Median means 7 prices were above the median and 7 below the median.

I. At least one of the homes was sold for more than $165,000.Total sales = 150K * 15 = 2250K

Lets say all the seven homes above the median were sold for 165K

Hence

165K * 7 + 130K * 8 = 1159K + 1040K = 2199K - Not high enough. Hence one home MUST have been above 165K

A, D and E left.

II. At least one of the homes was sold for more than $130,000 and less than $150,000.This is not true you can have the mean 150K even when 7 numbers are below 130K and 7 numbers are above 150K. I will not solve this scenario since this is intuitive.

III. At least one of the homes was sold for less than $130,000.This is not true since we can have 8 numbers at 130K and 7 numbers above 130K and have the mean 150K. I will not solve this scenario since this is intuitive.

D and E out. A remains.

CDM770234 wrote:

Can someone help me solve the following GMAT Prep Test 1 question:

23. Last month 15 homes were sold in town X. The average (Arithmetic Mean) price 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.

The answer choices are:

A. I only

B. II only

C. III only

D. I and II

E. I & III

I do not agree/understand the official answer!