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In a group of 100 students, 60 like Mathematics, 40 like Physics, and 20 like both. How many students like neither subject?
10
20
30
40
20
To find the number of students who like neither subject, we apply the principle of inclusion-exclusion. The total number of students liking at least one subject is 60 plus 40 minus 20, which equals 80. Subtracting this from the total group of 100 students gives 20 students who like neither.
To find the number of students who like neither subject, we apply the principle of inclusion-exclusion. The total number of students liking at least one subject is 60 plus 40 minus 20, which equals 80. Subtracting this from the total group of 100 students gives 20 students who like neither.
Set theory and quantitative aptitude form foundational components evaluated in recruitment exams conducted by the Railway Recruitment Board (RRB) and Staff Selection Commission (SSC).
Total students in the group equal 100
Number of students liking Mathematics or Physics or both is calculated using union and intersection formulas
Students liking neither subject represent the complement of the union set
Venn diagrams provide a visual approach to organize overlapping categories of data efficiently.
Option A is incorrect as it results from calculation errors.
Option B is correct because 100 minus 80 equals 20.
Option C and Option D miscalculate the intersection overlap.
B is correct тАФ 20 students like neither subject as calculated through the principle of inclusion-exclusion.
Regular practice of set theory identities will directly enhance your performance in both quantitative aptitude and logical reasoning sections of competitive exams.