标题: 求教prep一题输血~~ [打印本页] 作者: hhonglgf 时间: 2010-7-18 12:31 标题: 求教prep一题输血~~ If m is a positive odd integer between 2 and 30, then m is divisible by how many different positive prime numbers? 1. m is not divisible by 3 2. m is not divisible by 5
answer is A. 为什么啊？我咋那么不理解啊 求救求救作者: IShallFly 时间: 2010-7-18 12:46
2<m<30 => {3,5,7,9,11,13,15,17,19,21,23,25,27,29}
(1) m excludes {3,6,9,12,15,18,21,24,27}={5,7,11,13,17,19,23,25,29} 全部只可以被自己和1除
(2) m excludes {5,10,15,20,25}={3,7,9,11,13,17,19,21,23,27,29} 21除了自己和1還可以被7除
=> A作者: naturalwater 时间: 2010-7-18 12:51
条件1，可以排除3，9，15＝3＊5，21＝3＊7，27，剩下的奇数除了25都是prime number，而25＝5＊5，所以 m is divisible by only one positive prime number，充分 条件2，可以排除5，15，25。但是不能排除21＝3＊7，所以剩下的数，除了21有2个prime number，其他只有一个，所以不充分
