请教一道OG上的题目

goodssb

一道Data Sufficiency的题目,原题是这样的:

If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors.

(2) The difference of any two distinct positive factors of n is odd.

答案是B.

对于1我没有问题,是not sufficient,对2有疑问.答案的解释是这样的: if n>2 and n is odd, then 1 and n are factors of n and their difference is even. If n>2 and n is even, then 2 and n are factors of n and their difference is even. Thus, no integer greater than 2 satisfies this statement.

可是以6为例,2,3都是factors. 他们之间的差也是odd啊.

怎么理解这道题目呢.谢谢!

everhappyin

是不是少了一个n是“偶数”条件？

第一次打错了，不好意思

[此贴子已经被作者于2006-7-28 16:25:25编辑过]

caterpillarcn

以下是引用goodssb在2006-7-28 14:04:00的发言：

一道Data Sufficiency的题目,原题是这样的:

If the integer n is greater than 1, is n equal to 2?

(1) n has exactly two positive factors.

(2) The difference of any two distinct positive factors of n is odd.

答案是B.

对于1我没有问题,是not sufficient,对2有疑问.答案的解释是这样的: if n>2 and n is odd, then 1 and n are factors of n and their difference is even. If n>2 and n is even, then 2 and n are factors of n and their difference is even. Thus, no integer greater than 2 satisfies this statement.

可是以6为例,2,3都是factors. 他们之间的差也是odd啊.

怎么理解这道题目呢.谢谢!

不要忘记（2） 是讲any two positive distinct factors。 6肯定不符合：6-2=4 or 3-1=2
所有大于2的even numbers都不可以，所有odd numbers也不可以，所以只能是2了。楼主可以代入。

everhappyin

明白了，谢谢：）

goodssb

明白了,谢谢