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DILR ANSWER KEY & SOLUTION SLOT 1 CAT 2018

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DILR ANSWER KEY & SOLUTION SLOT 1 CAT 2018

PROBLEM 6

Directions for the Q1-Q4: 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: 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.

Answer the following: Q1. Based on the given information, which of the following statements MUST be FALSE? 1. In the teaching committee the number of educationalists is equal to the number of politicians. 2. In the administration committee the number of bureaucrats is equal to the number of educationalists. 3. The size of the research committee is less than the size of the teaching committee. 4. The size of the research committee is less than the size of the administration committee Q2. What is the number of bureaucrats in the administration committee? Q3. What is the number of educationalists in the research committee? G4. Which of the following CANNOT be determined uniquely based on the given information? 1. The size of the teaching committee 2. The size of the research committee 3. The total number of bureaucrats in the three committees 4. The total number of educationalists in the three committees

Twenty four people are part of three commitees 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 s 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. RESEARCH TEACHING ADMINSTRATION TOTAL

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. RESEARCH TEACHING ADMINISTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL

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. RESEARCH TEACHING ADMINISTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 24

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. RESEARCH TEACHING ADMINISTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 24

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. RESEARCH TEACHING ADMINISTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 24

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. RESEARCH TEACHING ADMINSTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 0.75a 0.75a 24

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. RESEARCH TEACHING ADMINSTRATION TOTAL BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 0.75a 0.75a 2.5a < research 24

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. TOTAL 2.5a 3(b+c)/2 RESEARCH TEACHING ADMINSTRATION BUREAUCRATS 0.75a 0.75a EDUCATIONALISTS (b+c)/2 POLITICIANS TOTAL 24

Twenty four people are part of three commitees 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 s 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. TOTAL 10 3(b+c)/2 RESEARCH TEACHING ADMINSTRATION BUREAUCRATS EDUCATIONALISTS (b+c)/2 POLITICIANS 0.2p 0.2p 0.6p TOTAL 24

Twenty four people are part of three commitees 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 s 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. TOTAL 10 3(b+c)/2 RESEARCH TEACHING ADMINSTRATION BUREAUCRATS EDUCATIONALISTS (b+c)/2 POLITICIANS 0.2p 0.2p 0.6p TOTAL 24

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. TOTAL 10 3(b+c)/2 RESEARCH TEACHING ADM NSTRATION BUREAUCRATS EDUCATIONALISTS (b+c)/2 POLITICIANS 3 TOTAL 24

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. TOTAL 10 3(b+c)/2 9 RESEARCH TEACHING ADM NSTRATION BUREAUCRATS EDUCATIONALISTS POLITICIANS TOTAL 2 or 1 4 or 5 3 24

Answer the following: Q1. Based on the given information, which of the following statements MUST be FALSE? 1. In the teaching committee the number of educationalists is equal to the number of politicians. 2. In the administration committee the number of bureaucrats is equal to the number of educationalists. 3. The size of the research committee is less than the size of the teaching committee. 4. The size of the research committee is less than the size of the administration committee Q2. What is the number of bureaucrats in the administration committee? Q3. What is the number of educationalists in the research committee? G4. Which of the following CANNOT be determined uniquely based on the given information? 1. The size of the teaching committee 2. The size of the research committee 3. The total number of bureaucrats in the three committees 4. The total number of educationalists in the three committees

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