IMC 2004 Q5
5. The sum of two numbers is 2. The difference between them is 4. What is their product?
- A −8
- B −3
- C 0
- D 3
- E 8
Intermediate Mathematical Challenge 2004, Question 5. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: B −3
Let the numbers be \(x\) and \(y\). Then \(x + y = 2\); \(x - y = 4\). Adding these equations gives \(2x = 6\), so \(x = 3\). Hence \(y = 2 - 3 = -1\) so the numbers are 3 and −1.
Solution © UK Mathematics Trust, from the IMC 2004 solutions.