Question

The average of four consecutive even numbers is 27. The largest of these numbers is _____ .

• A. 36
• B. 32
• C. 30
• D. 28

Hint:

When dealing with averages of consecutive numbers, use variables to represent the first number and build equations based on the number sequence.

Answer 1

The Correct Option is C

Let the four consecutive even numbers be \( x, x+2, x+4, x+6 \). The average of these numbers is 27, so: \[ \frac{x + (x+2) + (x+4) + (x+6)}{4} = 27 \] \[ \frac{4x + 12}{4} = 27 \] \[ 4x + 12 = 108 \] \[ 4x = 96 \] \[ x = 24 \] Thus, the four consecutive even numbers are 24, 26, 28, and 30. The largest number is 30.