请教Prep上的一道数学题

Last month 15 homes were sold in Town X.  The average (arithmetic mean) sale price ofthe homes was $150,000 and the median sale price was $130,000.  Which of the following statements must betrue?
I . At least one of the homes was sold for more than $165,000
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

答案：I only

请教大家本题思路，谢谢啦！