Question

An examination consists of 160 questions. One mark is given for every correct option. If a 1/4 mark is deducted for each wrong option and a half mark is deducted for every unanswered question, the person scores 79. If half a mark is deducted for every wrong option and 1/4 mark is deducted for every unanswered question, the person scores 76. Find the number of correct answers he wrote?

• A. 80
• B. 100
• C. 120
• D. 140

Hint:

Using substitution method for three variables often results in simpler arithmetic than elimination.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept:
This problem involves solving a system of linear equations with three variables representing correct (C), wrong (W), and unanswered (U) questions.

Step 2: Detailed Explanation:
1. Total questions: \( C + W + U = 160 \).
2. Equation 1: \( C - 0.25W - 0.5U = 79 \)
3. Equation 2: \( C - 0.5W - 0.25U = 76 \)
4. Subtract Eq 2 from Eq 1:
- \( (C - 0.25W - 0.5U) - (C - 0.5W - 0.25U) = 79 - 76 \)
- \( 0.25W - 0.25U = 3 \implies W - U = 12 \implies W = U + 12 \)
5. Substitute \( W = U + 12 \) into \( C + W + U = 160 \):
- \( C + (U + 12) + U = 160 \implies C + 2U = 148 \implies U = (148 - C) / 2 \)
6. Substitute into Eq 1:
- \( C - 0.25(U+12) - 0.5U = 79 \)
- \( C - 0.25U - 3 - 0.5U = 79 \implies C - 0.75U = 82 \)
- \( C - 0.75((148-C)/2) = 82 \)
- \( C - 55.5 + 0.375C = 82 \implies 1.375C = 137.5 \implies C = 100 \).

Step 3: Final Answer:
The number of correct answers is 100.