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# Last month 15 homes were sold in town X. The average

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Manager
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Last month 15 homes were sold in town X. The average [#permalink]  30 Jan 2006, 22:42
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Last month 15 homes were sold in town X. The average (arithmetic mean) sale price of the homes was \$150,000 and the median sale 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

A. I only
B. II only
C. III only
D. I and II
E. I and III
Manager
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lhotseface wrote:
E.
I and III.

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VP
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15 numbers....middle number is 130000. Numbers have to be greater than less than the median for 130000 to be the median.

Average could be 150000 but still there can't be any number b/w 130000 and 150000 if the smaller numbers below the median are really LOW and the larger numbers above the median are really HIGH.
Intern
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E. I & III

Median - Middle Number
Mean - Average

I is true because...

15 x 150,000 = 2,250,000
2,250,000 - (130,000)(8) = 1,210,000

Assume that the 7 numbers below the median are all equal to the median (the highest number they can get), which is 130,000.

1,210,000/7 = 172,857.142857 <- The average of the 7 houses above the median, which indicates at least 1 house will have the price of 172,857.142857.

II is not true because we may have real small numbers and real big numbers not in that interval.

III is true because there are numbers above or below the Median.
CEO
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Almost sure for A.

Will explain if correct.
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Manager
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If the first eight houses were all sold at the price of \$130,000, the median will be this \$130,000.

It is A
VP
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celiaXDN wrote:
If the first eight houses were all sold at the price of \$130,000, the median will be this \$130,000.

It is A

That's the perfect reasoning! That's why III is not necessarily true. So only A must be true.
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Manager
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good question

ffgmat wats the source ?????????
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Intern
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Hmm.. I actually did my reasonings correctly for Part I but failed at Part III. My reasoning for Part I contradicts Part III xD

Manager
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The answer is A. (from GMATPrep)

Thanks for explanation.
I am thinking this kind of questions will show in the test date? So difficult.
Manager
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really a tuff one.....was this in gmatprep test or the DS qestion excercise ?
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# Last month 15 homes were sold in town X. The average

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