Question

In an examination, a candidate scores 2 marks for every correct answer and loses 1 mark for every wrong answer. A candidate attempts all the 100 questions and scores 56 marks. How many questions did he answer correctly?

• A. 52
• B. 48
• C. 60
• D. 56

Hint:

Using the elimination method (adding/subtracting equations) is usually faster for these types of problems.

Answer 1

The Correct Option is A

Concept: This is a system of linear equations problem.

Step 1: Defining variables.
Let $x$ be correct answers and $y$ be wrong answers. Equation 1 (Total questions): $x + y = 100$. Equation 2 (Total marks): $2x - 1y = 56$.

Step 2: Solving the system.
Add the equations: $(x + y) + (2x - y) = 100 + 56 \Rightarrow 3x = 156$. equation x = 156 / 3 = 52 equation center 52 center