Question

Alice、Bob 和 Charlie 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：“我们离城镇至多 $5$ 英里。”Charlie 接着说：“其实最近的城镇至多在 $4$ 英里外。”结果三人的话都不正确。设到最近城镇的距离为 $d$ 英里。下列哪个区间是 $d$ 的所有可能取值？

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：900

解答：

Alice 的话不正确，说明 $d \lt 6$ 。Bob 的话不正确，说明 $d \gt 5$ 。Charlie 的话不正确，说明 $d \gt 4$ 。

合并这些条件可得 $5 \lt d$ 且 $d \lt 6$ ，因此 $d$ 位于区间 $(5, 6)$ 。

因此正确答案是 D。

Alice's statement tells us that $d \lt 6.$ Bob's statement tells us that $d \gt 5.$ Charlie's statement tells us that $d \gt 4.$

Combining all of these tells us that $5 \lt d$ and $d \lt 6,$ which means $d$ is in the interval $(5, 6).$

Thus, D is the correct answer.

2018 AMC 10A 第 5 题

答案：D

难度评级：900

解答：

其他年份的第 5 题