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

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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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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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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 $y$?

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

Spoiler: OA

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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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21 Aug 2018, 10:36

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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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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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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Intern

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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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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?

Math Revolution GMAT Instructor

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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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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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