Pass–fail composition: The average of 120 students is 30. Passed students average 40 and failed students average 10. What is 25% of the number of passed students?
Aptitude
Average
Difficulty: Easy
Choose an option
Answer
Correct Answer: 20
Explanation
Introduction / Context:Convert overall and subgroup averages to totals to find the number who passed. Once the passed count is known, take one quarter (25%) as requested.
Given Data / Assumptions:
- Total students = 120
- Overall average = 30 → total = 3600
- Passed average = 40
- Failed average = 10
Concept / Approach:Let x be the number who passed. Then 40x + 10(120 - x) = 3600. Solve for x, then compute 0.25x.
Step-by-Step Solution:
40x + 1200 - 10x = 360030x = 2400 ⇒ x = 8025% of passed = 0.25 * 80 = 20Verification / Alternative check:Totals: passed = 80 * 40 = 3200; failed = 40 * 10 = 400; sum = 3600, consistent with the overall total.
Why Other Options Are Wrong:
- 30, 40, 15, 25: not equal to one quarter of 80.
Common Pitfalls:Using an unweighted average or forgetting to subtract x when computing the failed count 120 - x.
Final Answer:20