In seven given numbers, the average of first four numbers is 4 and that of…
2024
In seven given numbers, the average of first four numbers is 4 and that of last four numbers is also 4. If the average of these seven numbers is 3, the fourth number is ?
- A.
3
- B.
4
- C.
7
- D.
11
Attempted by 9 students.
Show answer & explanation
Correct answer: D
Key idea: use the sums of the first four, the last four, and the total of seven to solve for the fourth number.
Let the seven numbers be a, b, c, d, e, f, g.
First four average 4 ⇒ a + b + c + d = 4 × 4 = 16.
Last four average 4 ⇒ d + e + f + g = 4 × 4 = 16.
All seven average 3 ⇒ total a + b + c + d + e + f + g = 7 × 3 = 21.
Add the first two equations: a + b + c + 2d + e + f + g = 32. Subtract the total sum equation (21) to get d = 32 − 21 = 11.
Answer: The fourth number is 11.