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Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

A bag contains only red marbles and green marbles. For every five marbles that are chosen, at least one will be red. For every six marbles that are chosen, at least one will be green. What is the largest number of marbles the bag can contain?

(A) $11$ (B) $10$ (C) $9$ (D) $8$ (E) $7$

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