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Last month 15 homes were sold in town X. the average sale

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

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New post 06 Apr 2008, 02:00
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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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Re: Mean and Median [#permalink]

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New post 06 Apr 2008, 03:16
sondenso wrote:
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
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Re: Mean and Median [#permalink]

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New post 06 Apr 2008, 03:18
I don't think that's a problem from OG or GMATPrep. Or is it?
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Re: Mean and Median [#permalink]

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New post 06 Apr 2008, 20:47
NightAlum wrote:
--> 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


Many thanks NightAlum,

That is exactly what I want to learn. This prob. was posted somewhere, but I did still not get the logic. Yeas, it is Gmatprep
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Re: Mean and Median [#permalink]

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New post 07 Apr 2008, 06:14
NightAlum wrote:
sondenso wrote:
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.
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Re: Mean and Median [#permalink]

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New post 07 Apr 2008, 08:07
I too think the answer should be I and III for that matter choice E.

If there are other strong reasons i would love to read abt them.
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Re: Mean and Median [#permalink]

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New post 07 Apr 2008, 18:21
Should be 'A'.

Total value of houses = 225,000

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.

Hence ans is A
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Re: Mean and Median [#permalink]

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New post 08 Apr 2008, 12:36
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.
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Re: Mean and Median [#permalink]

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New post 08 Apr 2008, 12:38
Ok, one thing i know, III is true.
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Re: Mean and Median [#permalink]

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New post 08 Apr 2008, 23:42
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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Re: Mean and Median   [#permalink] 08 Apr 2008, 23:42
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Last month 15 homes were sold in town X. the average sale

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