Recovering a missing value from partial averages: The average of nine numbers is 50. The average of the first five is 54 and the average of the last three is 52. Find the sixth number.
Aptitude
Average
Difficulty: Medium
Choose an option
Answer
Correct Answer: 24
Explanation
Introduction / Context:With the grand average and two block averages known, the single missing term equals the remainder after subtracting the two block totals from the grand total.Given Data / Assumptions:
- Average of 9 = 50
- Average of first 5 = 54
- Average of last 3 = 52
Concept / Approach:Translate averages to totals, then compute the sixth term: total9 - total first5 - total last3.Step-by-Step Solution:
Total of 9 = 9 * 50 = 450Total of first 5 = 5 * 54 = 270Total of last 3 = 3 * 52 = 156Sixth number = 450 - (270 + 156) = 24Verification / Alternative check:Recompose totals to confirm the grand total is maintained.Why Other Options Are Wrong:
- 34, 44, 30: Do not balance the totals to give a grand average of 50.
Common Pitfalls:Confusing positions or mistakenly subtracting from the wrong block sum.Final Answer:
24