In an objective competitive examination, each correct answer earns 4 marks and each wrong answer results in a penalty of 2 marks (i.e., 2 marks are deducted). A student attempts 150 questions and scores a total of 420 marks. How many of the student's answers were correct?

Introduction / Context:
This is an algebra-based aptitude question that asks you to reconstruct the number of correct answers from the total number of questions and the final score, given fixed marks for correct and incorrect responses. It tests your ability to set up and solve simple linear equations.

Given Data / Assumptions:

• Total questions attempted = 150.

• Marks for each correct answer = 4.

• Penalty for each wrong answer = 2 marks deducted (so -2 per wrong answer).

• Total score obtained by the student = 420 marks.

• Let the number of correct answers be C and the number of wrong answers be W. There are no unattempted questions in this scenario.

Concept / Approach:
We set up two equations: 1) A count equation based on the total number of questions: C + W = 150. 2) A marks equation based on scoring rules: 4C - 2W = 420. Solving this system of equations gives us the values of C and W. We then pick the option that matches the correct C value.

Step-by-Step Solution:
Step 1: Let C = number of correct answers, W = number of wrong answers. Step 2: Since 150 questions were attempted, we have: C + W = 150. Step 3: Each correct gives +4 marks, and each wrong gives -2 marks. The total score is 420 marks. So: 4C - 2W = 420. Step 4: From the first equation, W = 150 - C. Step 5: Substitute into the marks equation: 4C - 2(150 - C) = 420. Step 6: Simplify: 4C - 300 + 2C = 420 ⇒ 6C - 300 = 420 ⇒ 6C = 720 ⇒ C = 720 / 6 = 120. Step 7: Thus, the student answered 120 questions correctly.

Verification / Alternative check:
If C = 120, then W = 150 - 120 = 30. Marks from correct answers = 120 * 4 = 480. Penalty from wrong answers = 30 * 2 = 60. Net marks = 480 - 60 = 420, which matches the given total. Therefore the solution is consistent.

Why Other Options Are Wrong:
Option A (145 correct) would imply only 5 wrong answers; the resulting marks would be 145 * 4 - 5 * 2 = 580 - 10 = 570, not 420.
Option B (138 correct) gives 12 wrong answers; marks = 138 * 4 - 12 * 2 = 552 - 24 = 528, again incorrect.
Option C (125 correct) gives 25 wrong answers; marks = 125 * 4 - 25 * 2 = 500 - 50 = 450, which still does not match 420.

Common Pitfalls:
A common mistake is to forget that wrong answers subtract marks instead of earning zero, leading to a wrong equation like 4C = 420 instead of 4C - 2W = 420. Another error is to mis-handle signs when substituting W = 150 - C. Always write down both equations clearly and solve step by step to avoid arithmetic slips.

Final Answer:
The number of correct answers given by the student is 120.