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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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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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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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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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MathRevolution: Finish GMAT Quant Section with 10 minutes to spare
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"Only $79 for 1 month Online Course" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" NUS School Moderator Joined: 18 Jul 2018 Posts: 1024 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] ### Show Tags 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. Intern 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] ### Show Tags 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? NUS School Moderator Joined: 18 Jul 2018 Posts: 1024 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] ### Show Tags 21 Aug 2018, 10:36 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 = $$\frac{2xy}{{x+y}}$$ 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. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8235 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] ### Show Tags 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 _________________ MathRevolution: Finish GMAT Quant Section with 10 minutes to spare The one-and-only World’s First Variable Approach for DS and IVY Approach for PS with ease, speed and accuracy. "Only$79 for 1 month Online Course"
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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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