1999 AMC 8 第 6 题

Question

博、科、弗洛、乔和莫的钱数各不相同。乔和博都没有弗洛的钱多。博和科都比莫钱多。乔比莫钱多，但比博钱少。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?

博

Bo

科

Coe

弗洛

Flo

乔

Jo

莫

Moe

答案：E

知识点：逻辑推理不等式

难度评级：820

小提示：

排除所有已知比别人钱多的人

Eliminate anyone known to have more than someone else

大提示：

用每个比较关系找出谁的钱比莫多

Use each comparison to show who is above Moe

解答：

设

B, C, F, J

和

M

分别表示博、科、弗洛、乔和莫的钱数。

那么

J \lt F,\quad B \lt F\text{。}

还知道

B \gt M,\quad C \gt M\text{。}

最后，题目给出

M \lt J \lt B\text{。}

由第一组和第二组不等式可知

F \gt M

。

因此每个人的钱都比莫多。

所以正确答案是 E。

Let

B, C, F, J,

and

M

represent the amount of money that Bo, Coe, Flo, Jo, and Moe have respectively.

Then

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

We also have

B \gt M,\quad C \gt M.

Finally, we are given

M \lt J \lt B.

From the first and second inequalities, we can get that

F \gt M.

This shows that everyone has more money than Moe.

Thus, E is the correct answer.

1999 AMC 8 第 6 题

答案：E

难度评级：820

小提示：

大提示：

解答：

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