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If 1 + 1/(1+ 1/x) = 13/11, what is the value of x?
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MathRevolution
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If 1 + 1/(1+ 1/x) = 13/11, what is the value of x? [#permalink] New post  07 Oct 2019, 01:17
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[GMAT math practice question]

If \(1 + 1/(1+ \frac{1}{x}) = \frac{13}{11}\), what is the value of \(x\)?

\(A. \frac{1}{9}\)

\(B. \frac{2}{9}\)

\(C. \frac{1}{3}\)

\(D. \frac{4}{9}\)

\(E. \frac{5}{9}\)
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Re: If 1 + 1/(1+ 1/x) = 13/11, what is the value of x? [#permalink] New post  07 Oct 2019, 04:47
Answer is B
1+1/(1+1/x)=13/11

->1+1/((x+1)/x) .= 13/11
->1+x/(x+1)=13/11
->(x+1+x)/(x+1)=13/11
->11(2x+1)=13(x+1)
->22x+11=13x+13
->22x-13x=13-11
->9x=2
->x=2/9
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MathRevolution
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Re: If 1 + 1/(1+ 1/x) = 13/11, what is the value of x? [#permalink] New post  09 Oct 2019, 06:28
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=>

\(1 + 1 / ( 1 + (\frac{1}{x}) ) = \frac{13}{11}\)

\(=> 1 + 1 / ((\frac{x}{x}) + (\frac{1}{x})) = \frac{13}{11}\)

\(=> 1 + 1 / (\frac{(x+1)}{x}) = \frac{13}{11}\)

\(=> \frac{1 + x}{( x + 1 )} = \frac{13}{11}\)

\(=> \frac{(x + 1)}{(x + 1)} + \frac{x}{(x + 1)} = \frac{13}{11}\)

\(=> \frac{(2x + 1)}{(x + 1)} = \frac{13}{11}\)

\(=> 11(2x+1) = 13(x+1)\)

\(=> 22x + 11 = 13x + 13\)

\(=> 9x = 2\)

\(=> x = \frac{2}{9}\)

Therefore, B is the answer.
Answer: B
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Re: If 1 + 1/(1+ 1/x) = 13/11, what is the value of x? [#permalink] New post  12 Oct 2019, 16:02
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MathRevolution wrote:
[GMAT math practice question]

If \(1 + 1/(1+ \frac{1}{x}) = \frac{13}{11}\), what is the value of \(x\)?

\(A. \frac{1}{9}\)

\(B. \frac{2}{9}\)

\(C. \frac{1}{3}\)

\(D. \frac{4}{9}\)

\(E. \frac{5}{9}\)


Multiplying the fraction on the left hand side of the equation by x/x, we have:

1 + x/(x + 1) = 13/11

Multiplying the entire equation by (x + 1), we have:

x + 1 + x = (13x + 13)/11

2x + 1 = (13x + 13)/11

Multiplying the entire equation by 11, we have:

22x + 11 = 13x + 13

9x = 2

x = 2/9

Answer: B
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Re: If 1 + 1/(1+ 1/x) = 13/11, what is the value of x? [#permalink]
12 Oct 2019, 16:02
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