2018 AMC 12A 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.
Alice、Bob 和 Charlie 在徒步时想知道最近的城镇有多远。Alice 说：“我们离城镇至少 英里。”Bob 回答：“我们至多离城镇 英里。”Charlie 接着说：“其实最近的城镇至多在 英里外。”结果三个人的话都不正确。设 为到最近城镇的距离，单位为英里。下列哪个区间是 的所有可能取值的集合？
Alice, Bob, and Charlie were on a hike and were wondering how far away the nearest town was. When Alice said, “We are at least miles away,” Bob replied, “We are at most miles away.” Charlie then remarked, “Actually the nearest town is at most miles away.” It turned out that none of the three statements was true. Let be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of
小提示：
每句话都是假的，所以把每句话都换成它的否定
Each statement is false, so replace each with its negation
大提示：
“至少 ” 为假表示 ；“至多 ” 为假表示 ；“至多 ” 为假表示 。
“At least ” false means “at most ” false means “at most ” false means
解答：
否定这三句假话，得到 ，，和 。这些条件的交集是 ，也就是区间 。
所以正确答案是 D。
Negating the three false statements gives and The intersection of these conditions is that is, the interval
Thus, the correct answer is D.
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