In an examination, a student receives 4 marks for each correct answer and…
2024
In an examination, a student receives 4 marks for each correct answer and loses 1 mark for each incorrect answer. The student attempts all 200 questions and scores 400 marks. How many questions did the student answer correctly?
Answer: C. 120 — ConceptWhen every question is attempted, let c be the number answered correctly and let N − c be the number answered incorrectly. The total score equals…
- A.
60
- B.
100
- C.
120
- D.
150
Show answer & explanation
Correct answer: C
Concept
When every question is attempted, let c be the number answered correctly and let N − c be the number answered incorrectly.
The total score equals (marks per correct answer) × c − (penalty per incorrect answer) × (N − c).
Application
Let c be the number of correct answers. Then the number of incorrect answers is 200 − c.
Using the marking scheme, 4c − (200 − c) = 400.
Simplifying gives 4c − 200 + c = 400, so 5c = 600 and c = 120.
Cross-check
For 120 correct answers, 80 answers are incorrect. The net score is 4 × 120 − 80 = 480 − 80 = 400.
Result
Therefore, the student answered 120 questions correctly.