15 homes were sold

[thc013]

I would like some help in proving how I (choice A) is true.

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 for 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

[RonPurewal]

http://www.manhattangmat.com/forums/las ... t4373.html

note: this is one of a few gmatprep problems requiring an amount of work that can only be called "ridiculous". there aren't many - most gmat quant problems have concise, if arcane, solutions - but this is certainly one of them.