PK 2015 Q12
12. The product of the ages of a father and his son is 2015. What is the difference between their ages?
- A 29
- B 31
- C 34
- D 36
- E None of these
Pink Kangaroo 2015, Question 12. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 34
The prime factor decomposition of 2015 is \(5 \times 13 \times 31\), so the only possible pairs of ages are \(1 \times 2015\), \(5 \times 403\), \(13 \times 155\), \(31 \times 65\). The only realistic pair of ages is 65 and 31, with a difference of 34.
Solution © UK Mathematics Trust, from the PK 2015 solutions.