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Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+

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by Max@Math Revolution » Mon Aug 20, 2018 2:34 am

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[Math Revolution GMAT math practice question]

Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), which of the following is an expression for z, in terms of x and y?

A. 2xy / ( x + y )
B. 2( x + y ) / ( x - y )
C. 2( x - y ) / ( x + y )
D. 2( x + y ) / xy
E. xy / ( x + y )
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by Brent@GMATPrepNow » Mon Aug 20, 2018 5:54 am
Aside: The GMAT doesn't expect test-takers to know the term harmonic mean.
If there were ever a question involving harmonic mean, the definition of the term would be included.
Here's the definition: https://www.investopedia.com/terms/h/ha ... verage.asp

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by Max@Math Revolution » Wed Aug 22, 2018 12:39 am
=>

1/z = (1/2)(1/x + 1/y) = (1/2)( (x+y)/xy ) = (x+y)/(2xy)
Thus, z = 2xy / ( x + y ).

Therefore, A is the answer.
Answer: A
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by Max@Math Revolution » Sun Aug 26, 2018 11:19 am
Brent@GMATPrepNow wrote:Aside: The GMAT doesn't expect test-takers to know the term harmonic mean.
If there were ever a question involving harmonic mean, the definition of the term would be included.
Here's the definition: https://www.investopedia.com/terms/h/ha ... verage.asp

Cheers,
Brent
We can solve this question without understanding the definition of a harmonic mean when we use the original condition 1/z = (1/2)(1/x + 1/y).
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