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If 1 + 1/(1+ 1/x) is 13/11, what is x?

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by Max@Math Revolution » Tue Oct 22, 2019 2:28 am
[GMAT math practice question]

If 1 + 1/(1+ 1/x) is 13/11, what is 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 23, 2019 11:44 pm
=>

Since 1 + 1/(1+1/x)) = 13/11, we have 1 + x/(x+1) = 13/11. Finding a common denominator gives us (x+1)/(x+1) + x/(x+1) or (2x+1)/(x+1) = 13/11.
Then we have 11(2x+1) = 13(x+1), 22x+11 = 13x+13 or 9x = 2.
So, x = 2/9.

Therefore, B is the answer.
Answer: B
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