IMC 2012 Q4
4. All four digits of two 2-digit numbers are different. What is the largest possible sum of two such numbers?
- A 169
- B 174
- C 183
- D 190
- E 197
Intermediate Mathematical Challenge 2012, Question 4. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: C 183
The digits to be used must be 9, 8, 7, 6. If any of these were to be replaced by a smaller digit, then the sum of the two two-digit numbers would be reduced. For this sum to be as large as possible, 9 and 8 must appear in the ‘tens’ column rather than the ‘units’ column. So the largest possible sum is 97 + 86 or 96 + 87. In both cases the sum is 183.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).