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# Gmatprep Mean Median

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Manager
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Gmatprep Mean Median [#permalink]  02 Dec 2006, 19:24
Can someone pl. explain this
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Senior Manager
Joined: 23 May 2005
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i think u forgot to attach
_________________

Impossible is nothing

Manager
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Sorry, Fixed. Any takers
Manager
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interesting question [#permalink]  02 Dec 2006, 20:49
hi,

seems to me the answer could be A (I only).

II - it is not readily apparent to me why it must be true
III - even though median is 130K, all the lowest priced 8 homes could be priced 130K - so, no home need be less than 130K

I - "must be true" bcoz
mean is 150K - to see if all homes can be less than 165K, maximize price of lowest priced 8 homes to keep price of remaining highest priced 7 homes under or at 165K.
- since median is 130K, maximized price of lowest priced 8 homes is 130K each - hence their total is 1040K
- but total of highest priced 7 homes even if all of them are 165K each is 1155K only.
- so, max total of all 15 is 2195K which results in mean of less than 150K.
- i.e to get mean of 150K, the total has to be atleast 2250K.
- hence, atleast one home is above 165K.

plz let me know OA - if above is correct or wrong. thanks.
VP
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I just did it this morning. OA is A and I got it right. but I gotta say it is one of the toughest questions in the real exam environment.

1). to evaluate A.

Since it says at least one of them must be over 165000, you should try to make a case in which there is none over 165000. i.e. find the extreme case in which all are below this amount. try to make the highest price below it.

Case: make those lower than the median be the highest at 130000.
then get the sum of those higher than 130000:

150000*15 - 130000*8

then find the average of those above the median. divide the above by 7:
you get roughly 175000(calculate it yourself). so the average is even over 165000. then there must be at least one over 175000 among those above the median.

And this is an extreme case. so overall, there is at least one.

2). II is wrong.
because in the case above, u can have 8 homes at the media price. and the rest at the average price of about 175000.

3). wrong. in the above case, none is less than 130000.
Manager
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YIpe OA is A. Kicked my butt in the exam
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