1987 AMC 8 第 17 题

先试着解答 1987 AMC 8 第 17 题,然后核对你的答案与精心整理的解答,解答来自 LIVE by Po-Shen Loh。你也可以参加完整限时模拟考试、查看全部 1987 AMC 8 解答,或核对答案。

所有题目均经美国数学协会(MAA)官方合法授权使用。

17.

艾比、布雷特、卡尔和达娜坐在一排编号为 11 到 44 的四个座位上。乔看着他们说:“布雷特挨着卡尔。”“艾比坐在布雷特和卡尔之间。”然而乔的每一句话都是假的。布雷特实际坐在 33 号座位。谁坐在 22 号座位?
Abby, Bret, Carl, and Dana are seated in a row of four seats numbered 11 to 4.4. Joe looks at them and says: “Bret is next to Carl.” “Abby is between Bret and Carl.” However, each one of Joe’s statements is false. Bret is actually sitting in seat 3.3. Who is sitting in seat 2?2?
艾比
Abby
布雷特
Bret
卡尔
Carl
达娜
Dana
信息不足,无法确定
There is not enough information to be sure
答案:D
知识点:逻辑推理
小提示:
“布雷特挨着卡尔”是假的,所以卡尔不在 22 号或 44 号座位;卡尔只能在 11 号座位
“Bret is next to Carl” is false, so Carl is not in seat 22 or seat 4;4; the only remaining seat for Carl is seat 11
大提示:
卡尔在 11 号座位后,“艾比在布雷特和卡尔之间”是假的,所以艾比不能在 22 号座位;把艾比放进最后一个可行座位,再看剩下谁
Once Carl is in seat 1,1, “Abby is between Bret and Carl” is false, so Abby cannot be in seat 2;2; place Abby in the last open seat and see who is left
解答:
布雷特在 33 号座位。因为“布雷特挨着卡尔”是假的,卡尔不在 22 号或 44 号座位,所以卡尔必须在 11 号座位。
布雷特(33 号)和卡尔(11 号)之间的座位是 22 号。因为“艾比在布雷特和卡尔之间”是假的,艾比不在 22 号,所以艾比必须在 44 号。
因此达娜坐在 22 号座位。
所以正确答案是 D。
Bret is in seat 3.3. Since “Bret is next to Carl” is false, Carl is not in seat 22 or seat 4,4, so Carl must be in seat 1.1.
The seat between Bret (seat 33) and Carl (seat 11) is seat 2.2. Since “Abby is between Bret and Carl” is false, Abby is not in seat 2,2, so Abby must be in seat 4.4.
That leaves Dana in seat 2.2.
Thus, the correct answer is D .
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