The average of 15 quantities is 7. The average of 12 of them is 8. What is the…
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The average of 15 quantities is 7. The average of 12 of them is 8. What is the average of the remaining three numbers ?
- A.
3
- B.
6
- C.
5
- D.
3.5
Show answer & explanation
Correct answer: A
Concept: For a group of items, the total sum equals count × average (Sum = n × Average). When a whole group is split into two parts, the sum of the whole equals the sum of the parts — so a missing part's sum can be recovered by subtracting the known part's sum from the whole's sum, and its average by dividing that sum by its count.
Application:
Total sum of all 15 quantities = 15 × 7 = 105.
Sum of the 12 quantities = 12 × 8 = 96.
Sum of the remaining three quantities = 105 − 96 = 9.
Average of the remaining three quantities = 9 ÷ 3 = 3.
Cross-check:
Adding the parts back together confirms the total: 96 + 9 = 105, and 105 ÷ 15 = 7, matching the given overall average — so the remaining-group average of 3 is consistent.
