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Three-set Venn counting with given totals or bounds

This type of question, asked 4 times: 2021 Paper 18, 11 Apr 2023, 30 Jan 2024, 4 Apr 2024. All 4 questions below, oldest first.

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  1. Question 1

    2021 Paper 18

    70
    Out of all the patients in a hospital 89%89\% are found to be suffering from heart ailment and 98%98\% are suffering from lungs infection. If K%K\% of them are suffering from both ailments, then KK can not belong to the set:

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  2. Question 2

    11 Apr 2023

    69
    An organization awarded 48 medals in event ' AA ', 25 in event ' BB ' and 18 in event ' CC '. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events?

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  3. Question 3

    30 Jan 2024

    81
    A group of 40 students appeared in an examination of 3 subjects - Mathematics, Physics & Chemistry. It was found that all students passed in at least one of the subjects, 20 students passed in Mathematics, 25 students passed in Physics, 16 students passed in Chemistry, at most 11 students passed in both Mathematics and Physics, at most 15 students passed in both Physics and Chemistry, at most 15 students passed in both Mathematics and Chemistry. The maximum number of students passed in all the three subjects is

  4. Question 4

    4 Apr 2024

    82
    In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied Mathematics; at least 85 and at most 95 studied Physics; at least 75 and at most 90 studied Chemistry; 30 studied both Physics and Chemistry; 50 studied both Chemistry and Mathematics; 40 studied both Mathematics and Physics and 10 studied none of these subjects. Let mm and nn respectively be the least and the most number of students who studied all the three subjects. Then m+nm + n is equal to