AMC 8 2004 Problem 13
AMC8 2004 年第 13 题
逻辑推理（跨域）★★★☆☆
Amy, Bill and Celine are friends with different ages. Exactly one of the following statements is true.
I. Bill is the oldest.
II. Amy is not the oldest.
III. Celine is not the youngest.
Rank the friends from the oldest to youngest.
Amy，Bill 和 Celine 是不同年龄的朋友。下面的 3 个论断中，只有一个是正确的。
I.Bill 年龄最大
II.Amy 不是最大的.
III.Celine 不是最小的.
请把这 3 个朋友按照年龄从大到小排列。
- A.
- B.
- C.
- D.
- E.
正确答案 · Correct Answer
E
解析 · Solution
Solution 1
If Bill is the oldest, then Amy is not the oldest, and both statements I and II are true, so statement I is not the true one.
If Amy is not the oldest, and we know Bill cannot be the oldest, then Celine is the oldest. This would mean she is not the youngest, and both statements II and III are true, so statement II is not the true one.
Therefore, statement III is the true statement, and both I and II are false. From this, Amy is the oldest, Celine is in the middle, and lastly Bill is the youngest. This order is .
Bashing through/ eliminating the options
The first statement tells us that Bill is the oldest. In the answer choices, you can see that the first answer is the only option where Bill is the oldest. Bill being the oldest is false (as Amy not being the oldest in the answer choice is also a true statement, but we cannot have two true statements per our conditions), so we can eliminate that answer. Now we know that Bill isn't the oldest and could be the youngest or the second oldest. Don't forget, we have TWO false statements and only one true statement. The second statement where Amy is not the oldest is another false statement. So now we know Amy is the oldest, followed by Celine whom is the second oldest, and Bill, whom is the youngest.Thus, the answer is .
--Angela--
(amyxin0316)
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