AMC 8 2001 Problem 20

AMC8 2001 年第 20 题

逻辑推理（跨域）★★★☆☆

Kaleana shows her test score to Quay, Marty and Shana, but the others keep theirs hidden. Quay thinks, "At least two of us have the same score." Marty thinks, "I didn't get the lowest score." Shana thinks, "I didn't get the highest score." List the scores from lowest to highest for Marty (M), Quay (Q) and Shana (S).

Kaleana 向 Quay，Marty 和 Shana 展示了自己的考试成绩，但其他三人都隐藏了自己的成绩。 Quay 认为：“我们中至少有两个人有相同的分数。”Marty 认为：“我没有得到最低的分数。” Shana 认为： “我没有得到最高的分数。”请按从最低到最高的次序将 Marty（M）、Quay（Q）和 Shana（S）的分数列出来。

A. $\text{S,Q,M}$
B. $\text{Q,M,S}$
C. $\text{Q,S,M}$
D. $\text{M,S,Q}$
E. $\text{S,M,Q}$

正确答案 · Correct Answer

解析 · Solution

Solution 1

Since the only other score Quay knows is Kaleana's, and he knows that two of them have the same score, Quay and Kaleana must have the same score, and K=Q. Marty knows that he didn't get the lowest score, and the only other score he knows is Kaleana's, so Marty must know that Kaleana must have a lower score than him, and M>K. Finally, Shana knows that she didn't get the highest score, and the only other score she knows is Kaleana's, so Shana must know that Kaleana must have a higher score than her, and S<K. Putting these together and substituting

Q

for

K

, we have S<Q<M, and from least to greatest this is

\text{S, Q, M}

, therefore the answer is

\text{A}

继续练习

免费刷 2001 整卷 →