请教数学 PREP Q183

WesternCder

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？

piacia

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.

WesternCder

明白了，多谢！

zm_patrickS

对啊对啊 刚刚没想到 25不是prime