AMC8每日一题(2001年真题#03)

　　多年来，AMC还扮演为美国培育世界数学奥林匹克(IMO)选手的重 责大任。AMC的研究人员透过AMC 8、AMC 10、AMC 12、AIME一系列测验，找出绩优生参加美国数学奥林匹克(USAMO)，再从全美数十州筛选出24至30位精英，成立数学奥林匹克夏令营 (MOSP)。经过AMC的密集训练，事实证明，以1990年到2000年这十年为例，有九年由AMC集训的美国队赢得奖牌。AMC不但是美 国顶尖数学人才的人才库，更为学校提供了解申请入学者在数学科目上的学习成就与表现评估。AMC成功地为许多学生因测验成绩优良而进入理想学校。藉由设计 严谨的试题，达到激发应试者解决问题的能力，培养对数学的兴趣。试题由简至难兼具，使任何程度的学生都能感受到挑战，还可以筛选出特有天赋者。为了方便同学们的AMC备考，课窝考试网小编为大家收集整理了AMC课程历年真题练习，供大家学习参考，希望能为同学们的考试提供帮助。

2001 AMC 8 竞赛试题/第03题

Problem

Granny Smith has $63. Elberta has $2 more than Anjou and Anjou has one-third as much as Granny Smith. How many dollars does Elberta have?

Solution

Since Anjou has  the amount of money as Granny Smith and Granny Smith has $, Anjou has  dollars. Elberta has $more than this, so she has $, or .

2001 AMC 8 竞赛试题/第04题

Problem

The digits 1, 2, 3, 4 and 9 are each used once to form the smallest possible even five-digit number. The digit in the tens place is

Solution

Since the number is even, the last digit must be  or . To make the smallest possible number, the ten-thousands digit must be as small as possible, so the ten-thousands digit is . Simillarly, the thousands digit has second priority, so it must also be as small as possible once the ten-thousands digit is decided, so the thousands digit is . Similarly, the hundreds digit needs to be the next smallest number, so it is . However, for the tens digit, we can't use , since we already used  and the number must be even, so the units digit must be and the tens digit is  (The number is .)

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