数学Prep 难题请教？谢谢大伙了！

JohnDong · 发表于 2009-12-6 11:28:21

For a certain set of n numbers , when n>1 , is the average (arithmetic mean) equal to the median?
(不好意思，是我吧题目弄错了，原来的mean，应该改成median)
(1) if the n numbers in the set are listed in increasing order , then the difference between any pair of successive numbers in the set is 2.

(2) The range of the n numbers in the set is 2(n-1)

Last month 15 homes were sold in town x . The average ( arithmetic mean ) sale price of the homes was $150,000 and the median sale price was $130,000 . Which of the following statements must be true ?

I. At least one of the homes was sold for more than $1650,00 .

II. At least one of the homes was sold for more than $130,000 and less than $150,000 .

III. At least one of the homes was sold for less than $130,000 .

I only

II only

III only

I and II

I and III

At dinner party , 5 people were to be seated around a circular table . Two arrangements are considered different only when the positions of the people are different relative to each other . What is the total number of different possible seating arrangements for the group ?

5

10

24

32

120

xiaoyao750 · 发表于 2009-12-6 11:33:07

kray003 · 发表于 2009-12-6 12:05:27

EEC?
第一题是不是写错了

JohnDong · 发表于 2009-12-6 12:31:33

。

-- by 会员 xiaoyao750 (2009/12/6 11:33:07)

A

A

C

JohnDong · 发表于 2009-12-6 12:32:38

EEC?
第一题是不是写错了

-- by 会员 kray003 (2009/12/6 12:05:27)

请问，第三题，C是如何计算的？

kray003 · 发表于 2009-12-6 12:46:42

4*3*2

JohnDong · 发表于 2009-12-6 13:44:45

4*3*2

-- by 会员 kray003 (2009/12/6 12:46:42)

能解释一下么？对排列组合中的这种情况已经不太记得是怎么回事了？

谢谢！

a10285 · 发表于 2009-12-6 14:19:18

是这么来的：
（1）首先五个人如果是一字排开，则总数是P(5,5)
（2）因为是环形排列所以上下各减一，则总数为P(4,4)=4*3*2*1

环形排列与直线排列相比，就相当于少了一个元素。所以可以先求直线排列，再求圆形排列。

这类题的通解有NN总结了~
http://www.chasedream.com/show.aspx?id=101&cid=40

ziyefeishuan · 发表于 2009-12-6 14:20:32

5全排列.考虑到是圆桌子,所以只要相对位置不一样就可以,序数不同没关系以要除以5. 我的理解..

a10285 · 发表于 2009-12-6 14:25:38

同意LS，ls的是第二种正解~~

第一题如果题目没错的话，应该是D吧，
因为不管任何时候都有the average (arithmetic mean) equal to the mean
这是不是GMAC玩的文字游戏？？
请指正~

数学Prep 难题请教？谢谢大伙了！

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