GK 2018 Q17
17. There are three candidates standing for one position as student president and 130 students are voting. Sally has 24 votes so far, while Katie has 29 and Alan has 37. How many more votes does Alan need to be certain he will finish with the most votes?
- A 13
- B 14
- C 15
- D 16
- E 17
Grey Kangaroo 2018, Question 17. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 17
The number of votes left to be cast is 130 – (24 + 29 + 37) = 40. Let the number of these votes Alan receives be \(x\). Since Katie is the closest challenger to Alan, for Alan to be certain of having the most votes, \(37 + x > 29 + 40 - x\). Therefore \(2x > 32\) and hence \(x > 16\). Therefore Alan needs at least 17 more votes to be certain to finish with the most votes.
Solution © UK Mathematics Trust, from the GK 2018 solutions.