A test has 200 questions. A student gains 4 marks for each correct answer and loses 1 mark for each wrong answer. He attempted all 200 questions and scored exactly 200 marks. How many questions did he answer correctly?

Introduction: This is a linear system based on totals: the count of questions and the score. With all questions attempted, correct and wrong add to 200. Scoring creates a second linear relation to solve for the number correct.

Given Data / Assumptions:

• Total questions attempted = 200.
• +4 marks for correct; −1 mark for wrong.
• Total score = 200.

Concept / Approach: Let c = number correct and w = number wrong. Then c + w = 200 and 4c − w = 200. Solve simultaneously.

Step-by-Step Solution:

Verification / Alternative check: Then w = 120. Score = 4*80 − 120 = 320 − 120 = 200, matches perfectly.

Why Other Options Are Wrong: Substituting 82, 68, 60, 88 into the equations fails to produce a total of 200 marks with 200 attempts.

Common Pitfalls: Forgetting that all questions were attempted; c + w must equal 200.

Final Answer: 80