PK 2019 Q6
6. Pedro is asked to find three kangaroos whose weights are all whole numbers of kilograms and whose total weight is 97 kg. What is the largest possible weight of the lightest of the kangaroos Pedro could find?
- A 1 kg
- B 30 kg
- C 31 kg
- D 32 kg
- E 33 kg
Pink Kangaroo 2019, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 32 kg
Let \(J\) kg be the weight of the lightest kangaroo. Then the total weight of the three kangaroos is at least \(3J\) kg. And we know they weigh 97 kg in total, so \(3J \leq 97\), so \(J \leq 32\tfrac{1}{3}\). Hence the lightest is at most 32 kg. The three could have weights 32 kg, 32 kg and 33 kg.
Solution © UK Mathematics Trust, from the PK 2019 solutions.