GK 2019 Q14
14. Michael keeps dogs, cows, cats and kangaroos as pets. He has 24 pets in total and \(\tfrac{1}{8}\) of them are dogs, \(\tfrac{3}{4}\) are not cows and \(\tfrac{2}{3}\) are not cats. How many kangaroos does Michael keep?
- A 4
- B 5
- C 6
- D 7
- E 8
Grey Kangaroo 2019, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 7
Michael has 24 pets. Since \(\tfrac{1}{8}\) of them are dogs, he has 3 dogs. Since \(\tfrac{3}{4}\) are not cows, \(\tfrac{1}{4}\) of them are cows and hence he has 6 cows. Similarly, since \(\tfrac{2}{3}\) are not cats, \(\tfrac{1}{3}\) of them are cats and hence he has 8 cats. Therefore, the number of kangaroos he has is 24 − 3 − 6 − 8 = 7.
Solution © UK Mathematics Trust, from the GK 2019 solutions.