Venn Diagrams — Mains Questions

A survey was conducted among 200 residents of a colony regarding their preferences for three local newspapers: P, Q, and R. It was found that 100 read P, 120 read Q, and 80 read R. 50 read P and Q, 40 read Q and R, 30 read P and R. If 10 residents read none of the three newspapers, analyze the data to determine: (a) How many residents read all three newspapers? (b) How many residents read exactly one newspaper? (c) How many residents read at least two newspapers?

In a coaching institute, 60% of students passed in Quantitative Aptitude (QA), 50% in Logical Reasoning (LR), and 40% in English (E). 30% passed in QA and LR, 20% in LR and E, 15% in QA and E. If 5% of students passed in all three subjects, what percentage of students failed in all three subjects? Also, calculate the percentage of students who passed in exactly one subject.

In a survey of 180 households, 100 subscribe to Newspaper A, 80 to Newspaper B. If 20 households subscribe to neither, determine: (a) How many households subscribe to both Newspaper A and B? (b) How many households subscribe to only Newspaper A? (c) How many households subscribe to only Newspaper B?