PK 2020 Q18
18. There are some squares and triangles on the table. Some of them are blue and the rest are red. Some of these shapes are large and the rest are small. We know that
1. If the shape is large, it’s a square;
2. If the shape is blue, it’s a triangle.
Which of the statements A–E must be true?
- A All red figures are squares.
- B All squares are large.
- C All small figures are blue.
- D All triangles are blue.
- E All blue figures are small.
Pink Kangaroo 2020, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E All blue figures are small.
From statement 1 it follows that if a shape is not square, then it is not large; hence all triangles are small. Using statement 2 we see that blue figures are triangles and so are small. This shows that E is true. Suppose we had a set of shapes which consisted of one small blue triangle, one small red triangle, one small red square and one large red square. Then this satisfies statements 1 and 2 but it does not satisfy A, B, C or D. So they are not true in general.
Solution © UK Mathematics Trust, from the PK 2020 solutions.