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

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Director
Joined: 03 Sep 2006
Posts: 871
Last month 15 homes were sold in Town X. The average ( [#permalink]

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23 Jun 2007, 02:47
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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
Director
Joined: 14 Jan 2007
Posts: 774

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23 Jun 2007, 05:11
Should be 'A'.

Average is 150k. Total value = 15*150k = 2250k
The median is 130k.
To evaluate the stmt I:
Eight homes are with values 130k each. The remaining 7 will be of total value 1210k. This means the costliest home will have the value at least of 1210/7 = 170k (approx).
Hence the statement I is true.

II and III are not necessarily true.[/b]
Director
Joined: 03 Sep 2006
Posts: 871

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23 Jun 2007, 06:01
vshaunak@gmail.com wrote:
Should be 'A'.

Average is 150k. Total value = 15*150k = 2250k
The median is 130k.
To evaluate the stmt I:
Eight homes are with values 130k each. The remaining 7 will be of total value 1210k. This means the costliest home will have the value at least of 1210/7 = 170k (approx).
Hence the statement I is true.

II and III are not necessarily true.[/b]

Thanks very good, fast and logical explanation.
23 Jun 2007, 06:01
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