2000 PMWC Problems/Problem I5

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In a language college, $72\%$ students can speak Chinese, $65\%$ students can speak English, and $10\%$ students can speak neither Chinese nor English. Find the percentage of students who can speak both Chinese and English.


Since 10% of the students speak neither language, 90% must speak at least one language. Since 72% speak Chinese and 65% can speak English, we know, by Principle of Inclusion-Exclusion, that 72+65-90=47% of the students speak both languages.


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