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# can someone can please explain harmonic mean

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Manager
Joined: 17 May 2007
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can someone can please explain harmonic mean [#permalink]  23 Dec 2007, 16:50
i've tried searching the net but couldn't find anything useful

can someone please explain what is harmonic mean and an example or two?
CEO
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Re: can someone can please explain harmonic mean [#permalink]  23 Dec 2007, 17:01
gowani wrote:
i've tried searching the net but couldn't find anything useful

can someone please explain what is harmonic mean and an example or two?

I know this from the CFA Level 1 curriculum. harmonic mean is out of gmat scope.

its a more accurate measure of avgs.
harmonic mean < arithmetic mean

http://www.mathwords.com/h/harmonic_mean.htm
Manager
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Re: can someone can please explain harmonic mean [#permalink]  23 Dec 2007, 17:02
gowani wrote:
i've tried searching the net but couldn't find anything useful

can someone please explain what is harmonic mean and an example or two?

http://en.wikipedia.org/wiki/Harmonic_mean

An important result: AM>GM>HM unless the numbers are all equal

example:
You may have solved the problems without knowing that you are using HM.
example: Mr X travels 200 miles to city A, 50 miles/hour. On his return, his speed is 40 miles/hr.
What is the average speed?
Answer: HM of 50 and 40.

I havent seen Geometric mean in GMAT. So, I guess HM is out of the question. But it is worth knowing.
Manager
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below is a problem from gmat prep test #2. Does this not require harmonic mean? I have searched the forum and know how to now solve it.

A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?
Intern
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Gowani - How did you solve this problem quickly?
Manager
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A certain car averages 25 miles per gallon of gasoline when driven in the city and 40 miles per gallon when driven on the highway. According to these rates, which of the following is closest to the number of miles per gallon that the car averages when it is driven 10 miles in the city and then 50 miles on the highway?

City: 10 / 25 = .4
Highway: 50 / 40 = 1.25
Total Gallons: .4 + 1.25 = 1.65
Total Miles 10 + 50 = 60

Total Miles / Total Gallons: 60 / 1.65 = 37.36

hope my calculations are correct
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