GK 2016 Q18
18. Twelve girls met in a cafe. On average, they ate \(1\tfrac{1}{2}\) cupcakes each, although no cupcakes were actually divided. None of them ate more than two cupcakes and two of them ate no cupcakes at all. How many girls ate two cupcakes?
- A 2
- B 5
- C 6
- D 7
- E 8
Grey Kangaroo 2016, Question 18. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 8
The total number of cupcakes eaten by the girls is \(12 \times 1\tfrac{1}{2} = 18\). Two girls ate no cakes so the 18 cupcakes were eaten by 10 girls. Since no-one ate more than two cupcakes, the maximum number of cupcakes the 10 girls could have eaten is 10 × 2 = 20. For every girl who eats only one cupcake, the total of 20 is reduced by 1. Hence the number of girls who ate only one cupcake is 20 − 18 = 2 and hence the number of girls who ate two cupcakes is 8.
Solution © UK Mathematics Trust, from the GK 2016 solutions.