1999 AMC 8 第 6 题

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所有题目均经美国数学协会(MAA)官方合法授权使用。

6.

Bo、Coe、Flo、Jo 和 Moe 的钱数各不相同。Jo 和 Bo 都没有 Flo 的钱多。Bo 和 Coe 都比 Moe 钱多。Jo 比 Moe 钱多,但比 Bo 钱少。谁的钱最少?

Bo, Coe, Flo, Jo, and Moe have different amounts of money. Neither Jo nor Bo has as much money as Flo. Both Bo and Coe have more than Moe. Jo has more than Moe, but less than Bo. Who has the least amount of money?

Bo

Coe

Flo

Jo

Moe

答案:E
知识点:逻辑推理不等式
难度评级:820
解答:

B,C,F,JB, C, F, JMM 分别表示 Bo、Coe、Flo、Jo 和 Moe 的钱数。

那么 J<F,B<F. J \lt F,\quad B \lt F.

还知道 B>M,C>M. B \gt M,\quad C \gt M.

最后,题目给出 M<J<B. M \lt J \lt B.

由这些不等式可知 F>MF \gt M

因此每个人的钱都比 Moe 多。

所以正确答案是 E

Let B,C,F,J,B, C, F, J, and MM represent the amount of money that Bo, Coe, Flo, Jo, and Moe have respectively.

Then J<F,B<F. J \lt F,\quad B \lt F.

We also have B>M,C>M. B \gt M,\quad C \gt M.

Finally, we are given M<J<B. M \lt J \lt B.

From the first and second inequalities, we can get that F>M.F \gt M.

This shows that everyone has more money than Moe.

Thus, E is the correct answer.

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