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#### Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.  # Let z be the harmonic mean of x and y. If 1/z=(1/2)((1/x)+(1/y)), wh

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Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
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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Difficulty:   15% (low)

Question Stats: 90% (01:02) correct 10% (02:39) wrong based on 33 sessions

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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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NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1026
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
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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1
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 = $$\frac{2xy}{{x+y}}$$

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.
NUS School Moderator V
Joined: 18 Jul 2018
Posts: 1026
Location: India
Concentration: Finance, Marketing
WE: Engineering (Energy and Utilities)
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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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 = $$\frac{2xy}{{x+y}}$$
Intern  B
Joined: 04 Jul 2018
Posts: 9
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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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 = $$\frac{2xy}{{x+y}}$$

can you please outline the last step?
Math Revolution GMAT Instructor V
Joined: 16 Aug 2015
Posts: 8251
GMAT 1: 760 Q51 V42 GPA: 3.82
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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=>

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

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