求助一道PREP数学题

tinaren9081

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 $165,000.

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

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

(A) I only
(B) II only
(C) III only
(D) I and II
(E) I and III

在《完全详解》里也找到了，但没解答，NN们现身下吧

（答案选A）

tinaren9081

顶顶顶~~~

tinaren9081

I. 题目说最少一个home的售价超过165,000，如果是错误的，我们要找到一种情况是所有的home售价都低于165,000，也就是home售价最高值要小于165,000。

现在需要让最高值尽可能小，题中给出平均数是150,000，中位数是130,000，按数值的大小排好，可以使前8个数都为130,000（中位数是第8个），现在后7个数的总和为150,000×15-130,000×8=1,210,000，最小的数只可能为其平均值=1,210,000÷7=172,857.14（否则只要有一个数小于172,857.14，就必定会有另一个数大于172,857.14）。得出的最大数的最小可能值为172,857.14>165,000，选项I正确。

可以举出一种home prices的可能取值：
前14个数均为130,000，第15个数为430,000。

选项II、III均不正确。

-- by 会员 紫苏月白 (2011/7/21 14:01:26)

谢谢！！！