Question

In a set of three numbers, the average of the first two numbers is 7, the average of the last two numbers is 10, and the average of the first and the last numbers is 14. What is the average of the three numbers?

• A. 29/4
• B. 31/3
• C. 25/4
• D. 37/3

Answer 1

Answer:

B. 31/3

Solution: Given: The set of three numbers, the average of the first two numbers is 7, the average of the last two numbers is 10, and the average of the first and last numbers is 14. Concept: Average = (Sum of all observation/Number of observation) Calculation: Let the set of three number is respectively a, b, and c. According to the question The sum of first number is ⇒ a + b = 2 × 7 ⇒ a + b = 14 ----(1) The sum of the last two number is ⇒ b + c = 2 × 10 ⇒ b + c = 20 ----(2) The sum of the first and last number is ⇒ c + a = 2 × 14 ⇒ c + a = 28 ----(3) Add eq. (1), (2) and (3) ⇒ 2(a + b + c) = 14 + 20 + 28 ⇒ (14 + 20 + 28)/2 ⇒ 62/2 ⇒ 31 So, The average of the three number is ⇒ 31/3 ∴ The required average is 31/3. Short approach: The average of the three numbers is ⇒ (7 + 10 + 14)/3 ⇒ 31/3 ∴ The required average is 31/3.