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

There are twenty students in a class. Some of them sit in pairs so that exactly one third of the boys sit with a girl, and exactly one half of the girls sit with a boy. How many boys are there in the class?

(A) $9$ (B) $12$ (C) $15$ (D) $16$ (E) $18$

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