The arithmetic mean of three numbers is 147. If the mean of the first two…
2025
The arithmetic mean of three numbers is 147. If the mean of the first two numbers is 141, what is the third number?
- A.
18
- B.
159
- C.
19
- D.
158
Attempted by 2 students.
Show answer & explanation
Correct answer: B
Concept
The arithmetic mean of a group of numbers equals the sum of the numbers divided by how many there are, so sum = mean × count. If the sum of an entire group and the sum of a part of that group are both known, the remaining member(s) equal the difference between the two sums.
Application
Total sum of all three numbers = mean × count = 147 × 3 = 441.
Sum of the first two numbers = mean × count = 141 × 2 = 282.
Third number = total sum − sum of first two numbers = 441 − 282 = 159.
Cross-check
Adding the third number back to the first two numbers' sum reproduces the total: 282 + 159 = 441, and 441 / 3 = 147, matching the given overall mean.