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# If √4+ 1/n = 5√5/n, what is the value of n?

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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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If √4+ 1/n = 5√5/n, what is the value of n?  [#permalink]

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03 Jan 2019, 00:29
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90% (01:12) correct 10% (01:55) wrong based on 49 sessions

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[Math Revolution GMAT math practice question]

If $$\sqrt{4+ \frac{1}{n}} = 5\sqrt{\frac{5}{n}}$$, what is the value of $$n$$?

$$A. 31$$
$$B. 41$$
$$C. 51$$
$$D. 61$$
$$E. 71$$

_________________
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" "Free Resources-30 day online access & Diagnostic Test" "Unlimited Access to over 120 free video lessons - try it yourself" Director Joined: 06 Jan 2015 Posts: 682 Location: India Concentration: Operations, Finance GPA: 3.35 WE: Information Technology (Computer Software) Re: If √4+ 1/n = 5√5/n, what is the value of n? [#permalink] ### Show Tags 03 Jan 2019, 02:30 MathRevolution wrote: [Math Revolution GMAT math practice question] If $$\sqrt{4+ \frac{1}{n}} = 5\sqrt{\frac{5}{n}}$$, what is the value of $$n$$? $$A. 31$$ $$B. 41$$ $$C. 51$$ $$D. 61$$ $$E. 71$$ Squaring on both side the equation= $$\sqrt{4+ \frac{1}{n}} = 5\sqrt{\frac{5}{n}}$$ =$$4+ \frac{1}{n} = 25*\frac{5}{n}$$ ==>$$((25*5-1)/4)$$ ==>31 Hence A _________________ आत्मनॊ मोक्षार्थम् जगद्धिताय च Resource: GMATPrep RCs With Solution CEO Joined: 12 Sep 2015 Posts: 3857 Location: Canada Re: If √4+ 1/n = 5√5/n, what is the value of n? [#permalink] ### Show Tags 03 Jan 2019, 12:18 Top Contributor MathRevolution wrote: [Math Revolution GMAT math practice question] If $$\sqrt{4+ \frac{1}{n}} = 5\sqrt{\frac{5}{n}}$$, what is the value of $$n$$? $$A. 31$$ $$B. 41$$ $$C. 51$$ $$D. 61$$ $$E. 71$$ GIVEN: √(4 + 1/n) = 5√(5/n) Square both sides to get: [√(4 + 1/n)]² = [5√(5/n)]² Simplify left side and rewrite right side: 4 + 1/n = [5√(5/n)][5√(5/n)] Rewrite right side again: 4 + 1/n = (5)(5)√(5/n)√(5/n) Simplify right side again: 4 + 1/n = 25(5/n) Simplify right side: 4 + 1/n = 125/n Multiply both sides by n to get: 4n + 1 = 125 Subtract 1 from both sides to get: 4n = 124 Solve: n = 124/4 =31 Answer: A Cheers, Brent _________________ Test confidently with gmatprepnow.com Math Revolution GMAT Instructor Joined: 16 Aug 2015 Posts: 7618 GMAT 1: 760 Q51 V42 GPA: 3.82 Re: If √4+ 1/n = 5√5/n, what is the value of n? [#permalink] ### Show Tags 06 Jan 2019, 18:24 => $$\sqrt{4+ \frac{1}{n}} = 5\sqrt{\frac{5}{n}}$$ $$=> \sqrt{\frac{4n+1}{n}} = 5\sqrt{\frac{5}{n}}$$ $$=> \frac{4n+1}{n} = 25(\frac{5}{n})$$ $$=> \frac{4n+ 1}{n} = \frac{125}{n}$$ $$=> 4n+1 = 125$$ $$=> 4n = 124$$ $$=> n = 31$$ 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 √4+ 1/n = 5√5/n, what is the value of n?   [#permalink] 06 Jan 2019, 18:24
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