新模考数学题-求助

大家看看这道题怎么做?完全没有思路的说

For every positive even integer n, the function h(n) is defined to be the product of all the even integers form 2 to n, inclusive, if p is the smallest prime factor of h(100)+1, then p is

a) between 2 and 10

b) between 10 and 20

c) between 20 and 30

d) between 30 and 40

e) greater than 40

一点思路都没有，盼思路讲解。

还有一道题，觉得答案给错了似的

Last month 15 homes were sold in town x, the average sale price of the homes was $150000 and the median sale price was $130000, which of the following statement must be true.

1) at least one of the homes was sold for more than $165000

2) at least one of the homes was sold for more than $130000 and less than $150000

3) at least one of the homes was sold for less than $130000.

a) only 1

b) only 2

c) only 3

d) 1 and 2

e) 1 and 3

我觉得既然中数是130000，那一定有比它小的数，选c。但答案是a，不知道怎么得到的？

还有一道排列组合的题

At a dinner party, 5 people are to be seated around a circular table, two seating arrangments are considered differently only when the positions of the people are different relative to each other. what is the total number of different possible seating arrangments for the group.

a) 5

b)10

c)24

d) 32

e) 120

题目理解有问题，圆桌是不是要考虑？答案24 ，看样子是2P33 *P22, 这样的话跟圆桌没什么关系？

好难～！

顶一下。

1。没思路。我蒙E

2.C肯定不对，因为平均数是150000，中数及中数以下都为130000也可以。

我google到的：

1.可参考此链接

http://www.gmatclub.com/phpbb/viewtopic.php?p=123297&sid=9b0459f3d5af2b9bbd67f3bef3652976

Kate, Demi, Madona, Sharon, Britney and Nicole decided to lunch together in a restaurant. The waiter led them to a round table with six chairs.

How many different ways can they seat?> >

> >

Answer

There are 120 different possible seating arrangments.

Note that on a round table ABCDEF and BCDEFA is the same.

The first person can sit on any one of the seats. Now, for the second person there are 5 options, for the third person there are 4 options, for the forth person there are 3 options, for the fifth person there are 2 options and for the last person there is just one option.

Thus, total different possible seating arrangements are
= 5 * 4 * 3 * 2 * 1
= 120> >

圆桌显然要考虑 如果 A B C D E 站一排的话 就是P5/5 =120

小NN告诉我说 连起来气候就是 （P5/5）/5=24

我正想呢 大家发动一下

p是最小的质因子？那个讨论的链接怎么成了最大的质因子？请确认。

这个例子比较清楚，那么本题就应该是C(4,1)C(3,1)C(2,1)C(1,1)=24

明天就考，今天上来连续看到做不出来的题，

以下是引用endless_tao在2005-12-27 3:53:00的发言：

p是最小的质因子？那个讨论的链接怎么成了最大的质因子？请确认。

我觉得这个解释比较合理：

If n=2m, then h(n)=2^m*m!

Since the first term includes m!, all natural numbers from 2 to m would be a factor of h(n)=h(2m) and would not be a factor of h(n)+1. In other words any factor that h(n)+1 would have would be greater than m. （也就是说必然因子比m大）

In this case h(100)+1=2^50*50!+1, so the least prime factor would be greater than 50. So I would choose 5.

以下是引用julia_ggw在2005-12-27 4:28:00的发言：

这个例子比较清楚，那么本题就应该是C(4,1)C(3,1)C(2,1)C(1,1)=24

明天就考，今天上来连续看到做不出来的题，

pat,pat

祝考试顺利！