The average of fifteen numbers is 45. The average of the first six numbers is…
2022
The average of fifteen numbers is 45. The average of the first six numbers is 42.5 and the average of the last six numbers is 44.5. What is the average of the remaining three numbers, out of which two numbers are 41 and 46?
Answer: D. 51 — ConceptFor any group of n values, average = total sum ÷ n; equivalently, total sum = n × average. When a collection is split into disjoint groups, the total…
- A.
48
- B.
47
- C.
45
- D.
51
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Show answer & explanation
Correct answer: D
Concept
For any group of n values, average = total sum ÷ n; equivalently, total sum = n × average.
When a collection is split into disjoint groups, the total of the unaccounted group equals the grand total minus the totals of the known groups.
Application
The total of all fifteen numbers is 15 × 45 = 675.
The total of the first six numbers is 6 × 42.5 = 255.
The total of the last six numbers is 6 × 44.5 = 267.
The total of the remaining three numbers is 675 − 255 − 267 = 153.
Their average is 153 ÷ 3 = 51.
Cross-check
The two stated remaining values total 41 + 46 = 87, so the third value is 153 − 87 = 66. Then (41 + 46 + 66) ÷ 3 = 153 ÷ 3 = 51, confirming the result.
Therefore, the average of the remaining three numbers is 51.