The sum of the three numbers x, y and z is 3x, so y + z = 2x.

So the mean of y and z is the same as the mean of 2x.

Therefore the mean of y and z is x.

This problem is taken from the UKMT Mathematical Challenges.

You can find more short problems, arranged by curriculum topic, in our short problems collection.

Inequalities. Circle properties and circle theorems. Expanding and factorising quadratics. Generalising. Mathematical reasoning & proof. Creating and manipulating expressions and formulae. Simultaneous equations. Polynomial functions and their roots. 2D shapes and their properties. Regular polygons and circles.