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In a group of 300 employees, 120 prefer coffee, 180 prefer tea, and 60 prefer both. How many employees prefer neither coffee nor tea?
40
50
60
70
60
Use the formula: Neither=TotalтИТ(Group┬аA+Group┬аBтИТBoth). Simply calculate 300тИТ(120+180тИТ60)=300тИТ240=60.
Total employees = 300, Employees preferring coffee (C) = 120, Employees preferring tea (T) = 180, Employees preferring both (C тИй T) = 60
n(CтИкT)=n(C)+n(T)тИТn(CтИйT)
Use the formula: Neither=TotalтИТ(Group┬аA+Group┬аBтИТBoth). Simply calculate 300тИТ(120+180тИТ60)=300тИТ240=60.
Students often add 120 and 180 (300) and subtract it from the total, forgetting to add back the intersection (60) which is counted twice in the simple sum.
Calculate Union of Sets
Use the Principle of Inclusion-Exclusion to find the number of people who like at least one beverage (CтИкT).
n(CтИкT)=120+180тИТ60=240
Calculate Neither group
Subtract the number of people who like at least one beverage from the total number of employees to find those who like neither.
Neither=300тИТ240=60
C is correct because the number of employees preferring neither is 300тИТ(120+180тИТ60)=60.
This logic is essential for data interpretation questions in competitive exams where you often subtract overlapping data from total sets to find remaining populations.