1997 AMC 8 第 16 题

先试着解答 1997 AMC 8 第 16 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1997 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

16.

佩妮·普里赛斯利在三家公司各买了价值 $100\$ 100 的股票:阿拉巴马杏仁公司、波士顿豆业公司和加利福尼亚花椰菜公司。一年后,AA 上涨 20%20 \%,BB 下跌 25%25 \%,CC 不变。第二年,AA 比前一年下跌 20%20 \%,BB 比前一年上涨 25%25 \%,CC 仍不变。如果 AA、BB 和 CC 是这些股票的最终价值,那么
Penni Precisely buys $100\$ 100 worth of stock in each of three companies: Alabama Almonds, Boston Beans, and California Cauliflower. After one year, AA was up 20%,20 \%, BB was down 25%,25 \%, and CC was unchanged. For the second year, AA was down 20%20 \% from the previous year, BB was up 25%25 \% from the previous year, and CC was unchanged. If A,A, B,B, and CC are the final values of the stock, then
A=B=CA = B = C
A=B<CA = B \lt C
C<B=AC \lt B = A
A<B<CA \lt B \lt C
B<A<CB \lt A \lt C
答案:E
知识点:百分数
小提示:
先上涨百分之 2020,再下跌百分之 2020,并不会回到原值
A 2020 percent gain followed by a 2020 percent loss does not return to the start
大提示:
百分比变化要用乘法因子逐步计算
Apply each percent change multiplicatively
解答:
第一年后,AA 的价值变为 $100⋅1.2=$120, \$ 100 \cdot 1.2 = \$ 120\text{,}BB 的价值变为 $100⋅0.75=$75。 \$ 100 \cdot 0.75 = \$ 75\text{。}
第二年后,AA 的价值为 $120⋅0.8=$96, \$ 120 \cdot 0.8 = \$ 96\text{,}BB 的价值为 $75⋅1.25=$93.75。 \$ 75 \cdot 1.25 = \$ 93.75\text{。}
CC 价值仍不变,所以最终顺序是 B<A<C。 B \lt A \lt C\text{。}
所以正确答案是 E。
After the first year, AA’s stock’s worth goes up to $100⋅1.2=$120 \$ 100 \cdot 1.2 = \$ 120 and BB’s goes down to $100⋅0.75=$75. \$ 100 \cdot 0.75 = \$ 75.
After the second year, AA’s stock is worth $120⋅0.8=$96 \$ 120 \cdot 0.8 = \$ 96 and BB’s is worth $75⋅1.25=$93.75. \$ 75 \cdot 1.25 = \$ 93.75.
CC’s stock worth remains the same, so the ordering of the stock worths is now B<A<C. B \lt A \lt C.
Thus, E is the correct answer.
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