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

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by Max@Math Revolution » Mon Oct 07, 2019 1:00 am
[GMAT math practice question]

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

A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 5/9
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by Max@Math Revolution » Wed Oct 09, 2019 6:08 am
=>

1 + 1 / ( 1 + (1/x) ) = 13/11
=> 1 + 1 / ((x/x) + (1/x)) = 13/11
=> 1 + 1 / ((x+1)/x) = 13/11
=> 1 + x / ( x + 1 ) = 13/11
=> (x + 1) / (x + 1) + x / (x + 1) = 13/11
=> (2x + 1)/(x + 1) = 13/11
=> 11(2x+1) = 13(x+1)
=> 22x + 11 = 13x + 13
=> 9x = 2
=> x = 2/9

Therefore, B is the answer.
Answer: B
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by Scott@TargetTestPrep » Wed Oct 09, 2019 6:49 pm
Max@Math Revolution wrote:[GMAT math practice question]

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

A. 1/9
B. 2/9
C. 1/3
D. 4/9
E. 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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