IMC 2019 Q13
13. Megan writes down a list of five numbers. The mean of her first three numbers is −3. The mean of her first four numbers is 4. The mean of her first five numbers is −5.
What is the difference between her fourth number and her fifth number?
- A 66
- B 55
- C 44
- D 33
- E 22
Intermediate Mathematical Challenge 2019, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 66
From the given information, the sum of Megan’s first three numbers is −9, the sum of her first four numbers is 16, and the sum of her first five numbers is −25.
Therefore the fourth number is 16 − (−9) = 25, and the fifth number is −25 − 16 = −41. The difference between them is 25 − (−41) = 66.
Solution © UK Mathematics Trust, from the IMC 2019 solutions. Longer versions with investigations: Solutions and investigations (PDF).