请教3道DS~~~

Rainbeauty

Of the students who eat in a certain cafeteria, each student either likes or dislikes lima beans and each student either likes or dislikes brussels sprouts. Of these students, 2/3 dislike lima beans; and of those who dislike lima beans, 3/5 also dislike brussels sprouts. How many of the students like brussels sprouts but dislike lima beans?
(1) 120 students eat in the cafeteria.
(2) 40 of the students like lima beans.
这题给的答案是D 很费解 也就是说A也可以算出来 但是 只知道有120个学生怎么能算出来呢？我选的是E。我是这样分析的：根据1）和题干给定的条件，得到80 dislike lima beans且这80个人中，48个人dislike Brussels Sprouts 但是这样给了条件2）也不能算出有多少人like brussels sprouts 也就算不出答案...
不知道这样想对不？？？
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How many different prime numbers are factors of the positive integer n ?
(1) Four different prime numbers are factors of 2n.
(2) Four different prime numbers are factors of n2.
这题选B 1）我知道的不充分 但是2）怎么就可以了？
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If p is a positive odd integer, what is the remainder when p is divided by 4 ?
(1) When p is divided by 8, the remainder is 5.
(2) p is the sum of the squares of two positive integers
这题选D 同样，问条件2）怎么就可以了？？？

carbonzju

1） D either sufficient  both 1/2 could give us the figure, together with percentage above.
2) B  n^2 contains two n.
3) because *2+*2 / 2 is available, and p is odd, then p could be divided by 2 too. Then p could be divided by 4

backlighting

How many of the students like brussels sprouts but dislike lima beans?
喜欢bs的人中有多少不喜欢lb
不需要求出喜欢bs的有多少人
得到80 dislike lima beans且这80个人中，48个人dislike Brussels Sprouts ，剩下32个人like bs。答案应该就是32，所以充分。
第二个条件给了40人like lb，占总人数三分之一，得到总人数120，剩下的和1的条件一样了
所以选D

Rainbeauty

B  n^2 contains two n...这个我知道 但是怎么就知道How many different prime numbers are factors of the positive integer n ?
这中间有什么关系呢？
麻烦你啦 谢谢~~~

backlighting

n^2的prime factors 个数 等于 n的prime factors 个数