Group QuestionAnswer the following question based on the information given below.There is a group of 100 students. They study one or more of the 3 subjects among Geography, History and English. The number of students studying English is more than the number of students studying Geography, which, in turn, is more than the number of students who study History, which in turn is more than the number of students who study exactly 2 out of the 3 subjects, which in turn,is more than the number of students who study all 3 subjects. It is known that at least one student studies all 3 subjects.Q. What is the maximum number of students who study History? a)79b)80c)72d)82e)83Correct answer is option 'D'. Can you explain this answer?

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Answer the following question based on the information given below.

There is a group of 100 students. They study one or more of the 3 subjects among Geography, History and English. The number of students studying English is more than the number of students studying Geography, which, in turn, is more than the number of students who study History, which in turn is more than the number of students who study exactly 2 out of the 3 subjects, which in turn, is more than the number of students who study all 3 subjects. It is known that at least one student studies all 3 subjects.

Q. What is the maximum number of students who study History?

a)
79
b)
80
c)
72
d)
82
e)
83

Correct answer is option 'D'. Can you explain this answer?

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Solution: The number of students who study English is greater than those who study Geography, which is greater than those who study History, and the total of all students is equal to 100,
To maximise the students who study history, we only need to compare students who study exactly 2 and who study exactly 3, as all these will come under the individual subjects (students studying exactly 1 subject will be 0).
This can be done by assigning 49 students to all 3 subjects and assigning 51 (18,17,16), which should be distributed as equally as possible, to students studying exactly 2 subjects.
The number of students who study history is the least (when compared to those studying English and Geography), the number of students studying history = 49 + 17 + 16 = 82
Hence, option 4.

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Group QuestionAnswer the following question based on the information given below.There is a group of 100 students. They study one or more of the 3 subjects among Geography, History and English. The number of students studying English is more than the number of students studying Geography, which, in turn, is more than the number of students who study History, which in turn is more than the number of students who study exactly 2 out of the 3 subjects, which in turn,is more than the number of students who study all 3 subjects. It is known that at least one student studies all 3 subjects.Q. What is the maximum number of students who study History? a)79b)80c)72d)82e)83Correct answer is option 'D'. Can you explain this answer?

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