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II. Since the median $130k is less than average $150k, there has to be at least one house above median. However, they can all be above $150k and still average $150k. Consider a situation where first seven homes were very cheap and last seven were very expensive with $130 being the median 8th house. III. The price of the first eight houses could be $130 (being the lowest price) and average could still be $150k.
I. I am not sure about this one, but since II and III must not be true and there is no choice for none, I'll pick A.
Okay, lets try to prove that we can have no house sold for more than $165k. To do this the we should try to keep the prices as evenly distributed as possible and as close to $165k as possible. We know that total price of all homes is 150*15=$2,250k. (average*number of homes)
Lets consider first eight houses. To be as close to $165k we will use $130k which is the maximum possible value for the first 8 houses since median is $130k. The price of first seven houses cannot be more than the median. So the price of first 8 houses is 8*130=$1,040k.
Now consider houses 9 to 15. To ensure that no house is above $165k, we use the maximum possible value of $165k. So the value of seven houses 9 to 15 is 165*7=$1,155.
The maxium possible value of all homes is 1,040 + 1,155 = $2,195k which is less than $2,250.
Therefore, there has to be at least one home sold for more than $165k. There is no possible way to do it when average for 15 homes is $150k and median is $130k.
Re: gmatprep_mean_median_home price
24 Mar 2009, 15:04