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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.
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.
Most Upvoted Answer
There is a group of 100 students. They study one or more of the 3 subj...
Understanding the Problem
In this scenario, we have 100 students studying Geography, History, and English with specific relationships among the numbers of students in each category:
- Students studying English (E) > Students studying Geography (G) > Students studying History (H)
- Students studying exactly 2 subjects (X) < students="" studying="" all="" 3="" subjects="" (a)="" -="" at="" least="" one="" student="" studies="" all="" three="" subjects="" (a="" ≥="" 1)="" />Establishing Relationships
Using the given inequalities, we can denote:
- E > G > H > X > A
Let’s assign variables for each group:
- Let A = 1 (minimum number of students studying all three subjects)
- Let X = 2 (minimum for students studying exactly two subjects)
- Then, we have G > H > 2 > 1
Calculating Minimum Values
Assuming G = 3, we can estimate:
- H must be less than G, so H = 2
- Now, E must be greater than G, so E must be at least 4
Summing these values:
- A = 1
- X = 2
- H = 2
- G = 3
- E = 4
This gives:
1 + 2 + 2 + 3 + 4 = 12 students.
Maximizing English
To ensure E, G, and H maintain their relationships while maximizing E, we can continue this process:
If G = 35, then H must be less than 35, say H = 34, and X = 33. This can be maintained with A = 1.
- So, E must be at least 36 to maintain the hierarchy.
Conclusion
Thus, the minimum number of students studying English, considering the relationships and constraints, is 36. Therefore, the correct answer is option 'C'.
In this scenario, we have 100 students studying Geography, History, and English with specific relationships among the numbers of students in each category:
- Students studying English (E) > Students studying Geography (G) > Students studying History (H)
- Students studying exactly 2 subjects (X) < students="" studying="" all="" 3="" subjects="" (a)="" -="" at="" least="" one="" student="" studies="" all="" three="" subjects="" (a="" ≥="" 1)="" />Establishing Relationships
Using the given inequalities, we can denote:
- E > G > H > X > A
Let’s assign variables for each group:
- Let A = 1 (minimum number of students studying all three subjects)
- Let X = 2 (minimum for students studying exactly two subjects)
- Then, we have G > H > 2 > 1
Calculating Minimum Values
Assuming G = 3, we can estimate:
- H must be less than G, so H = 2
- Now, E must be greater than G, so E must be at least 4
Summing these values:
- A = 1
- X = 2
- H = 2
- G = 3
- E = 4
This gives:
1 + 2 + 2 + 3 + 4 = 12 students.
Maximizing English
To ensure E, G, and H maintain their relationships while maximizing E, we can continue this process:
If G = 35, then H must be less than 35, say H = 34, and X = 33. This can be maintained with A = 1.
- So, E must be at least 36 to maintain the hierarchy.
Conclusion
Thus, the minimum number of students studying English, considering the relationships and constraints, is 36. Therefore, the correct answer is option 'C'.
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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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer?.
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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer? for UPSC 2025 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about 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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer? covers all topics & solutions for UPSC 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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)37b)34c)36d)35e)32Correct answer is option 'C'. Can you explain this answer?.
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