AMC8 2001

AMC8 2001 · Q17

AMC8 2001 · Q17. It mainly tests Percent, Arithmetic misc.

For the game show *Who Wants To Be A Millionaire?*, the dollar values of each question are shown in the following table (where K = 1000). Between which two questions is the percent increase of the value the smallest? [Table: Question 1 to 15 values: 100,200,300,500,1K,2K,4K,8K,16K,32K,64K,125K,250K,500K,1000K]

在游戏节目《谁想成为百万富翁？》中，各题的美元价值如以下表格所示（其中K=1000）。哪两题之间的价值百分比增长最小？[表格：第1至15题价值：100,200,300,500,1K,2K,4K,8K,16K,32K,64K,125K,250K,500K,1000K]

(A) From 1 to 2 从1到2

(B) From 2 to 3 从2到3

(D) From 11 to 12 从11到12

(E) From 14 to 15 从14到15

Answer

Correct choice: (B)

正确答案：（B）

Solution

(B) The percent increase from $a$ to $b$ is given by $\dfrac{b-a}{a}(100\%)$ For example, the percent increase for the first two questions is $\dfrac{200-100}{100}(100\%)=100\%$ Each time the amount doubles there is a 100% increase. The only exceptions in this game are 2 to 3 (50%), 3 to 4 ($66\dfrac{2}{3}\%$) and 11 to 12 (about 95%). The answer is (B). OR $\begin{array}{r|rrrrrrrrrrrrrrr} \text{Question} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15\\ \text{Value} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K}\\ \%\ \text{Increase} & \text{—} & 100 & 50 & 66.7 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 95 & 100 & 100 & 100 \end{array}$

（B）从$a$增加到$b$的百分比增幅为 $\dfrac{b-a}{a}(100\%)$ 例如，前两题的百分比增幅是 $\dfrac{200-100}{100}(100\%)=100\%$ 每当数值翻倍，就会增加100%。这个游戏中唯一的例外是：2到3（50%）、3到4（$66\dfrac{2}{3}\%$）以及11到12（约95%）。答案是（B）。或者 $\begin{array}{r|rrrrrrrrrrrrrrr} \text{题号} & 1 & 2 & 3 & 4 & 5 & 6 & 7 & 8 & 9 & 10 & 11 & 12 & 13 & 14 & 15\\ \text{数值} & 100 & 200 & 300 & 500 & 1\text{K} & 2\text{K} & 4\text{K} & 8\text{K} & 16\text{K} & 32\text{K} & 64\text{K} & 125\text{K} & 250\text{K} & 500\text{K} & 1000\text{K}\\ \%\ \text{增幅} & \text{—} & 100 & 50 & 66.7 & 100 & 100 & 100 & 100 & 100 & 100 & 100 & 95 & 100 & 100 & 100 \end{array}$

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