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Last month 15 homes were sold in town X. the average sale [#permalink]

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06 Apr 2008, 02:00

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Last month 15 homes were sold in town X. the average sale price of he homes was 150000$ and the median sale price was 130000$. Which of the following statements must be true?

I. At least one of the homes was sold for more than 165000 II. At least one of the homes was sold for more than 130000 and less than 150000 III. At least one of the homes was sold for less than 130000

I only II only III only I and II I and III
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Last month 15 homes were sold in town X. the average sale price of he homes was 150000$ and the median sale price was 130000$. Which of the following statements must be true?

I. At least one of the homes was sold for more than 165000 II. At least one of the homes was sold for more than 130000 and less than 150000 III. At least one of the homes was sold for less than 130000

I only II only III only I and II I and III

Answer A (I think) I. We are looking to prove that no home was sold for more than 165K otherwise the statement holds true. Bearing in mind that mean = 150K --> 8/15*(150K-130K) = 7/15 (X-150K); find x to equal 172.9. Yes, at least one of the homes sold for more than 165K II. From I: Can be either way III. Can be either way

Last month 15 homes were sold in town X. the average sale price of he homes was 150000$ and the median sale price was 130000$. Which of the following statements must be true?

I. At least one of the homes was sold for more than 165000 II. At least one of the homes was sold for more than 130000 and less than 150000 III. At least one of the homes was sold for less than 130000

I only II only III only I and II I and III

Answer A (I think) I. We are looking to prove that no home was sold for more than 165K otherwise the statement holds true. Bearing in mind that mean = 150K --> 8/15*(150K-130K) = 7/15 (X-150K); find x to equal 172.9. Yes, at least one of the homes sold for more than 165K II. From I: Can be either way III. Can be either way

I don't think your answer is correct. My answer is I and III.

III is correct, obviously. Because the definition of median is the "middle" value in the list of numbers. Given that median is 130000, there should be 7 numbers which are smaller than 130000. Thus statement 3 is correct.

The median (8th term) is 130,000 Let's assume first 8 houses will cost 130,000 each. and remaining 7 houses will cost 121,000/7 = 170,000 approx. each. In this case, ii and iii will not hold good.

My answer is C. Only III is good here. I think the value $165,000 is arbitrary here. One must be below 130000 if the median is 130000. That is for sure.

I agree with vshaunak@gmail.com and came across the answer A in the same way. Set the first 8 houses equal to 130000 and you will see that II and III don't hold.
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