gmat prep question

yvonne12 wrote:Last month 15 homes were sold in Town X. The average sale price of the homes was 150k and the median sale price was 130k which of the following statements must be true?

I. at least on of the homes was sold for more tha 165k

II. '' '' was sold for more than 130k and less than 150k

III. " " was sold for less than 130k

please explain how I can arrive to the answer or how to approach this question.

ok this is going to be a difficult q to xplain .. the key word is what must be true ..

the median is 130k so when arranged in an asecneding order( according to prices) the 8th house is worth 130k and the houses 1-7 are less than or equal to 130k.. and the houses 8-15 are more than 130k.. now also given that the mean is 150k ..

so consider a situation where houses form 1-7 have a price equal to 130k ( which is the maximum value they can have ) then to make the mean equal to 150k then atleast one house has to be defnitely greater than 165k.. this situaiton wuld also hold true if the prices of houses(1-7) are less than 130k .. so A has to be true

now if u consider the same scenario u wuld see that the other two coinditions dosent have to be true .. so the answer is only 1 is true ..

thank you , I do understand