The average of 7 numbers is 30. The average of the first three of them is 23…
2017
The average of 7 numbers is 30. The average of the first three of them is 23 and the last three of them is 42. Then the fourth number is:
- A.
15
- B.
25
- C.
20
- D.
10
Show answer & explanation
Correct answer: A
Concept
The sum of a set of numbers equals its average multiplied by how many numbers there are (Sum = Average x Count). When a whole group is split into adjoining sub-groups, a single missing value can be recovered by subtracting the sub-group sums from the total sum.
Application
Seven numbers are split as: the first three, the single fourth number, and the last three. Compute each known sum, then isolate the fourth:
Total of all 7 numbers = 30 x 7 = 210.
Sum of the first three = 23 x 3 = 69.
Sum of the last three = 42 x 3 = 126.
Fourth number = Total - (first three) - (last three) = 210 - 69 - 126 = 15.
Cross-check
Add the parts back: 69 (first three) + 15 (fourth) + 126 (last three) = 210, and 210 / 7 = 30, which matches the given overall average. So the fourth number is 15.