Maths Olympiad Prep

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Problem 335

Combinatorics Difficulty 2.0 Find the answer CEMC Gauss (Grade 8) · Canada · 2004

There are 1313 trees on one side of the street on Trina's way from her house to school. Today, on her way to school, Trina put a chalk mark on every other tree, starting with the first she passed. When she goes home from school, she will put a chalk mark on every third tree, again starting with the first one she passes. By the time Trina arrives at home, how many of the 1313 trees will not have a chalk mark on them?

(A) 66 (B) 44 (C) 88 (D) 22 (E) 77

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