Can you solve this Oxford MAT problem?
If you’re looking to undertake an undergraduate degree in Mathematics, Computer Science or some combination of the two, you’ll need to take the MAT, Oxford’s aptitude / admissions test for its Mathematics courses.
I found this question that I’d love to share with you when I was browsing the past papers for the MAT.
The question is from the multiple choice part of the exam, where candidates are awarded 4 marks for the correct answer and no marks for working out.
Could you solve this question?
Hmmmm. This looks pretty complicated. The hardest bit of this question is working out what the hell is going on here! Once you’ve got a bit of a diagram the maths should be the easy part!
Feel free to have a go youself before scrolling on to see the solution!
The Solution!
This question really isn’t as difficult as it seems. You’d be forgiven for having a little panic when you first see it — these questions are only easy when you know what you’re doing!
I’ll admit I myself overcomplicated this question, but after looking at the diagram provided in the solutions it becomes quite apparent how you can solve this one.
The diagram above shows the relationship between a circle Cn of radius Rn and the circle Cn+1 of radius Rn+1.
The tangent to the circle Cn is shown above and we can indeed see that the tangent crosses the larger circle (Cn+1) at 2 places so we know we’ve probably drawn our tangent correctly. Happy days!
We know that tangents meet radii at 90° (think back to GCSE higher circle theorems) so we have a right angled triangle with hypotenuse Rn+1 and other sides 1 and Rn. Using Pythagoras gives (Rn+1)² = (Rn)² + 1.
Since (r1)² = 1 and (r2)² = 2 we know this pattern continues so when we get up to (r100)² = 100.
Therefore, the correct answer must be (d).
And there we have it!
Could you secure a place at Oxford?
Thank you for reading this article, I hope you learnt something new!
