The average of 7 numbers is 29. The average of first three of them is 23 and…
20172017
The average of 7 numbers is 29. The average of first three of them is 23 and the last three of them is 42. Then the fourth number is:
- A.
8
- B.
9
- C.
10
- D.
12
Attempted by 142 students.
Show answer & explanation
Correct answer: A
Concept
The average of a set of numbers equals their total sum divided by how many numbers there are, so Sum = Average × Count. When the same numbers are split into overlapping or adjacent groups, the sum of every individual number must still add up to the one grand total — a missing term is found by subtracting all the known partial sums from that total.
Application
Total of all 7 numbers = 29 × 7 = 203.
Sum of the first three numbers = 23 × 3 = 69.
Sum of the last three numbers = 42 × 3 = 126.
The first three, the fourth number, and the last three together make all seven, so: 69 + (fourth) + 126 = 203.
69 + 126 = 195, therefore fourth = 203 − 195 = 8.
Cross-check
Add the parts back: 69 + 8 + 126 = 203, which equals 29 × 7. The grand total is reproduced exactly, so the fourth number is 8.