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gmatprep_mean_median_home price

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gmatprep_mean_median_home price [#permalink] New post 24 Mar 2009, 10:25
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Re: gmatprep_mean_median_home price [#permalink] New post 24 Mar 2009, 11:17
I think its A

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.
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GMATprep practice question:mean_median:home price [#permalink] New post 24 Mar 2009, 13:36
I. -> It's not clear why it is must be true that at least one of the homes was sold for more than $165,000. It's not necessary. It can be just $160k or $155K.

Can anybody please explain this/solve this problem differently?
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Re: gmatprep_mean_median_home price [#permalink] New post 24 Mar 2009, 14:04
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   [#permalink] 24 Mar 2009, 14:04
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