IMC 2006 Q4
4. The mean, median and mode of the numbers in the boxes below are the same. What is the missing number?
| 7 | 7 | 5 | 7 | ? |
- A 6.5
- B 7
- C 8
- D 8.5
- E 9
Intermediate Mathematical Challenge 2006, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: E 9
Whatever number is placed in the fifth box, the median and mode of the numbers will both be 7. For the mean to equal 7, the total of the 5 numbers must be 35. This means that the missing number is 9.
Solution © UK Mathematics Trust, from the IMC 2006 solutions.