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percentages in a survey , senior version

Source: 2023 South Russian Girls MO - Assara Seniors p1

March 1, 2024
algebra

Problem Statement

A survey of participants was conducted at the Olympiad. 90% 90\% of the participants liked the first round, 60%60\% of the participants liked the second round, 90%90\% of the participants liked the opening of the Olympiad. Each participant was known to enjoy at least two of these three events. Determine the percentage of participants who rated all three events positively.