Oxford University MAT 2015 Solved Papers

Squaring all answers results in $\frac{7}{4}$ which is larger than (b) $\frac{25}{16}$. After squaring (c) simplifies to $\frac{10\times 9\times 8\times 7}{9\times 6!}$, which further simplifies to $\frac{7}{9}$ which is smaller than $\left(\mathit{a}\right)$. ${\log }_2\left(30\right)\approx 5$ and ${\log }_3\left(85\right)\approx 4$, hence (d) is smaller than (a) (after squaring). Comparing (a) with (e) after squaring results in a comparison of $\frac{7}{4}$ and $\frac{7+2\sqrt{6}}{9}$. As , (e) squared must be less than $\frac{13}{9}$ and hence less than $\frac{7}{4}$. The answer is (a).