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。
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
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。
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。
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
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，
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.
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！
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.
这句话有点不懂 ，为什么由这个式子可以推出最小的质因子大于50啊
就是因为这个呀：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）
所以：In this case h(100)+1=2^50*50!+1, so the least prime factor would be greater than 50
第一题
for every positive even integer n, the fonction h(n) is defined to be the product of all the even integers from 2 to n, inclusive.
So we could write the following:
h(2)=2=2*1
h(4)=2*4=(2*1)*(2*2)=2^2*(1*2)
h(6)=2*4*6=(2*1)*(2*2)*(2*3)=2^3*(1*2*3)
h(8)=2*4*6*8=(2*1)*(2*2)*(2*3)*(2*4)=2^4*(1*2*3*4)
...
You can see if n=2m then
h(n)=2^m*(1*2*...*m)=2^m*m!
This is exactly what you need ot know to solve the problem.
At a minimum the smallest prime factor is 53.
For any factorial + 1 the smallest factor (apart from 1) is greater then any of the members of the factorial
2! + 1 = 3: smallest factor is 3
3! + 1 = 7: smallest factor is 7
4! + 1 = 25: smallest factor is 5
5! + 1 = 121: smallest factor is 11
根据这两个帖子，可以得到答案应该大于50，因此选最后一个了？谁能知道到底最小的质因数是什么呢？
另，中数是一个数列从大到小或从小到大的排序中间的数吗？我以为只是从小到大。
第三道排列组合题，还有个条件呢，two seating arrangments are considered differently only when the positions of the people are different relative to each other. 难道不用考虑吗？大家再发动脑筋，牛牛们看过来啊！
还有第二道，怎么得出1答案的呢？
第三道排列组合题，还有个条件呢，two seating arrangments are considered differently only when the positions of the people are different relative to each other. 难道不用考虑吗？大家再发动脑筋，牛牛们看过来啊！
还有第二道，怎么得出1答案的呢？
这个条件很重要，也就是说先排列P55,然后根据这个条件除以5
这个条件很重要，也就是说先排列P55,然后根据这个条件除以5
为什么要除5啊,还是不明白,偶弱啊,请详细讲讲.
那第二题的答案1是怎么求出来的?
为什么要除5啊,还是不明白,偶弱啊,请详细讲讲.
那第二题的答案1是怎么求出来的?
五个人坐一圈，考虑是否是不同分配的时候只考虑相互位置不考虑每个人实际坐哪个位置。比如
1
2 5
3 4
和
5
1 4
2 3
算作一种分配。
谁能再给解释一下这道题目啊？
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.
答 （1）
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
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
解答的思路是什么？
明白啦！
5个人，全排列是P55=5！
那么5个人的圆桌排列就是5！/5=4！
谁能再给解释一下这道题目啊？
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.
答 （1）
唉，自己解释吧，刚问过别人
一看到average,先把总数算出来，我们把后面一大串0先去掉，假设average15,median13，好吧
那么total=15(homes)*15(dollar)=225
又因为median=13，也就是说第8项=13
那么从小到大排的话前7个都不能大于第8项，也就是最大也只能是13，那么前8个的总合最大就是8*13=104，那么后7个最小的总合就是225-104=121
那么，后7个的均值就是121/7=17.28...
这样的话即使你后面7个一样的价，也都大于16.5，即使有一个比均值小甚至小于16.5，那么肯定对应的，至少会有一个比均值还大，所以至少会有一个大于16.5，也就是条件1满足
再看条件2
如果前8个都是13 后面7个总合是121，价钱都一样的话就是每个17多，完全可以没有在13-15之间的
再看3他没说要求15个房子价钱都不一样
thanks!顶
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。
这题不要被题目吓倒，其实非常简单，思路是想h(100) 能被谁整除，由于H100是2-100偶数相乘，所以一定是50以下质数的倍数，因为任何50以下质数2倍都在2－100偶数里面。
如果h(100) 可以整除所有50以下质数，则h(100)+1一定不能被50以下质数整除，因为对于50以下的任何质数P你都可以这样改写 h(100)+1=P*K+1, k为正整数，因为P*K可以被P整除，所以P*K+1被P除，一定余1，故不可能整除。
故E为正确答案
我对第二题还有点感觉..其他也还看不出来
第二题.中间数是130000,前面的7个数也可以同样是130000排除3
我上面的假设其实是一种极限法
如果真的如此.那么前七个130000一共=910000 加中间数130000一共1040000
2250000-1040000=1210000,就是说在前八个数已经取最大极限的情况下,后七个较大的数总和为1210000
那么这七个数的平均数为1210000/7
结果比170000还要大.当然就会有1了,
同时更排除了2
第一题，我用一种白吃解法猜，在考场上，你想，２x4x6x8....x１００中应该有很多很多的０吧，那么结果一定是ＸＸＸ０００００００００００００１，那么猜E就很容易了．
第二题，比较简单的思路是想因为有奇数个数，如果平均值是１５0000,而且有130000,那么就一定要有1７０000，所以Ａ成立．因为大于150000的数是一定要有的,才可以和130000抗衡啊．那么关键问题是是否一定要有比130000小的呢？那你就用极端方法，如果没有的话，可以成立吗？也就是最小的数是130000，从逻辑上看当然可以成立，那Ｃ就出现漏洞了，不用算了．
第三题，请ＬＺ记住圆形排列是直线排列少一种情况的排列，这个法则是可讯的．
不过，至于前面大牛们提到的法则，关于最大质因子的，我很想请较哪里有这个通则啊？
额。。这个帖子怎么没回应？
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