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school offers three subjects: Mathematics, Art and Science

Source: New Zealand MO 2021 Round 1 p1

September 20, 2021
combinatorics

Problem Statement

A school offers three subjects: Mathematics, Art and Science. At least 80%80\% of students study both Mathematics and Art. At least 80%80\% of students study both Mathematics and Science. Prove that at least 80%80\% of students who study both Art and Science, also study Mathematics.
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