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

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Last month 15 homes were sold in Town X. The average [#permalink]

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23 Jul 2005, 02:59
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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

1. I only
2. II only
3. III only
4. I and II
5. I and III
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23 Jul 2005, 07:11
BG wrote:
think that 5) makes sense

I thought III was clearly wrong because the first eight low cost homes could be sold for 130000 and the the high 7 could be sold for any different values to match the mean.
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Fear Mediocrity, Respect Ignorance

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24 Jul 2005, 12:50
I think it is A, 1 only.

Pick the numbers:
Begin with III: At least one of the homes was sold for less than $130,000 Suppose, first 8 houses were sold for$130k:
8*130000+7X=2250000
X=~172000 (the average price of other 7 houses). That means, that it is possible, that no house was sold for less than 130000. Delete III.

Now II: At least one of the homes was sold for more than $130,000 and less than$150,000

Use the previous example: 8 houses were sold for 130000, and remaining houses were sold for 172000. Delete II.

As for III: At least one of the homes was sold for more than \$165,000
Again, suppose we sold first 8 houses for 130K(the greatest possible).
8*130k+7X=2250 where X=172k. From this we can conclude that at least 1 house would cost 172k or more. That satisfies our "<165k" term

Hope, somebody has more compact explanation
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