2015 AMC 12B 第 4 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。

4.

David、Hikmet、Jack、Marta、Rand 和 Todd 与另外 66 人参加了一场 1212 人赛跑。Rand 比 Hikmet 领先 66 个名次。Marta 比 Jack 落后 11 个名次。David 比 Hikmet 落后 22 个名次。Jack 比 Todd 落后 22 个名次。Todd 比 Rand 落后 11 个名次。Marta 得第 66 名。谁得第 88 名?

David, Hikmet, Jack, Marta, Rand, and Todd were in a 1212-person race with 66 other people. Rand finished 66 places ahead of Hikmet. Marta finished 11 place behind Jack. David finished 22 places behind Hikmet. Jack finished 22 places behind Todd. Todd finished 11 place behind Rand. Marta finished in 66th place. Who finished in 88th place?

David

Hikmet

Jack

Rand

Todd

答案:B
知识点:逻辑推理逆推法
难度评级:1130
解答:

Marta 第 66 名,所以 Jack 第 55 名。Jack 比 Todd 落后 22 名,所以 Todd 第 33 名。Todd 比 Rand 落后 11 名,所以 Rand 第 22 名。

Rand 比 Hikmet 领先 66 名,所以 Hikmet 第 88 名。(David 第 1010 名。)

因此,正确选项是 B

Marta is 66th, so Jack is 55th. Jack is 22 behind Todd, so Todd is 33rd. Todd is 11 behind Rand, so Rand is 22nd.

Rand is 66 ahead of Hikmet, so Hikmet is 88th. (David is 1010th.)

Thus, the correct answer is B.

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