IMC 2008 Q13
13. The mean of a sequence of 64 numbers is 64. The mean of the first 36 numbers is 36.
What is the mean of the last 28 numbers?
- A 28
- B 44
- C 72
- D 100
- E 108
Intermediate Mathematical Challenge 2008, Question 13. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 100
The sum of all 64 numbers is 64 × 64 = 642. The sum of the first 36 numbers is 36 × 36 = 362. So the sum of the remaining 28 numbers is 642 − 362 = (64 + 36)(64 − 36) = 2800. Therefore the mean of these 28 numbers is 100.
Solution © UK Mathematics Trust, from the IMC 2008 solutions.