CAT Exam Model Paper 3 with solutions for free online practice

(c) The harmonic mean of two numbers x and y is $\frac{2\mathit{x}\mathit{y}}{\left(\mathit{x}+\mathit{y}\right)}$ and the geometric mean is $\sqrt{\mathit{x}\mathit{y}}$.
∴ $\frac{\left(\frac{2\mathit{x}\mathit{y}}{\mathit{x}+\mathit{y}}\right)}{\sqrt{\mathit{x}\mathit{y}}}=\frac{12}{13}$,
squaring both sides, we get $\frac{2\mathit{x}\mathit{y}}{{\left(\mathit{x}+\mathit{y}\right)}^2}=\frac{144}{169}$ . Although this can be simplified to get the answer, the best way to proceed from here would to look out for the answer choices and figure out which pair of x and y satisfies the above equation. You will find the answer is (c).