GK 2016 Q10
10. Tim, Tom and Tam are triplets (three brothers born on the same day). Their twin brothers Jon and Jim are exactly three years younger. Which of the following numbers could be the sum of the ages of the five brothers?
- A 36
- B 53
- C 76
- D 89
- E 92
Grey Kangaroo 2016, Question 10. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 89
Let \(x\) be the age of each of Tim, Tom and Tam. Therefore the age of both Jon and Jim is \(x - 3\). Therefore the sum of all their ages is \(3x + 2(x - 3) = 5x - 6\) and \(5x - 6\) can also be written as \(5(x - 1) - 1\). Hence the sum of their ages is always one less than a multiple of 5. Of the options given, the only number for which this is true is 89 (when Tim, Tom and Tam are 19 and Jon and Jim are 16).
Solution © UK Mathematics Trust, from the GK 2016 solutions.