AMC12 2018 A

AMC12 2018 A · Q4

AMC12 2018 A · Q4. It mainly tests Logic puzzles.

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 $d$?

爱丽丝、鲍勃和查理徒步时想知道最近的城镇有多远。爱丽丝说：“我们至少6英里远。”鲍勃回答：“我们至多5英里远。”查理说：“其实最近的城镇至多4英里远。”结果三人的陈述都不真。设$d$为到最近城镇的英里距离。以下哪个区间是$d$的所有可能值的集合？

(A) (0, 4) (0, 4)

(B) (4, 5) (4, 5)

(D) (5, 6) (5, 6)

(E) (5, \infty) (5, \infty)

Answer

Correct choice: (D)

正确答案：（D）

Solution

Answer (D): Because the statements of Alice, Bob, and Charlie are all incorrect, the actual distance $d$ satisfies $d<6$, $d>5$, and $d>4$. Hence the actual distance lies in the interval $(5,6)$.

答案（D）：由于 Alice、Bob 和 Charlie 的陈述都不正确，实际距离 $d$ 满足 $d<6$、$d>5$ 以及 $d>4$。因此实际距离位于区间 $(5,6)$。

Topics

LM.001 Logic puzzles