through March the price is $1.2 \cdot 0.8 \cdot 1.25 = 1.2$ times the original.

To return to the original, April must multiply by $\dfrac{1}{1.2},$ a decrease of $1 - \dfrac{1}{1.2} = \dfrac{1}{6} \approx 16.7\%.$ To the nearest integer, $x = 17.$

Thus, the correct answer is B.

2009 AMC 12B 第 7 题

答案：B

难度评级：1330

解答：

其他年份的第 7 题