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Last month 15 homes were sold in Town x. The average sale

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Manager
Joined: 22 Jun 2008
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Schools: Darden School of Business (Class of 2012)
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Last month 15 homes were sold in Town x. The average sale [#permalink]  08 Sep 2008, 11:25
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Last month 15 homes were sold in Town x. The average sale price of the homes was \$150,000, and the median price was \$130,000. WHich of the following statements must be true?

I. at least one of the homes was sold for more than \$165,000
II. at least one of the homes was sold for more than \$130,000 and less than \$150,000
III. At least one of the homes was sold for less than \$130,000

I know that the median is the 8th number.
I imagine 7 numbers for 130k each and 7 numbers for 165k each plus the middle one gives less than the total, so I. is true and III. is false.
But can not imagine how to make a good shortcut to know whether II is false. Tks guys for your help
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Joined: 07 Nov 2007
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Location: New York
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Re: Shortcut for a DS (must be true) of statistics? [#permalink]  08 Sep 2008, 11:38
lordw wrote:
Last month 15 homes were sold in Town x. The average sale price of the homes was \$150,000, and the median price was \$130,000. WHich of the following statements must be true?

I. at least one of the homes was sold for more than \$165,000
II. at least one of the homes was sold for more than \$130,000 and less than \$150,000
III. At least one of the homes was sold for less than \$130,000

I know that the median is the 8th number.
I imagine 7 numbers for 130k each and 7 numbers for 165k each plus the middle one gives less than the total, so I. is true and III. is false.
But can not imagine how to make a good shortcut to know whether II is false. Tks guys for your help

assume they are in ascending order.
x1 x2 x3 x4 x5 x6 x7 130k x9 x10 x11 x12 x13 x14 x15

For I we need to find the least value of x9
this is possible when x1=...=x7=130k
and x9=x10..=x15 = y

8*130+ y*7=15*150
y= 1210/7 ~ 171.5K

so minimum value of x9 must be 171.5k which is > 165k

this case automatically elimantes II and III.
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Manager
Joined: 09 Jul 2007
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Re: Shortcut for a DS (must be true) of statistics? [#permalink]  08 Sep 2008, 22:04
Agreed and nice approach..only 1 is correct.
Re: Shortcut for a DS (must be true) of statistics?   [#permalink] 08 Sep 2008, 22:04
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