Q1.
An exam has 50 multiple choice questions. 5 marks are given for every correct answer and 2 negative marks for every wrong answer. What are the maximum possible marks in the exam? What are the minimum possible marks?
Answer
Maximum = 250 marks. Minimum = –100 marks.
The best case is all 50 answers correct.
50 × 5 = 250
The worst case is all 50 answers wrong.
50 × (–2) = –100
| Situation | Correct | Wrong | Total marks |
|---|---|---|---|
| Best possible | 50 | 0 | 250 |
| Mala’s result | 30 | 20 | 110 |
| Worst possible | 0 | 50 | –100 |
Why it happens: every correct answer pushes the score up by 5 and every wrong answer pulls it down by 2. To make the score as large as possible, use only pushes; to make it as small as possible, use only pulls. The score can go below zero here, which is exactly why the marks are written as integers.
Tip: if a student leaves a question blank instead of answering it wrongly, that question is worth 0, not –2. So a blank paper scores 0 — better than a fully wrong one.