Problem 3 · 2020 Math Kangaroo
Medium
Algebra & Patterns
difference-of-squares
How many integers are there between \(2020.9^2\) and \(2018.9 \times 2022.9\)?
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Answer: E — 4
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Hint 1 of 2
Compare 2020.9² with (2020.9−2)(2020.9+2).
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Hint 2 of 2
Their difference is a small fixed number — count the whole numbers in that gap.
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Approach: difference of two close products
- Write 2018.9×2022.9 = (2020.9−2)(2020.9+2) = 2020.9² − 4.
- So the two values differ by exactly 4, with 2020.9² the larger.
- An open interval of length 4 between two non-integers contains exactly 4 integers.
Mark:
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