In an examination scoring system, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If the student attempts all 60 questions and secures a total of 130 marks, how many questions were answered correctly?

Introduction / Context:
This question tests basic algebra and logical reasoning using a simple exam scoring rule. The student earns marks for correct answers and loses marks for wrong ones while attempting every question. Problems like this appear frequently in quantitative aptitude and reasoning sections, and they help evaluate your ability to set up equations based on word descriptions of scoring systems.

Given Data / Assumptions:

• Total number of questions attempted = 60.
• Marks for each correct answer = +4.
• Marks lost for each wrong answer = -1.
• Total marks obtained by the student = 130.
• Let the number of correct answers be C and wrong answers be W.
• Since all questions are attempted, C + W = 60.

Concept / Approach:
We convert the scoring rule into an algebraic expression. The total marks T are: T = 4 * C - 1 * W. Because C + W = 60, we can express W as 60 - C and substitute into the total marks expression. This yields a single linear equation in C, which we solve to determine the number of correct answers. These linear equations are foundational in many aptitude topics.

Step-by-Step Solution:
Step 1: Write the total questions equation: C + W = 60. Step 2: Express W in terms of C: W = 60 - C. Step 3: Write the total marks equation: T = 4C - W. Step 4: Given total marks T = 130, so 130 = 4C - W. Step 5: Substitute W = 60 - C into the marks equation: 130 = 4C - (60 - C). Step 6: Simplify: 130 = 4C - 60 + C = 5C - 60. Step 7: Rearrange to solve for C: 5C = 130 + 60 = 190. Step 8: Divide by 5: C = 190 / 5 = 38. Step 9: Therefore, the student answered 38 questions correctly.

Verification / Alternative check:
Compute W and total marks to confirm. Wrong answers: W = 60 - C = 60 - 38 = 22. Marks from correct answers: Marks_correct = 4 * 38 = 152. Penalty from wrong answers: Marks_wrong = -1 * 22 = -22. Total marks: T = 152 - 22 = 130. This matches the given total, which verifies that 38 correct answers is the right count.

Why Other Options Are Wrong:
35, 40, 42, and 36 all lead to different totals when you compute 4 * correct minus 1 * wrong with 60 questions. None of those totals equals 130, so those options do not satisfy the scoring conditions.

Common Pitfalls:
Students sometimes forget that all questions are attempted and mistakenly use only one equation, or they mix up the signs in the total marks formula. Others try trial and error with the options rather than forming the correct linear equation. Writing both the total questions equation and the total marks equation clearly, then substituting and solving systematically, is the safest method.

Final Answer:
The student answered 38 questions correctly.