IMC 2012 Q2
2. Three positive integers are all different. Their sum is 7. What is their product?
- A 12
- B 10
- C 9
- D 8
- E 5
Intermediate Mathematical Challenge 2012, Question 2. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: D 8
The following are the only triples of positive integers which sum to 7:
(1, 1, 5), (1, 2, 4), (1, 3, 3); (2, 2, 3).
In only one of these are the three integers all different, so the required integers are 1, 2, 4 and their product is 8.
Solution © UK Mathematics Trust, from the IMC 2012 solutions. Longer versions with investigations: Solutions and investigations (PDF).