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In a survey of 500 people, 250 like coffee, 300 like tea, and 100 like both. How many people like neither coffee nor tea?
50
100
150
200
50
To solve this problem, use the principle of inclusion-exclusion for sets: n(A U B) = n(A) + n(B) - n(A тИй B). Here, 250 + 300 - 100 = 450 people like either tea, coffee, or both, leaving 50 people who like neither out of the total 500.
To solve this problem, use the principle of inclusion-exclusion for sets: n(A U B) = n(A) + n(B) - n(A тИй B). Here, 250 + 300 - 100 = 450 people like either tea, coffee, or both, leaving 50 people who like neither out of the total 500.
Set theory foundations are essential for Data Interpretation and Logical Reasoning sections of RRB and SSC examinations, which draw from the broader domain of Applied Mathematics standardized by the National Board for Higher Mathematics (NBHM) in India.
The Principle of Inclusion-Exclusion is the fundamental rule for solving Venn diagram problems involving overlapping sets.
The total number of people is defined by the Universal set, while those who like neither represent the complement of the union of the two sets.
Railway Recruitment Board (RRB) exams frequently test these mathematical logical models to evaluate analytical aptitude.
Number of people who like only coffee = 250 - 100 = 150.
Number of people who like only tea = 300 - 100 = 200.
Total people liking at least one beverage = 150 (only coffee) + 200 (only tea) + 100 (both) = 450.
Option B (100) results from incorrectly subtracting the intersection only once without considering the total population count correctly.
A is correct тАФ 50 people like neither coffee nor tea as calculated by subtracting the union of tea and coffee lovers (450) from the total surveyed population (500).
Mastering set operations is directly applicable to solving data sufficiency and statistics questions in the Data Interpretation section of competitive exams like RRB Technician and NTPC.