Question

If the average (arithmetic mean) of five consecutive integers is 25, what is the largest of these integers?

• A. 25
• B. 26
• C. 27
• D. 28
• E. 29

Hint:

For consecutive integers, the average is always the middle number. The largest integer will be the middle number plus half of the total number of integers minus one.

Answer 1

The Correct Option is C

Let the five consecutive integers be \( x - 2, x - 1, x, x + 1, x + 2 \), where \( x \) is the middle integer. The average (mean) of these integers is given by: \[ \frac{(x - 2) + (x - 1) + x + (x + 1) + (x + 2)}{5} = 25. \] Simplify the numerator: \[ \frac{(x - 2) + (x - 1) + x + (x + 1) + (x + 2)}{5} = \frac{5x}{5}. \] Thus, we have: \[ \frac{5x}{5} = 25. \] Now, solve for \( x \): \[ x = 25. \] Therefore, the five consecutive integers are \( 23, 24, 25, 26, 27 \), and the largest integer is \( \boxed{27} \).