IMC 2004 Q22
22. In a maths exam with \(N\) questions, you score \(m\) marks for a correct answer to each of the first \(q\) questions and \(m + 2\) marks for a correct answer to each of the remaining questions. What is the maximum possible score?
- A \((m + 2)N - 2q\)
- B \(Nm\)
- C \(mq + (m + 2)q\)
- D \(N(m + 1)\)
- E \(Nm + q(m + 2)\)
Intermediate Mathematical Challenge 2004, Question 22. © UK Mathematics Trust. Original paper on ukmt.org.uk
Answer: A \((m + 2)N - 2q\)
If you answer all questions correctly, you receive \(m\) marks for each of the \(N\) questions plus an extra 2 marks for the last \((N - q)\) questions. So the maximum possible score \(= m \times N + 2 \times (N - q) = mN + 2N - 2q = (m + 2)N - 2q\).
Solution © UK Mathematics Trust, from the IMC 2004 solutions.