Maths Olympiad Prep

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Problem 29

Combinatorics Difficulty 1.0 Find the answer CEMC Gauss (Grade 8) · Canada · 2005

Fifty students were surveyed about their participation in hockey and baseball. The results of the survey were:

3333 students played hockey

2424 students played baseball

88 students played neither hockey nor baseball

How many of the students surveyed played both hockey and baseball?

(A) 11 (B) 77 (C) 99 (D) 1515 (E) 1616

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Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project. Solutions are the publisher's, linked not copied.