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# gmatprep_mean_median_home price

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Manager
Joined: 05 Jan 2009
Posts: 73

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24 Mar 2009, 11:25
Attachment:
mean_median.doc [46 KiB]

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Manager
Joined: 19 Oct 2008
Posts: 87

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24 Mar 2009, 12:17
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.
Manager
Joined: 05 Jan 2009
Posts: 73

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24 Mar 2009, 14:36
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?
Manager
Joined: 19 Oct 2008
Posts: 87

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24 Mar 2009, 15:04
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.

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This is not a quality discussion. It has been retired.

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To review the GMAT Club's Forums Posting Guidelines, please follow these links: Quantitative | Verbal Please note - we may remove posts that do not follow our posting guidelines. Thank you.
Re: gmatprep_mean_median_home price   [#permalink] 24 Mar 2009, 15:04
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# gmatprep_mean_median_home price

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