You may also like

problem icon

Areas and Ratios

Do you have enough information to work out the area of the shaded quadrilateral?

problem icon

Shape and Territory

If for any triangle ABC tan(A - B) + tan(B - C) + tan(C - A) = 0 what can you say about the triangle?

problem icon

Napoleon's Hat

Three equilateral triangles ABC, AYX and XZB are drawn with the point X a moveable point on AB. The points P, Q and R are the centres of the three triangles. What can you say about triangle PQR?

Mind Your Ps and Qs

Age 16 to 18 Short Challenge Level:

To do this question you need to be really sure what the two symbols $\Rightarrow$ and $\Leftrightarrow$ mean.

$p\Rightarrow q$ essentially means that IF $p$ is True THEN $q$ is true.

$p\Leftrightarrow q$ means that $p$ is true if and only if $q$ is true. Alternatively, they are either both true or both false.

To get started, pick one of the simpler looking statements for $p$.

Go through the other statements in turn and see which of them work as $q$ in $p\Rightarrow q$. You will soon be able to pair-off possible partners.

Finally, don't forget to read the details of the question carefully!