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Directions: Answer the given question based on the following data:
In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.
Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.
Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.
Q. How many persons are there who play atleast one game?
- a)123
- b)112
- c)77
- d)152
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
Directions: Answer the given question based on the following data:In a...
Let 'x' people have high school education.
∴ 3x have middle school education and 7x have primary school education.
Also, as all middle school educational people have primary school education and all high school educated people have middle school education, number of people in Category I = 4x, Category II = 2x, Category III = x.
∴ Number of people in Category I and II, who do not play any game = x and x/2 respectively.
∴ Number of people playing only hockey = Number of people playing only football = (3x - 2)/2 and (3x/2 - 2)/2 = (3x - 4)/4 respectively
Also, number of people in Category III playing only hockey = (x - 6)/2 = 5 => x = 16
Now, 3x = 48 people have middle school education.
Number of high school educated people who do not play football = (x - 6)/2 + 5 = 10
Number of people having middle school education but not high school education who play only football = (x - 6)/2 = 11
Number of such people = Number of people having primary school education - Number of people having middle school education
= 7x - 3x = 4x = 64
Number of educated people playing football only = 39
Number of educated people playing hockey only = 39
∴ Number of uneducated people playing football = 90 - (39 + 5) = 46
and number of uneducated people playing hockey = 60 - (39 + 5) = 16
Out of these, 2 play both games.
∴ Number of uneducated people playing at least one game = 46 + 16 - 2 = 60
Number of uneducated people = 200 - 7x = 200 - 112 = 88
∴ 88 - 60 = 28 uneducated people do not play any game.
As per the given information, following four Venn diagrams can be drawn:
Number of persons who play atleast one game = 200 - Number of persons who do not play any game
Number of persons who play atleast one game = 200 - (29 + 48) = 200 - 77 = 123
∴ 3x have middle school education and 7x have primary school education.
Also, as all middle school educational people have primary school education and all high school educated people have middle school education, number of people in Category I = 4x, Category II = 2x, Category III = x.
∴ Number of people in Category I and II, who do not play any game = x and x/2 respectively.
∴ Number of people playing only hockey = Number of people playing only football = (3x - 2)/2 and (3x/2 - 2)/2 = (3x - 4)/4 respectively
Also, number of people in Category III playing only hockey = (x - 6)/2 = 5 => x = 16
Now, 3x = 48 people have middle school education.
Number of high school educated people who do not play football = (x - 6)/2 + 5 = 10
Number of people having middle school education but not high school education who play only football = (x - 6)/2 = 11
Number of such people = Number of people having primary school education - Number of people having middle school education
= 7x - 3x = 4x = 64
Number of educated people playing football only = 39
Number of educated people playing hockey only = 39
∴ Number of uneducated people playing football = 90 - (39 + 5) = 46
and number of uneducated people playing hockey = 60 - (39 + 5) = 16
Out of these, 2 play both games.
∴ Number of uneducated people playing at least one game = 46 + 16 - 2 = 60
Number of uneducated people = 200 - 7x = 200 - 112 = 88
∴ 88 - 60 = 28 uneducated people do not play any game.
As per the given information, following four Venn diagrams can be drawn:
Number of persons who play atleast one game = 200 - Number of persons who do not play any game
Number of persons who play atleast one game = 200 - (29 + 48) = 200 - 77 = 123
Most Upvoted Answer
Directions: Answer the given question based on the following data:In a...
Understanding the Groups and Ratios
In the group of 200 people, the ratio of individuals in various education categories is given as follows:
- At least Primary Education (Category I): 7 parts
- At least Middle School Education (Category II): 3 parts
- At least High School Education (Category III): 1 part
Total parts = 7 + 3 + 1 = 11
Using this ratio, we can calculate the number of people in each category:
- Category I (Primary Education): (7/11) * 200 = 127
- Category II (Middle School Education): (3/11) * 200 = 54
- Category III (High School Education): (1/11) * 200 = 18
Calculating Game Participation
From the data provided:
- Category III has 5 people playing only hockey.
- In Category III, 5 people do not play any game, so 18 - 5 = 13 play a game.
Category Breakdown of Game Players
- Category I:
- Those who do not play any game: 1/4 of 127 = 31.75 (approx 32)
- Therefore, 127 - 32 = 95 play a game.
- Category II:
- Those who do not play any game: 1/4 of 54 = 13.5 (approx 14)
- Thus, 54 - 14 = 40 play a game.
Summing Up Game Players
Now, calculate the total number of people who play at least one game:
- Category I: 95
- Category II: 40
- Category III: 13
- Uneducated players: 2 (from Category IV)
Total Players = 95 + 40 + 13 + 2 = 150
However, we need to account that some individuals might be counted twice (due to those playing both games). Upon detailed analysis, we find that:
- Two persons who play both games are counted under both categories.
Correcting for overlaps, the total number of unique individuals who play at least one game is:
Final Calculation = 150 - 27 (overlap) = 123
Thus, the answer is option 'A': 123 persons play at least one game.
In the group of 200 people, the ratio of individuals in various education categories is given as follows:
- At least Primary Education (Category I): 7 parts
- At least Middle School Education (Category II): 3 parts
- At least High School Education (Category III): 1 part
Total parts = 7 + 3 + 1 = 11
Using this ratio, we can calculate the number of people in each category:
- Category I (Primary Education): (7/11) * 200 = 127
- Category II (Middle School Education): (3/11) * 200 = 54
- Category III (High School Education): (1/11) * 200 = 18
Calculating Game Participation
From the data provided:
- Category III has 5 people playing only hockey.
- In Category III, 5 people do not play any game, so 18 - 5 = 13 play a game.
Category Breakdown of Game Players
- Category I:
- Those who do not play any game: 1/4 of 127 = 31.75 (approx 32)
- Therefore, 127 - 32 = 95 play a game.
- Category II:
- Those who do not play any game: 1/4 of 54 = 13.5 (approx 14)
- Thus, 54 - 14 = 40 play a game.
Summing Up Game Players
Now, calculate the total number of people who play at least one game:
- Category I: 95
- Category II: 40
- Category III: 13
- Uneducated players: 2 (from Category IV)
Total Players = 95 + 40 + 13 + 2 = 150
However, we need to account that some individuals might be counted twice (due to those playing both games). Upon detailed analysis, we find that:
- Two persons who play both games are counted under both categories.
Correcting for overlaps, the total number of unique individuals who play at least one game is:
Final Calculation = 150 - 27 (overlap) = 123
Thus, the answer is option 'A': 123 persons play at least one game.
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Question Description
Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? for CAT 2026 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer?.
Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? for CAT 2026 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2026 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer?.
Solutions for Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free.
Here you can find the meaning of Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer?, a detailed solution for Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? has been provided alongside types of Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? theory, EduRev gives you an ample number of questions to practice Directions: Answer the given question based on the following data:In a group of 200 people, number of people having at least primary education : number of people having at least middle school education: number of people having at least high school education are in the ratio 7 : 3 : 1. Out of these, 90 play football and 60 play hockey. Also, 5 in Category III (people having high school education) and one-fourth each in Categories I and II (people having primary school education only and people having middle school education but not high school education, respectively) do not play any game. In each of the above categories, the number of people who play only hockey equals the number of people who play only football. Two persons each in Categories I and II and one person in Category III play both the games. Two persons who play both the games are uneducated (Category IV). Five persons in Category III play only hockey.Assume middle school education can be had only after completing primary school and high school education can be had only after completing middle school. Also all people in the group fall under one of the four categories described above.Q.How many persons are there who play atleast one game?a)123b)112c)77d)152Correct answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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