Oxford University MAT 2015 Solved Papers

Squaring all answers results in ‌

7

4

which is larger than (b) ‌

25

16

. After squaring (c) simplifies to ‌

10×9×8×7

9×6!

, which further simplifies to ‌

7

9

which is smaller than (a). log2(30)≈5 and log3(85)≈4, hence (d) is smaller than (a) (after squaring). Comparing (a) with (e) after squaring results in a comparison of ‌

7

4

and ‌

7+2√6

9

. As 2<√6<3, (e) squared must be less than ‌

13

9

and hence less than ‌

7

4

. The answer is (a).