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Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
Q. Which of the following CANNOT be determined uniquely based on the given information?
Twenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:
1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.
2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.
3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.
Q. Which of the following CANNOT be determined uniquely based on the given information?
- a)The size of the teaching committee
- b)The size of the research committee
- c)The total number of bureaucrats in the three committees
- d)The total number of educationalists in the three committees
Correct answer is option 'A'. Can you explain this answer?
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Verified Answer
InstructionsTwenty four people are part of three committees which are ...
Let us draw a table according to the information given.
It is given that the numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee. Let '4x' be the number of bureaucrats in Administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees. Let us assume that 'y' is the number of educationalists in the research committee and 'd' be the difference in the number of educationalists in Research and teaching committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee. Let '5z' be the number of total number of politicians.
We can say that
⇒10x+3y+5z = 24
We can see that each of x, y and z has to a natural number integer. If x > 1, then both y and z can't take any natural number.
Hence, we can say that x = 1.
At x = 1, 3y+5z = 24. If y = 1 or 2, Z is not an integer.
At x = 1 and y = 3, z = 1 which is the only possible solution.
We can see that 'd' can assume two possible values. d = 1 or 2.
From the table, we can not uniquely determine the size of the teaching committee. Hence, option A is the correct answer.
It is given that the numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee. Let '4x' be the number of bureaucrats in Administration committee.
The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees. Let us assume that 'y' is the number of educationalists in the research committee and 'd' be the difference in the number of educationalists in Research and teaching committees.
60% of the politicians are in the administration committee, and 20% are in the teaching committee. Let '5z' be the number of total number of politicians.
We can say that
⇒10x+3y+5z = 24
We can see that each of x, y and z has to a natural number integer. If x > 1, then both y and z can't take any natural number.
Hence, we can say that x = 1.
At x = 1, 3y+5z = 24. If y = 1 or 2, Z is not an integer.
At x = 1 and y = 3, z = 1 which is the only possible solution.
We can see that 'd' can assume two possible values. d = 1 or 2.
From the table, we can not uniquely determine the size of the teaching committee. Hence, option A is the correct answer.
Most Upvoted Answer
InstructionsTwenty four people are part of three committees which are ...
Understanding the Committees
The problem presents three committees: research, teaching, and administration, with specific constraints on membership types and sizes.
Key Constraints
- Equal Bureaucrats in Research and Teaching: The number of bureaucrats in the research committee equals that in the teaching committee.
- Bureaucrats in Research vs. Administration: Bureaucrats in the research committee are 75% of those in the administration committee.
- Educationalists Distribution: The teaching committee has fewer educationalists than the research committee, which has an average number of educationalists compared to the other two.
- Politicians Distribution: 60% of politicians are in the administration committee, and 20% are in the teaching committee.
Analysis of Committee Sizes
- The committees must have different sizes, which implies that the total number of members across all committees is 24.
- Since the sizes are distinct and based on the given constraints, you can derive relationships between the committees.
Determining Unique Values
- Teaching Committee Size: While you can infer relationships and the total number of members, the exact size of the teaching committee cannot be uniquely determined. This is due to the flexibility in distribution based on the percentage constraints for bureaucrats and educationalists.
- Research Committee Size: This can be calculated based on the relationships with the administration committee and given that the total is 24.
- Total Bureaucrats and Educationalists: These can be derived from the relationships established in the problem, allowing for unique values.
Conclusion
Thus, due to the multiple configurations that satisfy all conditions, the size of the teaching committee cannot be determined uniquely, making option 'A' the correct answer.
The problem presents three committees: research, teaching, and administration, with specific constraints on membership types and sizes.
Key Constraints
- Equal Bureaucrats in Research and Teaching: The number of bureaucrats in the research committee equals that in the teaching committee.
- Bureaucrats in Research vs. Administration: Bureaucrats in the research committee are 75% of those in the administration committee.
- Educationalists Distribution: The teaching committee has fewer educationalists than the research committee, which has an average number of educationalists compared to the other two.
- Politicians Distribution: 60% of politicians are in the administration committee, and 20% are in the teaching committee.
Analysis of Committee Sizes
- The committees must have different sizes, which implies that the total number of members across all committees is 24.
- Since the sizes are distinct and based on the given constraints, you can derive relationships between the committees.
Determining Unique Values
- Teaching Committee Size: While you can infer relationships and the total number of members, the exact size of the teaching committee cannot be uniquely determined. This is due to the flexibility in distribution based on the percentage constraints for bureaucrats and educationalists.
- Research Committee Size: This can be calculated based on the relationships with the administration committee and given that the total is 24.
- Total Bureaucrats and Educationalists: These can be derived from the relationships established in the problem, allowing for unique values.
Conclusion
Thus, due to the multiple configurations that satisfy all conditions, the size of the teaching committee cannot be determined uniquely, making option 'A' the correct answer.
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InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer?
Question Description
InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer?.
InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer?.
Solutions for InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? in English & in Hindi are available as part of our courses for CAT.
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Here you can find the meaning of InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? defined & explained in the simplest way possible. Besides giving the explanation of
InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer?, a detailed solution for InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? has been provided alongside types of InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? theory, EduRev gives you an
ample number of questions to practice InstructionsTwenty four people are part of three committees which are to look at research, teaching, and administration respectively. No two committees have any member in common. No two committees are of the same size. Each committee has three types of people: bureaucrats, educationalists, and politicians, with at least one from each of the three types in each committee. The following facts are also known about the committees:1. The numbers of bureaucrats in the research and teaching committees are equal, while the number of bureaucrats in the research committee is 75% of the number of bureaucrats in the administration committee.2. The number of educationalists in the teaching committee is less than the number of educationalists in the research committee. The number of educationalists in the research committee is the average of the numbers of educationalists in the other two committees.3. 60% of the politicians are in the administration committee, and 20% are in the teaching committee.Q.Which of the following CANNOT be determined uniquely based on the given information?a)The size of the teaching committeeb)The size of the research committeec)The total number of bureaucrats in the three committeesd)The total number of educationalists in the three committeesCorrect answer is option 'A'. Can you explain this answer? tests, examples and also practice CAT tests.
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