PK 2018 Q3
3. The sum of five consecutive integers is \(10^{2018}\). What is the middle number?
- A \(10^{2013}\)
- B \(5^{2017}\)
- C \(10^{2017}\)
- D \(2^{2018}\)
- E \(2 \times 10^{2017}\)
Pink Kangaroo 2018, Question 3. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E \(2 \times 10^{2017}\)
Let \(n\) be the middle number. Then the five numbers are \(n - 2\), \(n - 1\), \(n\), \(n + 1\), \(n + 2\) and have sum \(5n = 10^{2018}\).
Therefore \(n = \dfrac{10^{2018}}{5} = \dfrac{10 \times 10^{2017}}{5} = 2 \times 10^{2017}\).
Solution © UK Mathematics Trust, from the PK 2018 solutions.