MAH-CET Selection Criteria Questions [PDF]
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Instructions
Three reviewers Amal, Bimal, and Komal are tasked with selecting questions from a pool of 13 questions (Q01 to Q13). Questions can be created by external “subject matter experts” (SMEs) or by one of the three reviewers. Each of the reviewers either approves or disapproves a question that is shown to them. Their decisions lead to eventual acceptance or rejection of the question in the manner described below.
If a question is created by an SME, it is reviewed first by Amal, and then by Bimal. If both of them approve the question, then the question is accepted and is not reviewed by Komal. If both disapprove the question, it is rejected and is not reviewed by Komal. If one of them approves the question and the other disapproves it, then the question is reviewed by Komal. Then the question is accepted only if she approves it.
A question created by one of the reviewers is decided upon by the other two. If a question is created by Amal, then it is first reviewed by Bimal. If Bimal approves the question, then it is accepted. Otherwise, it is reviewed by Komal. The question is then accepted only if Komal approves it. A similar process is followed for questions created by Bimal, whose questions are first reviewed by Komal, and then by Amal only if Komal disapproves it. Questions created by Komal are first reviewed by Amal, and then, if required, by Bimal.
The following facts are known about the review process after its completion.
1. Q02, Q06, Q09, Q11, and Q12 were rejected and the other questions were accepted.
2. Amal reviewed only Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
3. Bimal reviewed only Q02, Q04, Q06 through Q09, Q12, and Q13.
4. Komal reviewed only Q01 through Q05, Q07, Q08, Q09, Q11, and Q12.
Question 1: How many questions created by Amal or Bimal were disapproved by at least one of the other reviewers?
a) 7
b) 4
c) 5
d) 2
1) Answer (C)
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Amal could have possibly created the questions :
Q07, Q09, Q12 of which all three of them were reviewed by two people each, and hence they must have been rejected by the first reviewer.
Bimal could have created the questions :
Q01, Q03, Q05, Q 11.
Q01, Q05 are reviewed only by Komal and hence did not have any rejection.
Q03, Q11 faced at least one rejection.
Hence a total of five questions.
Question 2: The approval ratio of a reviewer is the ratio of the number of questions (s)he approved to the number of questions (s)he reviewed. Which option best describes Amal’s approval ratio?
a) either 0.25 or 0.75
b) 0.25
c) lies between 0.25 and 0.50
d) lies between 0.25 and 0.75
2) Answer (D)
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Amal reviewed the questions :
Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
For Q2 – Amal can either approve or reject the question.
For Q3- Amal must approve the question.
For Q4 -Amal can either approve or reject the question.
For Q06 – Amal must reject the question.
For Q08 – Amal can either approve or reject the question.
For Q10 – Amal must approve the question.
For Q11 – Amal must reject the question.
For Q13- Amal can either approve or reject the question.
The approval ratio has a minimum of 2 questions only Q3, Q10, and a maximum of 6 questions Q02, Q3, Q04, Q08, Q10, Q13.
Hence 2/8 = 0.25 to 6/8 = 0.75
Question 3: How many questions were DEFINITELY disapproved by Bimal?
a) 3
b) 4
c) 7
d) 5
3) Answer (B)
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Q06 irrespective of the question prepared by Komal/SME Bimal must reject the question.
Q07, Q09, Q12 are prepared by Amal and were reviewed by Bimal first and Komal next for this to happen Bimal must reject these questions.
Hence a total of four questions were rejected by Bimal.
Question 4: How many questions were DEFINITELY created by the SMEs?
4) Answer: 3
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Q02, Q04, Q08 were prepared SME
Question 5: How many questions were DEFINITELY created by Komal?
5) Answer: 1
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Q10 was definitely prepared by Komal.
Question 6: How many questions were DEFINITELY created by Amal?
6) Answer: 3
Solution:
For a question created by externals(SME), the minimum number of reviews required is two and the maximum number of reviews is three to confirm the acceptance or the rejection.
For a question created by anyone among Amal, Bimal, Komal a question can be reviewed after one review or two reviews.
The information provided states :
Q02, Q06, Q09, Q11, and Q12 were rejected. Q01, Q03, Q04, Q05, Q07, Q08, Q10, Q13 were accepted.
For the questions :
Amal – Q02, Q03, Q04, Q06, Q08, Q10, Q11, and Q13.
Bimal – Q02, Q04, Q06, Q07, Q08, Q09, Q12, and Q13.
Komal – Q01, Q02, Q03, Q04, Q05, Q07, Q08, Q09, Q11, and Q12.
Q01 is reviewed by only Komal and is accepted hence Bimal must have prepared the question as it was accepted in a single review. (Bimal)
Q02-is reviewed by Amal, Bimal, and Komal and was rejected this has a possibility of being prepared by an external person and faced rejection by one among Amal and Bimal and Komal. (SME).
Q03-Was accepted and reviewed by Amal, Komal and hence must have been prepared by Bimal(Bimal).
Q04- Accepted and reviewed by the three of them and hence must have been prepared by an external expert. (SME).
Q05-Only reviewed by Komal and is accepted and hence must be prepared by Bimal. (Bimal)
Q06-Rejected and reviewed by Amal and Bimal. Hence could have been prepared by Komal or External and rejected by Bimal and Amal. (Komal/SME).
Q07-Accepted and reviewed by Bimal and Komal. Hence must have been prepared by Amal. (Amal).
Q08- Reviewed by Amal, Bimal, and Komal and is accepted. Hence must have been prepared by SME. (SME)
Q09- Reviewed by Bimal and Komal and is rejected. It must have been prepared by Amal and was rejected by both of them. (Amal).
Q10- Was reviewed by Amal and was accepted. Must have been prepared by Komal. (Komal)
Q11- Reviewed by Amal and Komal and was rejected. Must have been prepared by Bimal and rejected by both Amal and Komal. (Bimal)
Q12- Reviewed by Bimal and Komal and was rejected. Must have been prepared by Amal and was rejected by both Bimal and Komal. (Amal).
Q13- Reviewed by Amal and Bimal and was accepted. The question could have been prepared by Komal or SME. (Komal/SME).
Amal definitely prepared questions Q07, Q09, Q12.
Instructions
In the table below the check marks indicate all languages spoken by five people: Paula, Quentin, Robert, Sally and Terence. For example, Paula speaks only Chinese and English.
These five people form three teams, Team 1, Team 2 and Team 3. Each team has either 2 or 3 members. A team is said to speak a particular language if at least one of its members speak that language.
The following facts are known.
(1) Each team speaks exactly four languages and has the same number of members.
(2) English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team.
(3) None of the teams include both Quentin and Robert.
(4) Paula and Sally are together in exactly two teams.
(5) Robert is in Team 1 and Quentin is in Team 3.
Question 7: Apart from Chinese and English, which languages are spoken by Team 1?
a) Arabic and French
b) Basque and French
c) Arabic and Basque
d) Basque and Dutch
7) Answer (A)
Solution:
From statement 1 and 2,Each team speaks exactly four languages. English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team, multiple options are possible.
In the following tables: A, B, C can be any team among Team 1,Team 2,Team 3.
From the data given in the question, the person who speaks Arabic also speaks French. Thus the only option possible is ‘Table 2’.
According to statement 4, “Paula and Sally are together in exactly two teams.”
Sally knows Basque, thus, she will be in group A and B, with Paula.
According to statement 5, Robert(Arabic) is in Team 1 and Quentin(Dutch) is in Team 3.
Thus, Group C is Team 1 and Group A is Team 3.
From the table, the correct option is A.
Question 8: Who among the five people is a member of all teams?
a) Terence
b) Sally
c) Paula
d) No one
8) Answer (C)
Solution:
From statement 1 and 2,Each team speaks exactly four languages. English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team, multiple options are possible.
In the following tables: A, B, C can be any team among Team 1,Team 2,Team 3.
From the data given in the question, the person who speaks Arabic also speaks French. Thus the only option possible is ‘Table 2’.
According to statement 4, “Paula and Sally are together in exactly two teams.”
Sally knows Basque, thus, she will be in group A and B, with Paula.
According to statement 5, Robert(Arabic) is in Team 1 and Quentin(Dutch) is in Team 3.
Thus, Group C is Team 1 and Group A is Team 3.
From the table, the correct option is C.
Question 9: Who among the following four people is a part of exactly two teams?
a) Paula
b) Quentin
c) Sally
d) Robert
9) Answer (C)
Solution:
From statement 1 and 2,Each team speaks exactly four languages. English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team, multiple options are possible.
In the following tables: A, B, C can be any team among Team 1,Team 2,Team 3.
From the data given in the question, the person who speaks Arabic also speaks French. Thus the only option possible is ‘Table 2’.
According to statement 4, “Paula and Sally are together in exactly two teams.”
Sally knows Basque, thus, she will be in group A and B, with Paula.
According to statement 5, Robert(Arabic) is in Team 1 and Quentin(Dutch) is in Team 3.
Thus, Group C is Team 1 and Group A is Team 3.
From the table, the correct option is C.
Question 10: Who among the following four is not a member of Team 2?
a) Paula
b) Terence
c) Quentin
d) Sally
10) Answer (C)
Solution:
From statement 1 and 2,Each team speaks exactly four languages. English and Chinese are spoken by all three teams, Basque and French by exactly two teams and the other languages by exactly one team, multiple options are possible.
In the following tables: A, B, C can be any team among Team 1,Team 2,Team 3.
From the data given in the question, the person who speaks Arabic also speaks French. Thus the only option possible is ‘Table 2’.
According to statement 4, “Paula and Sally are together in exactly two teams.”
Sally knows Basque, thus, she will be in group A and B, with Paula.
According to statement 5, Robert(Arabic) is in Team 1 and Quentin(Dutch) is in Team 3.
Thus, Group C is Team 1 and Group A is Team 3.
From the table, the correct option is C.
