Problem 10 · 2010 Math Kangaroo
Medium
Algebra & Patterns
arithmetic-series
The sum of the first hundred positive odd numbers is subtracted from the sum of the first hundred positive even numbers. What is the result?
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Answer: C — 100
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Hint 1 of 2
Line up the even and odd numbers term by term.
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Hint 2 of 2
Each even number is exactly one more than the matching odd number.
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Approach: pair even with odd term-by-term
- Pair 2 with 1, 4 with 3, 6 with 5, ...: each even minus its odd partner is 1.
- There are 100 such pairs, so the difference is 100×1 = 100.
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