Can You Solve This EASY Oxford University Maths Question?

This puzzle comes from an Oxford University’s mathematics admission test. I must say back then we didn’t have any AI that would scramble out a series of words that turned out to be the solution in a matter of seconds.

Every maths puzzle is a way to invoke the Power Process as explained in Industrial Society and Its Future. There’s fundamentally no need or use to solving any of these maths puzzles. But if we can derive some level of satisfaction and meaning, I see no harm in doing that.

Once again, this is a good moment to pause the article and give the problem a go yourself. When you’re ready, keep reading for the solution. And if you come up with your own approach, feel free to share it in the comments — I’d love to see how you tackled it.

Don’t forget to subscribe to our YouTube channel for more maths puzzles, it’s my goal to reach 100k subscribers someday. Current Sub Count: 251

Solution

To start off, recall the general equation of a circle

This tells us the centre of the circle at (a,b) as well as the radius r.

We will do the same with the given equation, manipulating it into a general form in terms of k

The important point here is that the equation is only a circle if and only term on the right-hand side is greater than zero. This is to make sure that the equation has a positive radius

Our goal now is to solve this inequality. To solve any polynomial inequality, we factorize the expression and evaluate the behaviour of the graph.

Upon factorization, we get

We now plot the graph and see that

The shaded region is when the function is greater than zero, which means

Therefore the answer is (b).

How amazing :)

Subscribe to Our YouTube Channel

[embed]Math Games Hello my friends :)www.youtube.com

Buy me a coffee

Thank you for reading Math Games. You can help us grow by making a donation here.