IMC 2020 Q14
14. The result of the calculation 9 × 11 × 13 × 15 × 17 is the six-digit number ‘3n8185’.
What is the value of \(n\)?
- A 2
- B 4
- C 6
- D 8
- E 0
Intermediate Mathematical Challenge 2020, Question 14. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 2
Note that 9 × 11 × 13 × 15 × 17 is a multiple of 9. Therefore the sum of its digits is also a multiple of 9. The sum of the digits of ‘3n8185’ equals \(25 + n\). So \(n = 2\), since 27 is a multiple of 9.
Solution © UK Mathematics Trust, from the IMC 2020 solutions. Longer versions with investigations: Solutions and investigations (PDF).