IMC 2007 Q6
6. The sum of 9 consecutive positive whole numbers is 2007. What is the difference between the largest and smallest of these numbers?
- A 8
- B 9
- C 10
- D 18
- E 223
Intermediate Mathematical Challenge 2007, Question 6. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A 8
The difference between the largest and smallest of 9 consecutive whole numbers is 8, irrespective of the sum of the numbers. However in this case, since the average of the 9 numbers is 223, we can say they are 219, 220, …, 226, 227.
Solution © UK Mathematics Trust, from the IMC 2007 solutions.