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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. What is the number of bureaucrats in the administration committee?
Correct answer is '4'. Can you explain this answer?
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Twenty four people are part of three committees which are to look at ...
Let us draw a table according to the information given.
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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 the 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 total number of politicians.
We can say that
10x+3y+5z = 24
We can see that each of x, y and z has 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 = 14. 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 see that the number of bureaucrats in the administration committee = 4.
Most Upvoted Answer
Twenty four people are part of three committees which are to look at ...
Understanding the Problem
To solve the problem, we need to analyze the given facts systematically and derive the number of bureaucrats in each committee.
Committee Sizes
- Let the sizes of the committees be:
- Research Committee: R
- Teaching Committee: T
- Administration Committee: A
- We know that R, T, and A must be different numbers and sum to 24.
Bureaucrats Distribution
- Let the number of bureaucrats in the committees be:
- Research: B_R
- Teaching: B_T
- Administration: B_A
- From the facts:
- B_R = B_T
- B_R = 0.75 * B_A
Setting Up Equations
- Since B_R = B_T, we can denote them as B.
- B_R = B
- B_A = (4/3) * B
- Total bureaucrats = B + B + (4/3)B = (10/3)B
Educationalists Distribution
- Let:
- E_R = Educationalists in Research
- E_T = Educationalists in Teaching
- E_A = Educationalists in Administration
- It’s given that:
- E_R = (E_T + E_A) / 2
- E_T < />
Politicians Distribution
- Let:
- P_R = Politicians in Research
- P_T = Politicians in Teaching
- P_A = Politicians in Administration
- Given percentages:
- P_A = 0.6 * Total Politicians
- P_T = 0.2 * Total Politicians
- P_R = 0.2 * Total Politicians
Finding Bureaucrats in Administration
- Assume B = 4 (as it fits the conditions):
- B_R = B_T = 4
- B_A = 4/0.75 = 5.33 (not possible since it must be an integer)
- Assume B = 3:
- B_R = B_T = 3
- B_A = 3/0.75 = 4 (fits perfectly).
Thus, the number of bureaucrats in the Administration Committee is 4.
To solve the problem, we need to analyze the given facts systematically and derive the number of bureaucrats in each committee.
Committee Sizes
- Let the sizes of the committees be:
- Research Committee: R
- Teaching Committee: T
- Administration Committee: A
- We know that R, T, and A must be different numbers and sum to 24.
Bureaucrats Distribution
- Let the number of bureaucrats in the committees be:
- Research: B_R
- Teaching: B_T
- Administration: B_A
- From the facts:
- B_R = B_T
- B_R = 0.75 * B_A
Setting Up Equations
- Since B_R = B_T, we can denote them as B.
- B_R = B
- B_A = (4/3) * B
- Total bureaucrats = B + B + (4/3)B = (10/3)B
Educationalists Distribution
- Let:
- E_R = Educationalists in Research
- E_T = Educationalists in Teaching
- E_A = Educationalists in Administration
- It’s given that:
- E_R = (E_T + E_A) / 2
- E_T < />
Politicians Distribution
- Let:
- P_R = Politicians in Research
- P_T = Politicians in Teaching
- P_A = Politicians in Administration
- Given percentages:
- P_A = 0.6 * Total Politicians
- P_T = 0.2 * Total Politicians
- P_R = 0.2 * Total Politicians
Finding Bureaucrats in Administration
- Assume B = 4 (as it fits the conditions):
- B_R = B_T = 4
- B_A = 4/0.75 = 5.33 (not possible since it must be an integer)
- Assume B = 3:
- B_R = B_T = 3
- B_A = 3/0.75 = 4 (fits perfectly).
Thus, the number of bureaucrats in the Administration Committee is 4.
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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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. Can you explain this answer?
Question Description
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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. 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 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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. Can you explain this answer?.
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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. 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 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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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. What is the number of bureaucrats in the administration committee?Correct answer is '4'. Can you explain this answer?.
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