CAT — Assignment
25 questions, free to view. Click any question to see the answer and explanation.
Faculty members in a management school can belong to one of four departments – Finance and Accounting (F&A), Marketing and Strategy (M&S), Operations and Quants (O&Q) and Behaviour and Human Resources (B&H). The numbers of faculty members in F&A, M&S, O&Q and B&H departments are 9, 7, 5 and 3 respectively.
Prof. Pakrasi, Prof. Qureshi, Prof. Ramaswamy and Prof. Samuel are four members of the school's faculty who were candidates for the post of the Dean of the school. Only one of the candidates was from O&Q.
Every faculty member, including the four candidates, voted for the post. In each department, all the faculty members who were not candidates voted for the same candidate. The rules for the election are listed below.
1. There cannot be more than two candidates from a single department.
2. A candidate cannot vote for himself/herself.
3. Faculty members cannot vote for a candidate from their own department.
After the election, it was observed that Prof. Pakrasi received 3 votes, Prof. Qureshi received 14 votes, Prof. Ramaswamy received 6 votes and Prof. Samuel received 1 vote. Prof. Pakrasi voted for Prof. Ramaswamy, Prof. Qureshi for Prof. Samuel, Prof. Ramaswamy for Prof. Qureshi and Prof. Samuel for Prof. Pakrasi.
Which two candidates can belong to the same department?
Prof. Pakrasi and Prof. Samuel
Prof. Pakrasi and Prof. Qureshi
Prof. Qureshi and Prof. Ramaswamy
Prof. Ramaswamy and Prof. Samuel
Prof. Pakrasi and Prof. Qureshi
Step 1:
Using the given information and conditions (1)–(3):
- P received 3 votes.
- Since S voted for P, P received the remaining 2 votes from members of B & H. Therefore, P cannot belong to the B & H department, leaving one candidate from B & H.
- Q received 14 votes.
- Since R voted for Q, Q received 9 votes from F & A and 4 votes from O & Q.
- Hence, Q cannot belong to either F & A or O & Q. Consequently, there is no candidate from F & A, and one candidate belongs to O & Q. The remaining two candidates must come from M & S.
Further,
- Since S voted for P, P and S cannot belong to the same department.
- Since R voted for Q, Q and R cannot belong to the same department.
- Similarly, R and P cannot belong to the same department, and Q and S cannot belong to the same department.
Therefore,
- P and Q belong to the M & S department.
- Q and S belong to B & H and O & Q, in either order.
Step 2:
The vote distribution is as follows:
- P received 3 votes:
- From S
- From 2 members of B & H
- Q received 14 votes:
- From R
- From 9 members of F & A
- From 4 members of O & Q
- R received 6 votes:
- From P
- From 5 members of M & S
- S received 1 vote:
- From Q
The department-wise candidate allocation is:
- F & A: 9 faculty members, 9 members, no candidate
- M & S: 7 faculty members, 5 members, Candidates – P and Q
- O & Q: 5 faculty members, 4 members, Candidate – R or S
- B & H: 3 faculty members, 2 members, Candidate – S or R
Prof. Pakrasi and Prof. Qureshi can belong to the same department M & S.
Which of the following can be the number of votes that Prof. Qureshi received from a single department?
7
9
8
6
9
Step 1:
Using the given information and conditions (1)–(3):
- P received 3 votes.
- Since S voted for P, P received the remaining 2 votes from members of B & H. Therefore, P cannot belong to the B & H department, leaving one candidate from B & H.
- Q received 14 votes.
- Since R voted for Q, Q received 9 votes from F & A and 4 votes from O & Q.
- Hence, Q cannot belong to either F & A or O & Q. Consequently, there is no candidate from F & A, and one candidate belongs to O & Q. The remaining two candidates must come from M & S.
Further,
- Since S voted for P, P and S cannot belong to the same department.
- Since R voted for Q, Q and R cannot belong to the same department.
- Similarly, R and P cannot belong to the same department, and Q and S cannot belong to the same department.
Therefore,
- P and Q belong to the M & S department.
- Q and S belong to B & H and O & Q, in either order.
Step 2:
The vote distribution is as follows:
- P received 3 votes:
- From S
- From 2 members of B & H
- Q received 14 votes:
- From R
- From 9 members of F & A
- From 4 members of O & Q
- R received 6 votes:
- From P
- From 5 members of M & S
- S received 1 vote:
- From Q
The department-wise candidate allocation is:
- F & A: 9 faculty members, 9 members, no candidate
- M & S: 7 faculty members, 5 members, Candidates – P and Q
- O & Q: 5 faculty members, 4 members, Candidate – R or S
- B & H: 3 faculty members, 2 members, Candidate – S or R
Nine can be the number of votes that Prof. Qureshi received from a single department.
If Prof. Samuel belongs to B&H, which of the following statements is/are true?
Statement A: Prof. Pakrasi belongs to M&S.
Statement B: Prof. Ramaswamy belongs to O&Q.
Neither statement A nor statement B
Only statement A
Both statements A and B
Only statement B
Both statements A and B
Step 1:
Using the given information and conditions (1)–(3):
- P received 3 votes.
- Since S voted for P, P received the remaining 2 votes from members of B & H. Therefore, P cannot belong to the B & H department, leaving one candidate from B & H.
- Q received 14 votes.
- Since R voted for Q, Q received 9 votes from F & A and 4 votes from O & Q.
- Hence, Q cannot belong to either F & A or O & Q. Consequently, there is no candidate from F & A, and one candidate belongs to O & Q. The remaining two candidates must come from M & S.
Further,
- Since S voted for P, P and S cannot belong to the same department.
- Since R voted for Q, Q and R cannot belong to the same department.
- Similarly, R and P cannot belong to the same department, and Q and S cannot belong to the same department.
Therefore,
- P and Q belong to the M & S department.
- Q and S belong to B & H and O & Q, in either order.
Step 2:
The vote distribution is as follows:
- P received 3 votes:
- From S
- From 2 members of B & H
- Q received 14 votes:
- From R
- From 9 members of F & A
- From 4 members of O & Q
- R received 6 votes:
- From P
- From 5 members of M & S
- S received 1 vote:
- From Q
The department-wise candidate allocation is:
- F & A: 9 faculty members, 9 members, no candidate
- M & S: 7 faculty members, 5 members, Candidates – P and Q
- O & Q: 5 faculty members, 4 members, Candidate – R or S
- B & H: 3 faculty members, 2 members, Candidate – S or R
Both statements are true.
What best can be concluded about the candidate from O and Q?
It was either Prof. Ramaswamy or Prof. Samuel.
It was either Prof. Pakrasi or Prof. Qureshi.
It was Prof. Samuel.
It was Prof. Ramaswamy.
It was either Prof. Ramaswamy or Prof. Samuel.
Step 1:
Using the given information and conditions (1)–(3):
- P received 3 votes.
- Since S voted for P, P received the remaining 2 votes from members of B & H. Therefore, P cannot belong to the B & H department, leaving one candidate from B & H.
- Q received 14 votes.
- Since R voted for Q, Q received 9 votes from F & A and 4 votes from O & Q.
- Hence, Q cannot belong to either F & A or O & Q. Consequently, there is no candidate from F & A, and one candidate belongs to O & Q. The remaining two candidates must come from M & S.
Further,
- Since S voted for P, P and S cannot belong to the same department.
- Since R voted for Q, Q and R cannot belong to the same department.
- Similarly, R and P cannot belong to the same department, and Q and S cannot belong to the same department.
Therefore,
- P and Q belong to the M & S department.
- Q and S belong to B & H and O & Q, in either order.
Step 2:
The vote distribution is as follows:
- P received 3 votes:
- From S
- From 2 members of B & H
- Q received 14 votes:
- From R
- From 9 members of F & A
- From 4 members of O & Q
- R received 6 votes:
- From P
- From 5 members of M & S
- S received 1 vote:
- From Q
The department-wise candidate allocation is:
- F & A: 9 faculty members, 9 members, no candidate
- M & S: 7 faculty members, 5 members, Candidates – P and Q
- O & Q: 5 faculty members, 4 members, Candidate – R or S
- B & H: 3 faculty members, 2 members, Candidate – S or R
Either Prof. Ramaswamy or Prof. Samuel was from O & Q.
Which of the following statements is/are true?
Statement A: Non-candidates from M&S voted for Prof. Qureshi.
Statement B: Non-candidates from F&A voted for Prof. Qureshi.
Only statement A
Neither statement A nor statement B
Both statements A and B
Only statement B
Only statement B
Step 1:
Using the given information and conditions (1)–(3):
- P received 3 votes.
- Since S voted for P, P received the remaining 2 votes from members of B & H. Therefore, P cannot belong to the B & H department, leaving one candidate from B & H.
- Q received 14 votes.
- Since R voted for Q, Q received 9 votes from F & A and 4 votes from O & Q.
- Hence, Q cannot belong to either F & A or O & Q. Consequently, there is no candidate from F & A, and one candidate belongs to O & Q. The remaining two candidates must come from M & S.
Further,
- Since S voted for P, P and S cannot belong to the same department.
- Since R voted for Q, Q and R cannot belong to the same department.
- Similarly, R and P cannot belong to the same department, and Q and S cannot belong to the same department.
Therefore,
- P and Q belong to the M & S department.
- Q and S belong to B & H and O & Q, in either order.
Step 2:
The vote distribution is as follows:
- P received 3 votes:
- From S
- From 2 members of B & H
- Q received 14 votes:
- From R
- From 9 members of F & A
- From 4 members of O & Q
- R received 6 votes:
- From P
- From 5 members of M & S
- S received 1 vote:
- From Q
The department-wise candidate allocation is:
- F & A: 9 faculty members, 9 members, no candidate
- M & S: 7 faculty members, 5 members, Candidates – P and Q
- O & Q: 5 faculty members, 4 members, Candidate – R or S
- B & H: 3 faculty members, 2 members, Candidate – S or R
Only statement B is true.
Ananya Raga, Bhaskar Tala, Charu Veena, and Devendra Sur are four musicians. Each of them started and completed their training as students under each of three Gurus — Pandit Meghnath, Ustad Samiran, and Acharya Raghunath between 2013 and 2024, including both the years. Each Guru trains any student for consecutive years only, for a span of 2, 3, or 4 years, with each Guru having a different span. During some of these years, a student may not have trained under these Gurus; however, they never trained under multiple Gurus in the same year.
In none of these years, any of these Gurus trained more than two of these students at the same time. When two students train under the same Guru at the same time, they are referred to as Gurubhai, irrespective of their gender.
The following additional facts are known.
1. Ustad Samiran never trained more than one of these students in the same year.
2. Acharya Raghunath did not train any of these students during 2015-2018, as well as during 2021-24.
3. Ananya and Devendra were never Gurubhai; neither were Bhaskar and Charu. All other pairs of musicians were Gurubhai for exactly 2 years.
4. In 2013, Ananya and Bhaskar started their trainings under Pandit Meghnath and under Ustad Samiran, respectively.
In which of the following years were Ananya and Bhaskar Gurubhai?
2020
2018
2021
2014
2020
Step 1:
From Condition (1), Ustad Samiran never trains more than one of the four students in the same year. Therefore, each student must have trained under Ustad Samiran for 3 years.
Using Condition (2), Acharya Raghunath does not train any student during 2015–2018 and 2021–2024, creating two gaps of four years each. Hence, Acharya Raghunath trains every student for exactly 2 years.
From Condition (4), Ananya and Bhaskar began their training under Pandit Meghnath and Ustad Samiran, respectively, in 2013. Since no student can train under more than one guru simultaneously, Charu and Devendra must have started under Acharya Raghunath in 2013.
It also follows that Ananya and Bhaskar trained under Acharya Raghunath during 2019–2020, completing their two-year training period. As the training durations under the three gurus are 2, 3, and 4 years, and we have already determined that Acharya Raghunath trains for 2 years while Pandit Meghnath trains for 3 years, Ustad Samiran must train each student for 4 years.
Since Ananya started her training in 2013, and a student cannot train under two gurus at the same time, Bhaskar can train under Pandit Meghnath only during 2021–2024.
Now, applying Condition (3), among the six possible student pairs (AB, AC, AD, BC, BD, and CD), the pairs AD and BC cannot be gurubhais. Each of the remaining four pairs must be gurubhais for exactly 2 years.
Accordingly, Ananya and Charu train together under Pandit Meghnath during 2015 and 2016. Similarly, Bhaskar and Devendra train together during 2021 and 2022.
Step 2:
Under Ustad Samiran, each student has a distinct 3-year training period with no overlap. Therefore, Ananya must train during 2022–2024, as any other three-year period would overlap with her training under the other two gurus.
The remaining schedules can now be determined uniquely. Devendra trains under Ustad Samiran from 2016–2018, while Charu trains under Ustad Samiran from 2019–2021.
The complete schedule is shown in the table below.
Hence, Ananya and Bhaskar were gurubhai in 2020.
In which year did Charu begin her training under Pandit Meghnath?
2017
2015
2016
2021
2015
Step 1:
From Condition (1), Ustad Samiran never trains more than one of the four students in the same year. Therefore, each student must have trained under Ustad Samiran for 3 years.
Using Condition (2), Acharya Raghunath does not train any student during 2015–2018 and 2021–2024, creating two gaps of four years each. Hence, Acharya Raghunath trains every student for exactly 2 years.
From Condition (4), Ananya and Bhaskar began their training under Pandit Meghnath and Ustad Samiran, respectively, in 2013. Since no student can train under more than one guru simultaneously, Charu and Devendra must have started under Acharya Raghunath in 2013.
It also follows that Ananya and Bhaskar trained under Acharya Raghunath during 2019–2020, completing their two-year training period. As the training durations under the three gurus are 2, 3, and 4 years, and we have already determined that Acharya Raghunath trains for 2 years while Pandit Meghnath trains for 3 years, Ustad Samiran must train each student for 4 years.
Since Ananya started her training in 2013, and a student cannot train under two gurus at the same time, Bhaskar can train under Pandit Meghnath only during 2021–2024.
Now, applying Condition (3), among the six possible student pairs (AB, AC, AD, BC, BD, and CD), the pairs AD and BC cannot be gurubhais. Each of the remaining four pairs must be gurubhais for exactly 2 years.
Accordingly, Ananya and Charu train together under Pandit Meghnath during 2015 and 2016. Similarly, Bhaskar and Devendra train together during 2021 and 2022.
Step 2:
Under Ustad Samiran, each student has a distinct 3-year training period with no overlap. Therefore, Ananya must train during 2022–2024, as any other three-year period would overlap with her training under the other two gurus.
The remaining schedules can now be determined uniquely. Devendra trains under Ustad Samiran from 2016–2018, while Charu trains under Ustad Samiran from 2019–2021.
The complete schedule is shown in the table below.
Charu began her training under Pandit Meghnath in 2015.
In which of the following years were Bhaskar and Devendra Gurubhai?
2015
2022
2018
2020
2022
Step 1:
From Condition (1), Ustad Samiran never trains more than one of the four students in the same year. Therefore, each student must have trained under Ustad Samiran for 3 years.
Using Condition (2), Acharya Raghunath does not train any student during 2015–2018 and 2021–2024, creating two gaps of four years each. Hence, Acharya Raghunath trains every student for exactly 2 years.
From Condition (4), Ananya and Bhaskar began their training under Pandit Meghnath and Ustad Samiran, respectively, in 2013. Since no student can train under more than one guru simultaneously, Charu and Devendra must have started under Acharya Raghunath in 2013.
It also follows that Ananya and Bhaskar trained under Acharya Raghunath during 2019–2020, completing their two-year training period. As the training durations under the three gurus are 2, 3, and 4 years, and we have already determined that Acharya Raghunath trains for 2 years while Pandit Meghnath trains for 3 years, Ustad Samiran must train each student for 4 years.
Since Ananya started her training in 2013, and a student cannot train under two gurus at the same time, Bhaskar can train under Pandit Meghnath only during 2021–2024.
Now, applying Condition (3), among the six possible student pairs (AB, AC, AD, BC, BD, and CD), the pairs AD and BC cannot be gurubhais. Each of the remaining four pairs must be gurubhais for exactly 2 years.
Accordingly, Ananya and Charu train together under Pandit Meghnath during 2015 and 2016. Similarly, Bhaskar and Devendra train together during 2021 and 2022.
Step 2:
Under Ustad Samiran, each student has a distinct 3-year training period with no overlap. Therefore, Ananya must train during 2022–2024, as any other three-year period would overlap with her training under the other two gurus.
The remaining schedules can now be determined uniquely. Devendra trains under Ustad Samiran from 2016–2018, while Charu trains under Ustad Samiran from 2019–2021.
The complete schedule is shown in the table below.
Bhaskar and Devendra were Gurubhai in 2022.
Which of the following statements is TRUE?
Ananya was training under Ustad Samiran in 2015.
Charu was training under Ustad Samiran in 2019.
Ananya was training under Ustad Samiran in 2018.
Charu was training under Ustad Samiran in 2018.
Charu was training under Ustad Samiran in 2019.
Step 1:
From Condition (1), Ustad Samiran never trains more than one of the four students in the same year. Therefore, each student must have trained under Ustad Samiran for 3 years.
Using Condition (2), Acharya Raghunath does not train any student during 2015–2018 and 2021–2024, creating two gaps of four years each. Hence, Acharya Raghunath trains every student for exactly 2 years.
From Condition (4), Ananya and Bhaskar began their training under Pandit Meghnath and Ustad Samiran, respectively, in 2013. Since no student can train under more than one guru simultaneously, Charu and Devendra must have started under Acharya Raghunath in 2013.
It also follows that Ananya and Bhaskar trained under Acharya Raghunath during 2019–2020, completing their two-year training period. As the training durations under the three gurus are 2, 3, and 4 years, and we have already determined that Acharya Raghunath trains for 2 years while Pandit Meghnath trains for 3 years, Ustad Samiran must train each student for 4 years.
Since Ananya started her training in 2013, and a student cannot train under two gurus at the same time, Bhaskar can train under Pandit Meghnath only during 2021–2024.
Now, applying Condition (3), among the six possible student pairs (AB, AC, AD, BC, BD, and CD), the pairs AD and BC cannot be gurubhais. Each of the remaining four pairs must be gurubhais for exactly 2 years.
Accordingly, Ananya and Charu train together under Pandit Meghnath during 2015 and 2016. Similarly, Bhaskar and Devendra train together during 2021 and 2022.
Step 2:
Under Ustad Samiran, each student has a distinct 3-year training period with no overlap. Therefore, Ananya must train during 2022–2024, as any other three-year period would overlap with her training under the other two gurus.
The remaining schedules can now be determined uniquely. Devendra trains under Ustad Samiran from 2016–2018, while Charu trains under Ustad Samiran from 2019–2021.
The complete schedule is shown in the table below.
Let us check each statement:
1. Ananya was training under Ustad Samiran in 2015, is not true.
2. Charu was training under Ustad Samiran in 2019, is true.
3. Ananya was training under Ustad Samiran in 2018, is not true
4. Charu was training under Ustad Samiran in 2018, is not true.
Between 2013-24, there were 4 years when only two of these four musicians were training under these three Gurus. These years were 2017, 2018, 2023 and 2024.
Step 1:
From Condition (1), Ustad Samiran never trains more than one of the four students in the same year. Therefore, each student must have trained under Ustad Samiran for 3 years.
Using Condition (2), Acharya Raghunath does not train any student during 2015–2018 and 2021–2024, creating two gaps of four years each. Hence, Acharya Raghunath trains every student for exactly 2 years.
From Condition (4), Ananya and Bhaskar began their training under Pandit Meghnath and Ustad Samiran, respectively, in 2013. Since no student can train under more than one guru simultaneously, Charu and Devendra must have started under Acharya Raghunath in 2013.
It also follows that Ananya and Bhaskar trained under Acharya Raghunath during 2019–2020, completing their two-year training period. As the training durations under the three gurus are 2, 3, and 4 years, and we have already determined that Acharya Raghunath trains for 2 years while Pandit Meghnath trains for 3 years, Ustad Samiran must train each student for 4 years.
Since Ananya started her training in 2013, and a student cannot train under two gurus at the same time, Bhaskar can train under Pandit Meghnath only during 2021–2024.
Now, applying Condition (3), among the six possible student pairs (AB, AC, AD, BC, BD, and CD), the pairs AD and BC cannot be gurubhais. Each of the remaining four pairs must be gurubhais for exactly 2 years.
Accordingly, Ananya and Charu train together under Pandit Meghnath during 2015 and 2016. Similarly, Bhaskar and Devendra train together during 2021 and 2022.
Step 2:
Under Ustad Samiran, each student has a distinct 3-year training period with no overlap. Therefore, Ananya must train during 2022–2024, as any other three-year period would overlap with her training under the other two gurus.
The remaining schedules can now be determined uniquely. Devendra trains under Ustad Samiran from 2016–2018, while Charu trains under Ustad Samiran from 2019–2021.
The complete schedule is shown in the table below.
Between 2013-24, there were 4 years when only two of these four musicians were training under these three Gurus. These years were 2017, 2018, 2023 and 2024.
Eight gymnastics players numbered 1 through 8 underwent a training camp where they were coached by three coaches - Xena, Yuki, and Zara. Each coach trained at least two players.Yuki trained only even numbered players, while Zara trained only odd numbered players. After the camp, the coaches evaluated the players and gave integer ratings to the respective players trained by them on a scale of 1 to 7, with 1 being the lowest rating and 7 the highest.
The following additional information is known.
1. Xena trained more players than Yuki.
2. Player-1 and Player-4 were trained by the same coach, while the coaches who trained Player-2, Player-3 and Player-5 were all different.
3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got a unique rating.
4. The average of the ratings of all the players was 4.
5. Player-2 got the highest rating.
6. The average of the ratings of the players trained by Yuki was twice that of the player strained by Xena and two more than that of the players trained by Zara.
7. Player-4’s rating was double of Player-8's and less than Player-5’s.
What best can be concluded about the number of players coached by Zara?
Exactly 3
Either 2 or 3
Exactly 2
Either 2 or 3 or 4
Exactly 2
Step 1:
From conditions (3) and (4), exactly two players received the same rating.
Let the repeated rating be N.
Then,
(1 + 2 + 3 + 4 + 5 + 6 + 7 + N) / 8 = 4
⇒ N = 4
Hence, Players 5 and 7 both received a rating of 4.
Since Xena trained more players than Yuki, there are two possible distributions:
- Possibility 1:
- Xena trains 3 players.
- Yuki trains 2 players.
- Zara trains 3 players.
- Possibility 2:
- Xena trains 4 players.
- Yuki trains 2 players.
- Zara trains 2 players.
For Possibility 1,
X = 38/13, which is not an integer and is therefore not feasible.
For Possibility 2,
X = 3, which satisfies the conditions.
Thus,
- Xena trained 4 players with an average score of 3, giving a total score of 12.
- Yuki trained 2 players with an average score of 6, giving a total score of 12.
- Zara trained 2 players with an average score of 4, giving a total score of 8.
Step 2:
From condition (5), Player 2 received a rating of 7.
Also, Player 4 received a rating of 2, and Player 8 received a rating of 1.
The known ratings are:
- Player 2 → 7
- Player 4 → 2
- Player 5 → 4
- Player 7 → 4
- Player 8 → 1
Yuki trained only two players, whose ratings add up to 12.
The only possible combination is 7 and 5.
Since 7 belongs to Player 2, the rating 5 must belong to Player 6.
As Yuki trained only even-numbered players and only Player 6 remains, Players 2 and 6 must have been trained by Yuki.
Zara's trainees have a total score of 8.
This total can be obtained either as 2 + 6 or 4 + 4.
Since the rating 2 belongs to Player 4, who is even-numbered, and Zara trained only odd-numbered players, the 2 + 6 combination is not possible.
Therefore, Zara must have trained Players 5 and 7, both of whom have a rating of 4.
The remaining players—1, 3, 4, and 8—were trained by Xena.
Thus, the final assignments are:
- Player 1 → Rating 3/6, Trained by Xena
- Player 2 → Rating 7, Trained by Yuki
- Player 3 → Rating 6/3, Trained by Xena
- Player 4 → Rating 2, Trained by Xena
- Player 5 → Rating 4, Trained by Zara
- Player 6 → Rating 5, Trained by Yuki
- Player 7 → Rating 4, Trained by Zara
- Player 8 → Rating 1, Trained by Xena
What was the rating of Player-7?
Step 1:
From conditions (3) and (4), exactly two players received the same rating.
Let the repeated rating be N.
Then,
(1 + 2 + 3 + 4 + 5 + 6 + 7 + N) / 8 = 4
⇒ N = 4
Hence, Players 5 and 7 both received a rating of 4.
Since Xena trained more players than Yuki, there are two possible distributions:
- Possibility 1:
- Xena trains 3 players.
- Yuki trains 2 players.
- Zara trains 3 players.
- Possibility 2:
- Xena trains 4 players.
- Yuki trains 2 players.
- Zara trains 2 players.
For Possibility 1,
X = 38/13, which is not an integer and is therefore not feasible.
For Possibility 2,
X = 3, which satisfies the conditions.
Thus,
- Xena trained 4 players with an average score of 3, giving a total score of 12.
- Yuki trained 2 players with an average score of 6, giving a total score of 12.
- Zara trained 2 players with an average score of 4, giving a total score of 8.
Step 2:
From condition (5), Player 2 received a rating of 7.
Also, Player 4 received a rating of 2, and Player 8 received a rating of 1.
The known ratings are:
- Player 2 → 7
- Player 4 → 2
- Player 5 → 4
- Player 7 → 4
- Player 8 → 1
Yuki trained only two players, whose ratings add up to 12.
The only possible combination is 7 and 5.
Since 7 belongs to Player 2, the rating 5 must belong to Player 6.
As Yuki trained only even-numbered players and only Player 6 remains, Players 2 and 6 must have been trained by Yuki.
Zara's trainees have a total score of 8.
This total can be obtained either as 2 + 6 or 4 + 4.
Since the rating 2 belongs to Player 4, who is even-numbered, and Zara trained only odd-numbered players, the 2 + 6 combination is not possible.
Therefore, Zara must have trained Players 5 and 7, both of whom have a rating of 4.
The remaining players—1, 3, 4, and 8—were trained by Xena.
Thus, the final assignments are:
- Player 1 → Rating 3/6, Trained by Xena
- Player 2 → Rating 7, Trained by Yuki
- Player 3 → Rating 6/3, Trained by Xena
- Player 4 → Rating 2, Trained by Xena
- Player 5 → Rating 4, Trained by Zara
- Player 6 → Rating 5, Trained by Yuki
- Player 7 → Rating 4, Trained by Zara
- Player 8 → Rating 1, Trained by Xena
What was the rating of Player-6?
Step 1:
From conditions (3) and (4), exactly two players received the same rating.
Let the repeated rating be N.
Then,
(1 + 2 + 3 + 4 + 5 + 6 + 7 + N) / 8 = 4
⇒ N = 4
Hence, Players 5 and 7 both received a rating of 4.
Since Xena trained more players than Yuki, there are two possible distributions:
- Possibility 1:
- Xena trains 3 players.
- Yuki trains 2 players.
- Zara trains 3 players.
- Possibility 2:
- Xena trains 4 players.
- Yuki trains 2 players.
- Zara trains 2 players.
For Possibility 1,
X = 38/13, which is not an integer and is therefore not feasible.
For Possibility 2,
X = 3, which satisfies the conditions.
Thus,
- Xena trained 4 players with an average score of 3, giving a total score of 12.
- Yuki trained 2 players with an average score of 6, giving a total score of 12.
- Zara trained 2 players with an average score of 4, giving a total score of 8.
Step 2:
From condition (5), Player 2 received a rating of 7.
Also, Player 4 received a rating of 2, and Player 8 received a rating of 1.
The known ratings are:
- Player 2 → 7
- Player 4 → 2
- Player 5 → 4
- Player 7 → 4
- Player 8 → 1
Yuki trained only two players, whose ratings add up to 12.
The only possible combination is 7 and 5.
Since 7 belongs to Player 2, the rating 5 must belong to Player 6.
As Yuki trained only even-numbered players and only Player 6 remains, Players 2 and 6 must have been trained by Yuki.
Zara's trainees have a total score of 8.
This total can be obtained either as 2 + 6 or 4 + 4.
Since the rating 2 belongs to Player 4, who is even-numbered, and Zara trained only odd-numbered players, the 2 + 6 combination is not possible.
Therefore, Zara must have trained Players 5 and 7, both of whom have a rating of 4.
The remaining players—1, 3, 4, and 8—were trained by Xena.
Thus, the final assignments are:
- Player 1 → Rating 3/6, Trained by Xena
- Player 2 → Rating 7, Trained by Yuki
- Player 3 → Rating 6/3, Trained by Xena
- Player 4 → Rating 2, Trained by Xena
- Player 5 → Rating 4, Trained by Zara
- Player 6 → Rating 5, Trained by Yuki
- Player 7 → Rating 4, Trained by Zara
- Player 8 → Rating 1, Trained by Xena
For how many players the ratings can be determined with certainty?
Step 1:
From conditions (3) and (4), exactly two players received the same rating.
Let the repeated rating be N.
Then,
(1 + 2 + 3 + 4 + 5 + 6 + 7 + N) / 8 = 4
⇒ N = 4
Hence, Players 5 and 7 both received a rating of 4.
Since Xena trained more players than Yuki, there are two possible distributions:
- Possibility 1:
- Xena trains 3 players.
- Yuki trains 2 players.
- Zara trains 3 players.
- Possibility 2:
- Xena trains 4 players.
- Yuki trains 2 players.
- Zara trains 2 players.
For Possibility 1,
X = 38/13, which is not an integer and is therefore not feasible.
For Possibility 2,
X = 3, which satisfies the conditions.
Thus,
- Xena trained 4 players with an average score of 3, giving a total score of 12.
- Yuki trained 2 players with an average score of 6, giving a total score of 12.
- Zara trained 2 players with an average score of 4, giving a total score of 8.
Step 2:
From condition (5), Player 2 received a rating of 7.
Also, Player 4 received a rating of 2, and Player 8 received a rating of 1.
The known ratings are:
- Player 2 → 7
- Player 4 → 2
- Player 5 → 4
- Player 7 → 4
- Player 8 → 1
Yuki trained only two players, whose ratings add up to 12.
The only possible combination is 7 and 5.
Since 7 belongs to Player 2, the rating 5 must belong to Player 6.
As Yuki trained only even-numbered players and only Player 6 remains, Players 2 and 6 must have been trained by Yuki.
Zara's trainees have a total score of 8.
This total can be obtained either as 2 + 6 or 4 + 4.
Since the rating 2 belongs to Player 4, who is even-numbered, and Zara trained only odd-numbered players, the 2 + 6 combination is not possible.
Therefore, Zara must have trained Players 5 and 7, both of whom have a rating of 4.
The remaining players—1, 3, 4, and 8—were trained by Xena.
Thus, the final assignments are:
- Player 1 → Rating 3/6, Trained by Xena
- Player 2 → Rating 7, Trained by Yuki
- Player 3 → Rating 6/3, Trained by Xena
- Player 4 → Rating 2, Trained by Xena
- Player 5 → Rating 4, Trained by Zara
- Player 6 → Rating 5, Trained by Yuki
- Player 7 → Rating 4, Trained by Zara
- Player 8 → Rating 1, Trained by Xena
Who all were the players trained by Xena?
Player-1, Player-3, Player-4
Player-1, Player-3, Player-4, Player-6
Player-1, Player-3, Player-4, Player-8
Player-1, Player-4, Player-6, Player-8
Player-1, Player-3, Player-4, Player-8
Step 1:
From conditions (3) and (4), exactly two players received the same rating.
Let the repeated rating be N.
Then,
(1 + 2 + 3 + 4 + 5 + 6 + 7 + N) / 8 = 4
⇒ N = 4
Hence, Players 5 and 7 both received a rating of 4.
Since Xena trained more players than Yuki, there are two possible distributions:
- Possibility 1:
- Xena trains 3 players.
- Yuki trains 2 players.
- Zara trains 3 players.
- Possibility 2:
- Xena trains 4 players.
- Yuki trains 2 players.
- Zara trains 2 players.
For Possibility 1,
X = 38/13, which is not an integer and is therefore not feasible.
For Possibility 2,
X = 3, which satisfies the conditions.
Thus,
- Xena trained 4 players with an average score of 3, giving a total score of 12.
- Yuki trained 2 players with an average score of 6, giving a total score of 12.
- Zara trained 2 players with an average score of 4, giving a total score of 8.
Step 2:
From condition (5), Player 2 received a rating of 7.
Also, Player 4 received a rating of 2, and Player 8 received a rating of 1.
The known ratings are:
- Player 2 → 7
- Player 4 → 2
- Player 5 → 4
- Player 7 → 4
- Player 8 → 1
Yuki trained only two players, whose ratings add up to 12.
The only possible combination is 7 and 5.
Since 7 belongs to Player 2, the rating 5 must belong to Player 6.
As Yuki trained only even-numbered players and only Player 6 remains, Players 2 and 6 must have been trained by Yuki.
Zara's trainees have a total score of 8.
This total can be obtained either as 2 + 6 or 4 + 4.
Since the rating 2 belongs to Player 4, who is even-numbered, and Zara trained only odd-numbered players, the 2 + 6 combination is not possible.
Therefore, Zara must have trained Players 5 and 7, both of whom have a rating of 4.
The remaining players—1, 3, 4, and 8—were trained by Xena.
Thus, the final assignments are:
- Player 1 → Rating 3/6, Trained by Xena
- Player 2 → Rating 7, Trained by Yuki
- Player 3 → Rating 6/3, Trained by Xena
- Player 4 → Rating 2, Trained by Xena
- Player 5 → Rating 4, Trained by Zara
- Player 6 → Rating 5, Trained by Yuki
- Player 7 → Rating 4, Trained by Zara
- Player 8 → Rating 1, Trained by Xena
Anjali, Bipasha, and Chitra visited an entertainment park that has four rides. Each ride lasts one hour and can accommodate one visitor at one point. All rides begin at 9 am and must be completed by 5 pm except for Ride-3, for which the last ride has to be completed by 1 pm. Ride gates open every 30 minutes, e.g. 10 am, 10:30 am, and so on. Whenever a ride gate opens, and there is no visitor inside, the first visitor waiting in the queue buys the ticket just before taking the ride. The ticket prices are Rs. 20, Rs. 50, Rs. 30 and Rs. 40 for Rides 1 to 4, respectively. Each of the three visitors took at least one ride and did not necessarily take all rides. None of them took the same ride more than once. The movement time from one ride to another is negligible, and a visitor leaves the ride immediately after the completion of the ride. No one takes a break inside the park unless mentioned explicitly.
The following information is also known.
1. Chitra never waited in the queue and completed her visit by 11 am after spending Rs. 50 to pay for the ticket(s).
2. Anjali took Ride-1 at 11 am after waiting for 30 mins for Chitra to complete it. It was the only ride where Anjali waited.
3. Bipasha began her first of three rides at 11:30 am. All three visitors incurred the same amount of ticket expense by 12:15 pm.
4. The last ride taken by Anjali and Bipasha was the same, where Bipasha waited 30 mins for Anjali to complete her ride. Before standing in the queue for that ride, Bipasha took a 1-hour coffee break after completing her previous ride.
What was the total amount spent on tickets (in Rs.) by Bipasha?
90
120
100
110
110
Step 1:
From conditions (1) and (2), it can be inferred that Chitra completed Ride 3 from 9:00 AM to 10:00 AM and Ride 1 from 10:00 AM to 11:00 AM. This follows because Anjali had to wait for 30 minutes to complete Ride 1, which finished at 11:00 AM.
From condition (3), Bipasha paid for only one ride until 12:15 PM, i.e., Ride 2, which ran from 11:30 AM to 12:30 PM. Since Bipasha completed three rides in total, she could not have taken Ride 3, as it ended at 1:00 PM.
The schedule at this stage is:
- Anjali: Ride 1 – Unknown, Ride 2 – Unknown, Ride 3 – Unknown, Ride 4 – Unknown
- Bipasha: Ride 2 – 11:30 AM to 12:30 PM, Ride 3 – Not taken
- Chitra: Ride 1 – 10:00 AM to 11:00 AM, Ride 3 – 9:00 AM to 10:00 AM, Ride 2 and Ride 4 – Not taken
Step 2:
Using condition (4), Bipasha's schedule can be determined as follows:
- 11:30 AM – 12:30 PM: Ride 2
- 12:30 PM – 1:30 PM: Free
- 1:30 PM – 2:30 PM: Coffee break
- 2:30 PM – 3:00 PM: Waiting
- 3:00 PM – 4:00 PM: Ride 4
Since Bipasha waited from 2:30 PM to 3:00 PM for Anjali to complete the previous ride, her final ride started at 3:00 PM and ended at 4:00 PM.
Hence, the final schedule is:
- Anjali
- Ride 1: 11:00 AM – 12:00 PM
- Ride 2: 1:00 PM – 2:00 PM
- Ride 3: 12:00 PM – 1:00 PM
- Ride 4: 2:00 PM – 3:00 PM
- Bipasha
- Ride 2: 11:30 AM – 12:30 PM
- Ride 4: 3:00 PM – 4:00 PM
- Chitra
- Ride 1: 10:00 AM – 11:00 AM
- Ride 3: 9:00 AM – 10:00 AM
Total amount spent on tickets (in Rs.) by Bipasha is Rs. 110.
Which ride was taken by all three visitors?
Ride-4
Ride-3
Ride-2
Ride-1
Ride-1
Step 1:
From conditions (1) and (2), it can be inferred that Chitra completed Ride 3 from 9:00 AM to 10:00 AM and Ride 1 from 10:00 AM to 11:00 AM. This follows because Anjali had to wait for 30 minutes to complete Ride 1, which finished at 11:00 AM.
From condition (3), Bipasha paid for only one ride until 12:15 PM, i.e., Ride 2, which ran from 11:30 AM to 12:30 PM. Since Bipasha completed three rides in total, she could not have taken Ride 3, as it ended at 1:00 PM.
The schedule at this stage is:
- Anjali: Ride 1 – Unknown, Ride 2 – Unknown, Ride 3 – Unknown, Ride 4 – Unknown
- Bipasha: Ride 2 – 11:30 AM to 12:30 PM, Ride 3 – Not taken
- Chitra: Ride 1 – 10:00 AM to 11:00 AM, Ride 3 – 9:00 AM to 10:00 AM, Ride 2 and Ride 4 – Not taken
Step 2:
Using condition (4), Bipasha's schedule can be determined as follows:
- 11:30 AM – 12:30 PM: Ride 2
- 12:30 PM – 1:30 PM: Free
- 1:30 PM – 2:30 PM: Coffee break
- 2:30 PM – 3:00 PM: Waiting
- 3:00 PM – 4:00 PM: Ride 4
Since Bipasha waited from 2:30 PM to 3:00 PM for Anjali to complete the previous ride, her final ride started at 3:00 PM and ended at 4:00 PM.
Hence, the final schedule is:
- Anjali
- Ride 1: 11:00 AM – 12:00 PM
- Ride 2: 1:00 PM – 2:00 PM
- Ride 3: 12:00 PM – 1:00 PM
- Ride 4: 2:00 PM – 3:00 PM
- Bipasha
- Ride 2: 11:30 AM – 12:30 PM
- Ride 4: 3:00 PM – 4:00 PM
- Chitra
- Ride 1: 10:00 AM – 11:00 AM
- Ride 3: 9:00 AM – 10:00 AM
Ride 1 was taken by all three visitors.
Which were all the rides that Anjali completed by 2:00 pm?
Ride-1, Ride-2, and Ride-3
Ride-1 and Ride-3
Ride-1, Ride-2, and Ride-4
Ride-1 and Ride-4
Ride-1, Ride-2, and Ride-3
Step 1:
From conditions (1) and (2), it can be inferred that Chitra completed Ride 3 from 9:00 AM to 10:00 AM and Ride 1 from 10:00 AM to 11:00 AM. This follows because Anjali had to wait for 30 minutes to complete Ride 1, which finished at 11:00 AM.
From condition (3), Bipasha paid for only one ride until 12:15 PM, i.e., Ride 2, which ran from 11:30 AM to 12:30 PM. Since Bipasha completed three rides in total, she could not have taken Ride 3, as it ended at 1:00 PM.
The schedule at this stage is:
- Anjali: Ride 1 – Unknown, Ride 2 – Unknown, Ride 3 – Unknown, Ride 4 – Unknown
- Bipasha: Ride 2 – 11:30 AM to 12:30 PM, Ride 3 – Not taken
- Chitra: Ride 1 – 10:00 AM to 11:00 AM, Ride 3 – 9:00 AM to 10:00 AM, Ride 2 and Ride 4 – Not taken
Step 2:
Using condition (4), Bipasha's schedule can be determined as follows:
- 11:30 AM – 12:30 PM: Ride 2
- 12:30 PM – 1:30 PM: Free
- 1:30 PM – 2:30 PM: Coffee break
- 2:30 PM – 3:00 PM: Waiting
- 3:00 PM – 4:00 PM: Ride 4
Since Bipasha waited from 2:30 PM to 3:00 PM for Anjali to complete the previous ride, her final ride started at 3:00 PM and ended at 4:00 PM.
Hence, the final schedule is:
- Anjali
- Ride 1: 11:00 AM – 12:00 PM
- Ride 2: 1:00 PM – 2:00 PM
- Ride 3: 12:00 PM – 1:00 PM
- Ride 4: 2:00 PM – 3:00 PM
- Bipasha
- Ride 2: 11:30 AM – 12:30 PM
- Ride 4: 3:00 PM – 4:00 PM
- Chitra
- Ride 1: 10:00 AM – 11:00 AM
- Ride 3: 9:00 AM – 10:00 AM
The rides that Anjali completed by 2 pm are Ride 1, Ride 2 and Ride 3.
How many rides did Anjali and Chitra take in total?
Step 1:
From conditions (1) and (2), it can be inferred that Chitra completed Ride 3 from 9:00 AM to 10:00 AM and Ride 1 from 10:00 AM to 11:00 AM. This follows because Anjali had to wait for 30 minutes to complete Ride 1, which finished at 11:00 AM.
From condition (3), Bipasha paid for only one ride until 12:15 PM, i.e., Ride 2, which ran from 11:30 AM to 12:30 PM. Since Bipasha completed three rides in total, she could not have taken Ride 3, as it ended at 1:00 PM.
The schedule at this stage is:
- Anjali: Ride 1 – Unknown, Ride 2 – Unknown, Ride 3 – Unknown, Ride 4 – Unknown
- Bipasha: Ride 2 – 11:30 AM to 12:30 PM, Ride 3 – Not taken
- Chitra: Ride 1 – 10:00 AM to 11:00 AM, Ride 3 – 9:00 AM to 10:00 AM, Ride 2 and Ride 4 – Not taken
Step 2:
Using condition (4), Bipasha's schedule can be determined as follows:
- 11:30 AM – 12:30 PM: Ride 2
- 12:30 PM – 1:30 PM: Free
- 1:30 PM – 2:30 PM: Coffee break
- 2:30 PM – 3:00 PM: Waiting
- 3:00 PM – 4:00 PM: Ride 4
Since Bipasha waited from 2:30 PM to 3:00 PM for Anjali to complete the previous ride, her final ride started at 3:00 PM and ended at 4:00 PM.
Hence, the final schedule is:
- Anjali
- Ride 1: 11:00 AM – 12:00 PM
- Ride 2: 1:00 PM – 2:00 PM
- Ride 3: 12:00 PM – 1:00 PM
- Ride 4: 2:00 PM – 3:00 PM
- Bipasha
- Ride 2: 11:30 AM – 12:30 PM
- Ride 4: 3:00 PM – 4:00 PM
- Chitra
- Ride 1: 10:00 AM – 11:00 AM
- Ride 3: 9:00 AM – 10:00 AM
Anjali and Chitra take 6 Rides in total.
What was the total amount spent on tickets (in Rs.) by Anjali?
Step 1:
From conditions (1) and (2), it can be inferred that Chitra completed Ride 3 from 9:00 AM to 10:00 AM and Ride 1 from 10:00 AM to 11:00 AM. This follows because Anjali had to wait for 30 minutes to complete Ride 1, which finished at 11:00 AM.
From condition (3), Bipasha paid for only one ride until 12:15 PM, i.e., Ride 2, which ran from 11:30 AM to 12:30 PM. Since Bipasha completed three rides in total, she could not have taken Ride 3, as it ended at 1:00 PM.
The schedule at this stage is:
- Anjali: Ride 1 – Unknown, Ride 2 – Unknown, Ride 3 – Unknown, Ride 4 – Unknown
- Bipasha: Ride 2 – 11:30 AM to 12:30 PM, Ride 3 – Not taken
- Chitra: Ride 1 – 10:00 AM to 11:00 AM, Ride 3 – 9:00 AM to 10:00 AM, Ride 2 and Ride 4 – Not taken
Step 2:
Using condition (4), Bipasha's schedule can be determined as follows:
- 11:30 AM – 12:30 PM: Ride 2
- 12:30 PM – 1:30 PM: Free
- 1:30 PM – 2:30 PM: Coffee break
- 2:30 PM – 3:00 PM: Waiting
- 3:00 PM – 4:00 PM: Ride 4
Since Bipasha waited from 2:30 PM to 3:00 PM for Anjali to complete the previous ride, her final ride started at 3:00 PM and ended at 4:00 PM.
Hence, the final schedule is:
- Anjali
- Ride 1: 11:00 AM – 12:00 PM
- Ride 2: 1:00 PM – 2:00 PM
- Ride 3: 12:00 PM – 1:00 PM
- Ride 4: 2:00 PM – 3:00 PM
- Bipasha
- Ride 2: 11:30 AM – 12:30 PM
- Ride 4: 3:00 PM – 4:00 PM
- Chitra
- Ride 1: 10:00 AM – 11:00 AM
- Ride 3: 9:00 AM – 10:00 AM
The total amount spent on tickets by Anjali is Rs. 140.
Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown's currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars.
Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country's local currency. Each traveler had different spends (in the country's local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country's local currency).
The total "Travel Cost" for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.
The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:
i. Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.
ii. Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira's Travel Cost was 4000.
iii. Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.
What is the sum of Travel Costs for all travelers in Zentars?
How many Zentars did Lian spend in the two countries he visited?
What was Jano's total spend in the two countries he visited, in Aurels?
One Brin is equivalent to how many Crowns?
0.5
0.125
4
8
4
Which of the following statements is NOT true about money spent in the local currency?
Jano spent 2000 in Aurevia
Lian spent 2000 in Cyrenia
Jano spent 2000 in Cyrenia
Kira spent 1000 in Aurevia
Jano spent 2000 in Aurevia
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