CAT 2016 Quantitative Ability

$\mathit{x}+\frac{1}{\mathit{y}+\frac{1}{\mathit{z}}}=\frac{68}{21}=3+\frac{5}{21}$

As x is a natural number, the only possible value of x is 3.

∴ $\mathit{y}+\frac{1}{\mathit{z}}=\frac{21}{5}=4+\frac{1}{5}$

As y and z are natural numbers, the only possible values of y and z are 4 and 5 respectively.

x + y + z= 3 + 4 + 5=12