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

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New post 20 Aug 2018, 03:40
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[Math Revolution GMAT math practice question]

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

\(A. \frac{2xy}{( x + y )}\)
\(B. \frac{2( x + y )}{( x – y )}\)
\(C. \frac{2( x – y )}{( x + y )}\)
\(D. \frac{2( x + y )}{xy}\)
\(E. \frac{xy}{( x + y )}\)

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Re: Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), wh  [#permalink]

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New post 21 Aug 2018, 10:36
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jhueglin wrote:
Afc0892 wrote:
Harmonic Mean is given by = \(\frac{N (No. of elements)}{{1/a_1 + 1/a_2 +1/a_3...}}\)
Z = \(\frac{2}{{1/x +1/y}}\)
Solving gives Z = \(\frac{2xy}{{x+y}}\)
A is the answer.



can you please outline the last step?


Sure,

Z = \(\frac{{2}}{{1/x +1/y}}\)
taking LCM in the denominator gives

Z = \(\frac{{2}}{{(x+y)/xy}}\)

Z = 2*\(\frac{xy}{{x+y}}\)

Z = \(\frac{2xy}{{x+y}}\)

Hope it's clear.
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New post 20 Aug 2018, 03:51
Harmonic Mean is given by = \(\frac{N (No. of elements)}{{1/a_1 + 1/a_2 +1/a_3...}}\)
Z = \(\frac{2}{{1/x +1/y}}\)
Solving gives Z = \(\frac{2xy}{{x+y}}\)
A is the answer.
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Re: Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), wh  [#permalink]

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New post 21 Aug 2018, 07:43
Afc0892 wrote:
Harmonic Mean is given by = \(\frac{N (No. of elements)}{{1/a_1 + 1/a_2 +1/a_3...}}\)
Z = \(\frac{2}{{1/x +1/y}}\)
Solving gives Z = \(\frac{2xy}{{x+y}}\)
A is the answer.



can you please outline the last step?
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Re: Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), wh  [#permalink]

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New post 22 Aug 2018, 01:44
=>

\(\frac{1}{z} = (\frac{1}{2})(\frac{1}{x} + \frac{1}{y}) = (\frac{1}{2})(\frac{(x+y)}{xy}) = \frac{(x+y)}{(2xy)}\)
Thus, \(z = \frac{2xy}{( x + y ).}\)


Therefore, A is the answer.
Answer: A
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Re: Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), wh   [#permalink] 22 Aug 2018, 01:44
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