急求一题数学解答

raul911911

请教一道题，并说下解题思路：

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 statments must be true?

1. At least one of the homes was sold for more than $165,000

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

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

A. 1 only

B. 2 only

C. 3 only

D. 1 and 2

E. 1 and 3

答案是A, 我选的是E, 为什么不对？

Daphne619

题目的意思相当于15个数的平均数是150000,第8个数是130000,前7个数<=130000,后7个数>=130000,

极端情况可以是前14个数都是130000,最后一个是15*150000-14*130000.