Correct Answer:
C. 129
The correct answer is C: 129. To solve this problem, we need to find the five consecutive odd integers whose sum is 625. A straightforward approach is to determine the average of these numbers, which will also be the middle number since there's an odd count of integers.
- Divide the sum by the number of integers: 625 ÷ 5 = 125.
- This means the middle odd integer is 125.
- Since they are consecutive odd integers, they will be symmetrical around 125. The five consecutive odd integers are therefore:
- 125 - 4 = 121
- 125 - 2 = 123
- 125 (the middle number)
- 125 + 2 = 127
- 125 + 4 = 129
- The largest of these five consecutive odd integers is 129.
Let's analyze the incorrect options:
- Option A: 125 is incorrect because this is the middle integer of the sequence, not the largest. While it's a crucial step in finding the solution, it's not the final answer to the question asked.
- Option B: 127 is incorrect because it is the second largest integer in the sequence, not the absolute largest. It is one step below the correct largest integer.
- Option D: 131 is incorrect. If 131 were the largest integer, the sequence would be 123, 125, 127, 129, 131. The sum of these numbers would be 5 × 127 (the middle number) = 635, which is not 625.