Last month 15 homes were sold in Town X. The average sale price of the homes was $150, 000 and the median sale price was $130,000. Which of the following 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
OA: A
I chose A correctly but I felt like I guessed. I knew it was not II and III because you can have a bunch of homes selling for 130K, and one home for a really high price, over 165K (hence I). Is this the correct train of thought? I just was not sure how to quickly ensure that there had to be a home that was above 165,000