AMC10 2018 A

AMC10 2018 A · Q5

AMC10 2018 A · Q5. It mainly tests Linear inequalities, 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 $d$?

Alice、Bob 和 Charlie 在徒步时想知道最近的城镇有多远。Alice 说：“我们至少有 6 英里远。”Bob 回答：“我们最多 5 英里远。”Charlie 然后说：“实际上最近的城镇最多 4 英里远。”结果三人的陈述都不正确。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

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).

因为 Alice、Bob 和 Charlie 的陈述都不正确，实际距离 $d$ 满足 $d < 6$、$d > 5$ 和 $d > 4$。因此实际距离在区间 $(5, 6)$ 内。

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