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2022 Math Kangaroo

Problem 2

Problem 2 · 2022 Math Kangaroo Medium
Number Theory divisionoff-by-one

How many positive three-digit numbers are divisible by 13?

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Answer: B — 69
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Hint 1 of 2
Count multiples of 13 up to 999, then remove those below 100.
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Hint 2 of 2
Use floor division: how many multiples of 13 are at most 999, and how many at most 99?
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Approach: count multiples by floor division
  1. Multiples of 13 up to 999: 999 / 13 = 76 (whole part).
  2. Multiples of 13 up to 99: 99 / 13 = 7.
  3. Three-digit ones: 76 − 7 = 69.
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