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# If 1/x-1/y=1/z, what is the value of y, in terms of x and z?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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If 1/x-1/y=1/z, what is the value of y, in terms of x and z?  [#permalink]

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22 Feb 2019, 00:18
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15% (low)

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78% (01:12) correct 23% (02:24) wrong based on 40 sessions

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[GMAT math practice question]

If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$?

$$A. \frac{xz}{(z-x)}$$
$$B. \frac{xz}{(x-z)}$$
$$C. \frac{x}{z(z-x)}$$
$$D. \frac{z}{x(x-z)}$$
$$E. xz(z-x)$$

_________________
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" CEO Status: GMATINSIGHT Tutor Joined: 08 Jul 2010 Posts: 2978 Location: India GMAT: INSIGHT Schools: Darden '21 WE: Education (Education) If 1/x-1/y=1/z, what is the value of y, in terms of x and z? [#permalink] ### Show Tags 22 Feb 2019, 01:22 MathRevolution wrote: [GMAT math practice question] If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$? $$A. \frac{xz}{(z-x)}$$ $$B. \frac{xz}{(x-z)}$$ $$C. \frac{x}{z(z-x)}$$ $$D. \frac{z}{x(x-z)}$$ $$E. xz(z-x)$$ $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$ $$\frac{1}{x}-\frac{1}{z}=\frac{1}{y}$$ $$\frac{(z-x)}{zx}=\frac{1}{y}$$ Taking reciprocal at both sides. $$\frac{zx}{(z-x)}=y$$ Answer: Option A _________________ Prosper!!! GMATinsight Bhoopendra Singh and Dr.Sushma Jha e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772 Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi http://www.GMATinsight.com/testimonials.html ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION Senior Manager Joined: 20 Mar 2018 Posts: 382 Location: Ghana Concentration: Finance, Real Estate Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z? [#permalink] ### Show Tags 22 Feb 2019, 01:33 Asked y interms of x and z ,Therefore answer should be y= blah blah x blah blah z 1/x-1/y=1/z Now let’s eliminate the denominators with the LCM (xyz) ( xyz)•1/(x) - (xyz)•1/y= (xyz)•1/z yz - xz = xy yz -xy = xz y(z - x) = xz y = xz/(z - x) Answer is A Posted from my mobile device Senior Manager Joined: 04 Aug 2010 Posts: 477 Schools: Dartmouth College Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z? [#permalink] ### Show Tags 22 Feb 2019, 05:36 MathRevolution wrote: [GMAT math practice question] If $$\frac{1}{x}-\frac{1}{y}=\frac{1}{z}$$, what is the value of $$y$$, in terms of $$x$$ and $$z$$? $$A. \frac{xz}{(z-x)}$$ $$B. \frac{xz}{(x-z)}$$ $$C. \frac{x}{z(z-x)}$$ $$D. \frac{z}{x(x-z)}$$ $$E. xz(z-x)$$ Let $$x=1$$ and $$y=\frac{3}{2}$$, with the result that $$\frac{1}{z} = 1 - \frac{2}{3} = \frac{1}{3}$$, so $$z=3$$. Since the question stem asks for the value of y, the correct answer must yield $$\frac{3}{2}$$ when x=1 and z=3. Since B and D include x-z and thus will yield a negative result, eliminate B and D. Since E includes only multiplication and thus cannot yield $$\frac{3}{2}$$, eliminate E. Between A and C, only A yields $$\frac{3}{2}$$: $$\frac{xz}{z-x} = \frac{1*3}{3-1} = \frac{3}{2}$$ _________________ GMAT and GRE Tutor Over 1800 followers GMATGuruNY@gmail.com New York, NY If you find one of my posts helpful, please take a moment to click on the "Kudos" icon. Available for tutoring in NYC and long-distance. For more information, please email me at GMATGuruNY@gmail.com. Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 8033 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If 1/x-1/y=1/z, what is the value of y, in terms of x and z? [#permalink] ### Show Tags 24 Feb 2019, 07:00 => Making $$y$$ the subject of the equation $$\frac{1}{x} – \frac{1}{y} = \frac{1}{z}$$ yields $$\frac{1}{y} = \frac{1}{x} – \frac{1}{z} = \frac{(z-x)}{xz}$$, and $$y = \frac{xz}{(z-x)}.$$ Therefore, the answer is A. 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: If 1/x-1/y=1/z, what is the value of y, in terms of x and z?   [#permalink] 24 Feb 2019, 07:00
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