Question

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 $6$ 英里。”Bob 回答：“我们至多离城镇 $5$ 英里。”Charlie 接着说：“其实最近的城镇至多在 $4$ 英里外。”结果三个人的话都不正确。设 $d$ 为到最近城镇的距离，单位为英里。下列哪个区间是 $d$ 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 $6$ miles away," Bob replied, "We are at most $5$ miles away." Charlie then remarked, "Actually the nearest town is at most $4$ miles away." It turned out that none of the three statements was true. Let $d$ be the distance in miles to the nearest town. Which of the following intervals is the set of all possible values of $d?$

$(0, 4)$

$(4, 5)$

$(4, 6)$

$(5, 6)$

$(5, \infty)$

答案：D

知识点：逻辑推理不等式

难度评级：1200

解答：

否定这三句假话，得到 $d \lt 6$ ， $d \gt 5$ ，和 $d \gt 4$ 。这些条件的交集是 $5 \lt d \lt 6$ 也就是区间 $(5, 6)$ 。

所以正确答案是 D。

Negating the three false statements gives $d \lt 6,$ $d \gt 5,$ and $d \gt 4.$ The intersection of these conditions is $5 \lt d \lt 6,$ that is, the interval $(5, 6).$

Thus, the correct answer is D.

2018 AMC 12A 第 4 题

答案：D

难度评级：1200

解答：

其他年份的第 4 题