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In a group of 100 students, each student studies one or more subjects amongst P,C,M. The number of students studying M is more than that for P, which, in turn is more than that of C, which, in turn is more than the number of students studying exactly two subjects, which, in turn is more than those studying exactly three subjects. At least one student studied exactly three subjects.
Q.1 If it is known that exactly half the students study M, what is the maximum possible number of students that study all the three subjects?
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In a group of 100 students, each student studies one or more subjects ...
Analysis of the given information:
- The number of students studying M is more than P, which is more than C.
- The number of students studying exactly two subjects is more than those studying exactly three subjects.
- At least one student studied exactly three subjects.

Given: Half of the students study M.

Maximum possible number of students studying all three subjects:
- Since half of the students study M, there are 50 students studying M.
- Let's assume x students study all three subjects.
- The number of students studying exactly two subjects will be more than x.
- The number of students studying exactly three subjects will be less than x.

Calculating the maximum possible number of students studying all three subjects:
- Let's start with the assumption that all students studying exactly two subjects are studying M and P.
- This means the number of students studying exactly two subjects is equal to the number of students studying M and P but not C.
- So, if x students are studying all three subjects, the number of students studying exactly two subjects will be x.
- Thus, the number of students studying exactly two subjects = x.
- We know that the number of students studying exactly two subjects is more than those studying exactly three subjects.
- Therefore, the maximum possible value of x can be 24, considering the constraints given.
Therefore, the maximum possible number of students that study all three subjects is 24.
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In a group of 100 students, each student studies one or more subjects amongst P,C,M. The number of students studying M is more than that for P, which, in turn is more than that of C, which, in turn is more than the number of students studying exactly two subjects, which, in turn is more than those studying exactly three subjects. At least one student studied exactly three subjects. Q.1 If it is known that exactly half the students study M, what is the maximum possible number of students that study all the three subjects?
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