2015/16 AHSMC Part 1 Problem 9

Problem 9 of 16

In a class with $20$ students, $14$ wear glasses, $15$ wear braces, $17$ wear ear-rings and $18$ wear wigs. What is the minimum number of students in this class who wear all four items?

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Solution

We have $6$ students not wearing glasses, $5$ students not wearing braces, $3$ students not wearing ear-rings and $2$ students not wearing wigs. Even if these are $6+5+3+2=16$ different students, we still have $20-16=4$ students wearing all four items. The answer is (A).

University of Alberta

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