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UKMT Junior Mathematical Challenge, 2017

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The positive integers from 1 to 150 inclusive are placed in a 10 by 15 grid so that each cell contains exactly one integer. Then the multiples of 3 are given a red mark, the multiples of 5 are given a blue mark, and the multiples of 7 are given a green mark. How many cells have more than 1 mark?

(A) $10$ (B) $12$ (C) $15$ (D) $18$ (E) $19$

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