# 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. If it is known that exactly half the students study English, then what is the maximum number of students who study all three?a)16b)18c)15d)17e)19Correct answer is option 'C'. Can you explain this answer? Related Test: Decision Making MCQ Quiz - 1

## UPSC Question Raj Kumari Aug 09, 2020
Solution: If exactly 50 students study English, the maximum values for Geography and History are 49 and 48. A maximum of 147 instances from 100 students. v The students who study exactly 3 is less than the number who study exactly 2, by trial and error we can say the maximum value of exactly 3 would be around 17. (17 x 3) + (18 x 2) + 19 + 20 + 21 = 147 instances from 17 + 18 + 19 + 20 + 21 =95 students v Number of students only add upto 95, maximum value of students who study exactly 3 is at most 16. (16 x 3) + (17 x 2) + 20 + 22 + 23 = 147 instances from 16 + 17 + 20 + 22 + 23 = 98 students We can see that 16 is also not possible and the solution would be 15: (15 x 3) + (17 x 2) + 21 + 23 + 24 = 147 instances from 15 + 17 + 21 + 23 + 24 = 100 students. Hence, option 3.