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# √r + 2/√r = 4. What is the value of r + 4/r?

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Math Revolution GMAT Instructor
Joined: 16 Aug 2015
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GMAT 1: 760 Q51 V42
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√r + 2/√r = 4. What is the value of r + 4/r?  [#permalink]

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26 Mar 2019, 02:09
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Difficulty:

35% (medium)

Question Stats:

63% (01:12) correct 37% (01:19) wrong based on 38 sessions

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[GMAT math practice question]

$$√r + \frac{2}{√r} = 4$$. What is the value of $$r + \frac{4}{r}$$?

$$A. 12$$
$$B. 14$$
$$C. 16$$
$$D. 32$$
$$E. 64$$

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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" Senior Manager Joined: 04 Aug 2010 Posts: 474 Schools: Dartmouth College Re: √r + 2/√r = 4. What is the value of r + 4/r? [#permalink] ### Show Tags 26 Mar 2019, 03:31 MathRevolution wrote: [GMAT math practice question] $$√r + \frac{2}{√r} = 4$$. What is the value of $$r + \frac{4}{r}$$? $$A. 12$$ $$B. 14$$ $$C. 16$$ $$D. 32$$ $$E. 64$$ Apply the following identity: $$(a+b)² = a² + b² + 2ab$$ $$√r + \frac{2}{√r} = 4$$ $$(√r + \frac{2}{√r})² = 4²$$ $$(√r)² + (\frac{2}{√r})² + 2(√r)(\frac{2}{√r}) = 16$$ $$r + \frac{4}{r} + 4 = 16$$ $$r + \frac{4}{r} = 12$$ . _________________ 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: 8001 GMAT 1: 760 Q51 V42 GPA: 3.82 √r + 2/√r = 4. What is the value of r + 4/r? [#permalink] ### Show Tags 28 Mar 2019, 01:41 => $$(√r + \frac{2}{√r})^2 = r + 2(√r)(\frac{2}{√r}) + \frac{4}{r} = r + \frac{4}{r} + 4 = 4^2 = 16$$ So, $$r + \frac{4}{r} = 16 -4 = 12.$$ 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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√r + 2/√r = 4. What is the value of r + 4/r?   [#permalink] 28 Mar 2019, 01:41
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