Question:
If the average (arithmetic mean) of five consecutive integers is 25, what is the largest of these integers?
If the average (arithmetic mean) of five consecutive integers is 25, what is the largest of these integers?
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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.
Updated On: Oct 6, 2025
- 25
- 26
- 27
- 28
- 29
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The Correct Option is C
Solution and Explanation
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 \( \boxed{27} \).
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