AMC 8 1997 Problem 16
AMC8 1997 年第 16 题
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Penni Precisely buys $100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%, BB was down 25%, and CC was unchanged. For the second year, AA was down 20% from the previous year, BB was up 25% from the previous year, and CC was unchanged. If A, B, and C are the final values of the stock, then
Penni Precisely 购买三家公司各 $100 的股票：Alabama Almonds、Boston Beans 和 California Cauliflower。一年后，AA 上涨 20%，BB 下跌 25%，CC 不变。第二年，AA 在前一年的基础上下跌 20%，BB 在前一年的基础上上涨 25%，CC 不变。若 A、B、C 分别是这些股票的最终价值，则
- A.A=B=C
- B.A=B<C
- C.C<B=A
- D.A<B<C
- E.B<A<C
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
AA is after one year. After the second year, AA is .
BB is after one year. After the second year, BB is
CC remains unchanged throughout, and stays at 100.
Thus, B < A < C, and the right answer is
AA will be at the end.
BB will be at the end.
CC will be unchanged at 100.
Since all the fractions are under 1, will be highest value.
Since is only away from 1, while is away from 1, is closer to 1, and will be closer to the original value.
Thus, B < A < C, and the right answer is
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