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 66 人参加了一场 1212 人赛跑。Rand 比 Hikmet 早 66 个名次完成。Marta 比 Jack 晚 11 个名次。David 比 Hikmet 晚 22 个名次。Jack 比 Todd 晚 22 个名次。Todd 比 Rand 晚 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
难度评级:960
小提示:

从 Marta 的第 66 名往回推。

Work backward from Marta’s 66th place

大提示:

Hikmet 比 Rand 晚 66 个名次。

Hikmet is 66 places behind Rand

解答:

Marta 是第 66 名,所以 Jack 是第 55 名。Jack 比 Todd 晚 22 个名次,所以 Todd 是第 33 名;Todd 比 Rand 晚 11 个名次,所以 Rand 是第 22 名。

Hikmet 比 Rand 晚 66 个名次,所以 Hikmet 是第 88 名。

所以正确答案是 B

Marta finished 66th, so Jack finished 55th. Since Jack finished 22 places behind Todd, Todd finished 33rd. Since Todd finished 11 place behind Rand, Rand finished 22nd.

Hikmet finished 66 places behind Rand, so Hikmet finished 88th.

Thus, the correct answer is B.

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