Problem Solving

Last month 15 homes were sold in Town X. The average sale price of the homes was $150000 and the median sale price was $130000.Which of the foll must be true??

I. At least one of the homes was sold for more than $165000

II.At least one of the homes was sold for more than 130000 and less than 150000

III. At least one of the homes was sold for less than 130000


I only

II only

III only

I and II

I and III

I'd say it's A - I Only. From the question, we know that the sum of the 15 prices must be $2,250,000 and that 8th price (when prices arranged from lowest to highest) must be $130,000. So, the first 7 prices must all be less than or equal to $130,000.

Statement I - the most money we can get out of the first 8 houses is 8x130,000 = 1,040,000. For the average to be 150,000, we must get $1,210,000 out of the last 7 houses. If none of the last 7 houses sold for over 165,000, the most we could get out of that group would be 7x165,000 = $1,155,000, which would not be sufficient for the average to be $150K. Therefore, statement I must be true.

Statement II - again assume the first 8 houses all sold for $130,000. Then the last 7 must get us $1,210,000. For this to occur the average of the last 7 must be about $172,857. So, we could acheive the required mean and average with 8 houses at $130K and 7 houses at about $172,857. Therefore, statement II is not necessarily true.

Statement III - As the previous example illustrates, the first 8 houses could all sell for $130K and the median would still be $130K, so this is not necessarily true.

i agree A should be the answer. my reasoning is the same as mscling52

The answer is A!! Thanks guys