GK 2019 Q6
6. Five friends all brought some cakes with them when they met. Each of them gave a cake to each of the others. They then ate all the cakes they had just been given. As a result, the total number of cakes they had between them decreased by half. How many cakes did the five friends have at the start?
- A 20
- B 24
- C 30
- D 40
- E 60
Grey Kangaroo 2019, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 40
Each of the five friends gave a cake to the four other people. Therefore the number of cakes given away and then eaten was 4 × 5 = 20. Since this decreased the total number of cakes they had by half, the total number of cakes they had at the start was 2 × 20 = 40.
Solution © UK Mathematics Trust, from the GK 2019 solutions.