The sum of 2023 consecutive integers is 2023. What is the sum of digits of the largest of these integers?
A 4 B 5 C 6 D 7 E 8
A
Let the middle integer of the list be n. Since the 2023 digits are consecutive, the complete list is n − 1011, n − 1010, ..., n − 1, n, n + 1, ..., n + 1010, n + 1011 with sum 2023n. Therefore 2023n = 2023 and so n = 1. Hence the largest integer of the list is 1 + 1011 = 1012, which has digit sum 4.
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