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

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

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New post 03 Jan 2019, 00:29
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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 \(n\)?

\(A. 31\)
\(B. 41\)
\(C. 51\)
\(D. 61\)
\(E. 71\)

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

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

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

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New post 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
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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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