Question

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.

$\text{Bill, Amy, Celine}$

$\text{Amy, Bill, Celine}$

$\text{Celine, Amy, Bill}$

$\text{Celine, Bill, Amy}$

$\text{Amy, Celine, Bill}$

Solution:

If Bill were oldest, then statements I and II would both be true, so Bill is not oldest.

If Celine were oldest, then statements II and III would both be true, so Celine is not oldest.

Therefore Amy is oldest. Statements I and II are false, so statement III must be the single true statement. Thus Celine is not youngest, leaving Bill youngest.

The order is Amy, Celine, Bill.

Thus, E is the correct answer.

2004 AMC 8 Problem 13

Solution:

Problem 13 in Other Years