GK 2019 Q19
19. The integers from 1 to \(n\), inclusive, are equally spaced in order round a circle. The diameter through the position of the integer 7 also goes through the position of 23, as shown. What is the value of \(n\)?
- A 30
- B 32
- C 34
- D 36
- E 38
Grey Kangaroo 2019, Question 19. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B 32
Since the integer 7 is joined by a diameter to the integer 23, we can deduce that there are 23 − 7 + 1 = 15 integers between them on each side. Therefore there are 2 × 15 + 2 = 32 integers in total round the circle. Hence the value of \(n\) is 32.
Solution © UK Mathematics Trust, from the GK 2019 solutions.