2015 AMC 10B 第 5 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。

5.

David、Hikmet、Jack、Marta、Rand 和 Todd 与另外

6

人参加了一场

12

人赛跑。Rand 比 Hikmet 早

6

个名次完成。Marta 比 Jack 晚

1

个名次。David 比 Hikmet 晚

2

个名次。Jack 比 Todd 晚

2

个名次。Todd 比 Rand 晚

1

个名次。Marta 得第

6

名。谁得第

8

名？

David, Hikmet, Jack, Marta, Rand, and Todd were in a

12

-person race with

6

other people. Rand finished

6

places ahead of Hikmet. Marta finished

1

place behind Jack. David finished

2

places behind Hikmet. Jack finished

2

places behind Todd. Todd finished

1

place behind Rand. Marta finished in

6

th place. Who finished in

8

th place?

David

Hikmet

Jack

Rand

Todd

答案：B

知识点：逻辑推理

难度评级：960

小提示：

从 Marta 的第

6

名往回推。

Work backward from Marta’s

6

th place

大提示：

Hikmet 比 Rand 晚

6

个名次。

Hikmet is

6

places behind Rand

解答：

Marta 是第

6

名，所以 Jack 是第

5

名。Jack 比 Todd 晚

2

个名次，所以 Todd 是第

3

名；Todd 比 Rand 晚

1

个名次，所以 Rand 是第

2

名。

Hikmet 比 Rand 晚

6

个名次，所以 Hikmet 是第

8

名。

所以正确答案是 B。

Marta finished

6

th, so Jack finished

5

th. Since Jack finished

2

places behind Todd, Todd finished

3

rd. Since Todd finished

1

place behind Rand, Rand finished

2

nd.

Hikmet finished

6

places behind Rand, so Hikmet finished

8

th.

Thus, the correct answer is B.