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In a survey of 350 students in a college, 150 students were found to be taking tea and 225 taking coffee, 100 were taking both tea and coffee. Find how many students were taking neither tea nor coffee?
85
65
75
55
75
Use the Principle of Inclusion-Exclusion directly: Subtract the intersection from the sum of individual groups and deduct this result from the universal set total.
Total students (U) = 350, Students taking tea (T) = 150, Students taking coffee (C) = 225, Students taking both (T \cap C) = 100.
n(T∪C)=n(T)+n(C)−n(T∩C)
Use the Principle of Inclusion-Exclusion directly: Subtract the intersection from the sum of individual groups and deduct this result from the universal set total.
Students often add 150 and 225 but forget to subtract the 100 who were counted twice, or they forget to subtract the union from the total universal set.
Calculate the number of students taking at least one beverage
Apply the union formula for sets T and C to find students who drink either tea, coffee, or both: n(T∪C)=150+225−100.
n(T∪C)=150+225−100=275
Calculate students taking neither
Subtract the union of T and C from the total number of students in the college: 350−275.
350−275=75
C is correct because the number of students taking neither tea nor coffee is calculated as 350 - 275 = 75.
This set theory logic is fundamental for solving Data Interpretation questions involving Venn diagrams in exams like CAT, GMAT, and bank PO exams.