Problem 20 · 2023 Math Kangaroo
Medium
Algebra & Patterns
Number Theory
arithmetic-seriesdigit-sum
The sum of 2023 consecutive integers is 2023. What is the sum of the digits of the biggest of those numbers?
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Answer: A — 4
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Hint 1 of 2
The sum of an odd number of consecutive integers equals the middle term times how many there are.
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Hint 2 of 2
Find the middle value, step out to the biggest term, then add its digits.
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Approach: use the middle-term formula for consecutive integers
- For 2023 consecutive integers, the sum equals 2023 times the middle term.
- Since the sum is 2023, the middle term is 1.
- The biggest term is 1 + 1011 = 1012, whose digit sum is 1+0+1+2 = 4.
- So the answer is 4 (A).
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