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请教数学 PREP Q183

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楼主
发表于 2010-12-14 04:20:01 | 只看该作者 回帖奖励 |倒序浏览 |阅读模式
If m is a positive oddinteger between 2 and 30, then m is divisible by how many different positiveprime numbers?

(1) m is not divisible by 3.
(2) m is not divisible by 5.
【答案】A
为什么答案是A呢?





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沙发
发表于 2010-12-14 06:12:04 | 只看该作者
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27

(1) m is not divisible by 3.
5, 7, 11, 13, 17, 19, 23, 25
Each one only has one prime number as its factor.  So condition 1 is sufficient.

(2) m is not divisible by 5.
3, 7, 9, 11, 13, 17, 19, 21, 23, 27
21= 3 * 7.  So 21 has two prime numbers as factors while the rest of the numbers only have one prime number as their factor. So condition 2 is not sufficient.
板凳
 楼主| 发表于 2010-12-14 08:00:46 | 只看该作者
3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27

(1) m is not divisible by 3.
5, 7, 11, 13, 17, 19, 23, 25
Each one only has one prime number as its factor.  So condition 1 is sufficient.

(2) m is not divisible by 5.
3, 7, 9, 11, 13, 17, 19, 21, 23, 27



21= 3 * 7.  So 21 has two prime numbers as factors while the rest of the numbers only have one prime number as their factor. So condition 2 is not sufficient.
-- by 会员 sdcar2010 (2010/12/14 6:12:04)



明白了,多谢!
地板
发表于 2010-12-14 08:09:54 | 只看该作者
对啊对啊 刚刚没想到 25不是prime
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