请教prep数学，想不明白

sjmdlycs

Last month 15 homes were sold in Town X. The arithmetic mean sale price of the homes is $150,000 and the median price was $130,000. Which of the following statements must be true?



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 oe of the homes was sold for less than $130,000.



Answer choices

I only

II only

III only

I and II

I and III



答案：A
？？

sjmdlycs

恩恩，想明白了，好绕啊~~~

msufcufou

平均数15，有15家。总数是225。中数13，举一种情况，如果其他7个都是13，那么就有104了，如果要保证平均数在15，那么剩下7个要有17多才行。所以一一定对，其他两个不一定。
第二点，上面的情况就没有。
第三点，上面的情况也没有。

jingjane222

二三明显不对
一的话
mediam是130000.说明8个最便宜的房子加起来最多就是130000乘8
mean是150000,如果另外7个房子要把mean拉到150000,（他们平均价钱-150000）乘7 要等于（150000-130000）乘8..所以他们的平均价钱-150000=22857.XXX最贵的房子肯定大于等于这个数,就是150000+22857=172857.
所以至少有一个大于165000.

tianya

同问一下