AMC 8 2001 Problem 17

AMC8 2001 年第 17 题

百分比★★★☆☆

For the game show Who Wants To Be A Millionaire?, the dollar values of each question are shown in the table below (where K = 1000). Between which two questions is the percent increase of the value the smallest?

对于游戏节目《谁想成为百万富翁？》，每个问题的价值（单位：美元）如下表所示（其中 K＝ 1000）。在哪两个问题之间，哪两个价值增加的百分比最小？

A. $\text{From 1 to 2}$ / 从 1 到 2
B. $\text{From 2 to 3}$ / 从 2 到 3
C. $\text{From 3 to 4}$ / 从 3 到 4
D. $\text{From 11 to 12}$ / 从 11 到 12
E. $\text{From 14 to 15}$ / 从 14 到 15

正确答案 · Correct Answer

解析 · Solution

Solution 1

Notice that in two of the increases, the dollar amount doubles. The increases in which this is not true is 2 to 3, 3 to 4, and 11 to 12. We can disregard 11 to 12 since that increase is almost 2 times. The increase from 2 to 3 is

\displaystyle \frac{300-200}{200}

\displaystyle \frac{1}{2}

, so it's only multiplied by a factor of 1.5. The increase from 3 to 4 is

\displaystyle \frac{500-300}{300}

\displaystyle \frac{2}{3}

, so it is multiplied by a factor of

1.\bar{6}

. Therefore, the smallest percent increase is

\text{From 2 to 3}, \text{B}

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