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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 minimum number of students who study  English? 
  • a)
    37
  • b)
    34
  • c)
    36
  • d)
    35
  • e)
    32
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
There is a group of 100 students. They study one or more of the 3 subj...
Solution: The number of students studying English is given to be greater than the number of students studying either of the other two subjects and also greater than those studying exactly 2 or exactly 3 subjects.
To find the minimum number of students who study English, assign minimum values for those who study all the three (1) and those who study exactly 2 (keep students studying English and Geography as 2 and the other two sharing as 0) and distribute the remaining nearly equally (33 for English, 32 each for other subjects).
This is done to keep English as the highest number.
The minimum number of students who study English = 33 + 2 + 1 = 36
Hence, option 3.
This question is part of UPSC exam. View all CAT courses
Most Upvoted Answer
There is a group of 100 students. They study one or more of the 3 subj...
Minimum Number of Students Studying English:
Students can study one or more of the 3 subjects: Geography, History, and English. Let's determine the minimum number of students studying English based on the given conditions.
Students studying English > Students studying Geography > Students studying History
Students studying exactly 2 subjects > Students studying all 3 subjects

Minimum Number of Students Studying All 3 Subjects:
Since it is known that at least one student studies all 3 subjects, the minimum number of students studying all 3 subjects is 1.

Minimum Number of Students Studying Exactly 2 Subjects:
The number of students studying exactly 2 out of the 3 subjects must be more than the number of students studying all 3 subjects. So, the minimum number of students studying exactly 2 subjects is 2.

Minimum Number of Students Studying History:
The number of students studying History is less than the number of students studying exactly 2 subjects. So, the minimum number of students studying History is 1.

Minimum Number of Students Studying Geography:
The number of students studying Geography is less than the number of students studying History. So, the minimum number of students studying Geography is 1.

Minimum Number of Students Studying English:
The number of students studying English is more than the number of students studying Geography. Since the minimum number of students studying Geography is 1, the minimum number of students studying English is 1 + 1 + 1 + 1 = 4.
Therefore, the minimum number of students studying English is 4, which is more than the given options. This indicates that there might be a mistake in the provided answer choices.
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