Engineering Board Exam Reviewer · Venn Diagrams · hard

In a club of 100 members, 80 swim, 75 cycle, and 70 run. What is the least possible number of members who do all three?

Answer

B. 25

Solution

The members who do NOT swim, cycle, or run number 20, 25, and 30. At most 20+25+30=75 members are missing at least one activity, so at least 100-75=25 do all three (attained when those groups do not overlap).

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