Question

The average of five numbers is 21. If one number is excluded, their average is 19. What is the excluded number?

• A. 27
• B. 29
• C. 31
• D. 25

Hint:

To find the excluded number, calculate the difference in the total sum before and after excluding a number.

Answer 1

The Correct Option is B

Let the five numbers be \( x_1, x_2, x_3, x_4, x_5 \). The average of these five numbers is 21, so the sum of these five numbers is: \[ \frac{x_1 + x_2 + x_3 + x_4 + x_5}{5} = 21 \quad \Rightarrow \quad x_1 + x_2 + x_3 + x_4 + x_5 = 105 \] When one number is excluded, the average of the remaining four numbers is 19, so their sum is: \[ \frac{x_1 + x_2 + x_3 + x_4}{4} = 19 \quad \Rightarrow \quad x_1 + x_2 + x_3 + x_4 = 76 \] The excluded number is the difference between the sum of the five numbers and the sum of the four numbers: \[ x_5 = 105 - 76 = 29 \]