Musicians | CAT 2025 Slot 2 DILR | Wide Wordy | Moderate
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? Moderate
1. 2014
2. 2021
3. 2020
4. 2018
Answer & Explanation
Correct Answer: 2020
From the conditions, Ananya and Bhaskar must be Gurubhai for exactly two years. Gurubhai status can arise only when two students train under the same Guru in the same year. Ustad Samiran never trains more than one student in a year, so no Gurubhai relationships can occur under him. Acharya Raghunath trains only in two isolated two‑year blocks (2013–14 and 2019–20), and each block can host at most one Gurubhai pair. Since Ananya cannot be paired with Devendra and Bhaskar cannot be paired with Charu, the available Raghunath slots are already forced onto other admissible pairs. Hence, Ananya and Bhaskar’s Gurubhai years must occur under Pandit Meghnath. Using the final consistent year‑wise schedule, Ananya and Bhaskar are together under Pandit Meghnath during 2020 and one other adjacent year. Among the given answer options, 2020 is the only year that necessarily belongs to their Gurubhai overlap irrespective of how the remaining flexible years are arranged. Therefore, 2020 is the correct answer.
Steps to make the table:
Phase 1: Fix training spans and Raghunath slots
1. Each guru trains for a different duration: 2, 3, and 4 continuous years.
2. Acharya Raghunath is available only in two isolated windows: 2013–14 and 2019–20. Hence, his training span must be exactly 2 years.
3. This leaves Pandit Meghnath and Ustad Samiran with spans of 3 years and 4 years respectively.
4. To satisfy the given gurubhai overlap conditions, assign Meghnath a 3-year span and Samiran a 4-year span.
5. From Fact 4, Ananya starts with Meghnath in 2013 and Bhaskar starts with Samiran in 2013.
6. Therefore, neither Ananya nor Bhaskar can take Raghunath’s 2013–14 slot, as that would overlap with their starting guru.
7. Hence, Ananya and Bhaskar must take Raghunath in 2019–20, leaving Charu and Devendra to take Raghunath in 2013–14.
Phase 2: Fix schedules for Ananya and Bhaskar
8. Ananya must complete her 3-year training under Meghnath starting in 2013.
So, Ananya studies under Meghnath from 2013 to 2015.
9. Bhaskar must complete his 4-year training under Samiran starting in 2013.
So, Bhaskar studies under Samiran from 2013 to 2016.
10. Bhaskar’s Meghnath training must occur after his Raghunath period of 2019–20.
The only viable placement is 2022–2024.
11. Ananya’s Samiran training must begin after her Raghunath period (2019–20) and must not overlap Bhaskar’s Meghnath slot excessively.
The consistent placement is 2021–2024.
Phase 3: Fix schedules for Charu and Devendra
12. Devendra must be gurubhai with Bhaskar for exactly two years under Samiran.
13. Bhaskar’s Samiran span is 2013–16, so Devendra’s 4-year Samiran span must overlap this window for exactly two years.
14. The only placement satisfying this is 2015–2018, overlapping in 2015 and 2016.
15. Devendra’s Meghnath training must follow his Samiran period.
16. To ensure Bhaskar and Devendra are gurubhai under Meghnath in the year 2022, Devendra’s Meghnath span is placed from 2020 to 2022.
17. Charu must be gurubhai with Ananya for exactly two years, partially under Meghnath and partially under Samiran.
18. Ananya’s Meghnath span is 2013–15, so Charu’s 3-year Meghnath span must overlap this for one year.
The only placement is 2015–2017.
19. To complete the gurubhai requirement with Ananya, Charu’s 4-year Samiran span must overlap Ananya’s Samiran span in exactly one year.
20. Placing Charu’s Samiran span from 2018 to 2021 achieves this overlap in 2021.
Final Working Table (2013–2024)
Spans: M=3 yrs, S=4 yrs, R=2 yrs.
R Groups:
Group 1 (R=2013–2014): C, D
Group 2 (R=2019–2020): A, B
| Musician | M (3 years) | S (4 years) | R (2 years) |
| Ananya (A) | 2013–2015 | 2021–2024 | 2019–2020 |
| Bhaskar (B) | 2022–2024 | 2013–2016 | 2019–2020 |
| Charu (C) | 2015–2017 | 2018–2021 | 2013–2014 |
| Devendra (D) | 2020–2022 | 2015–2018 | 2013–2014 |
In which year did Charu begin her training under Pandit Meghnath? Hard
1. 2021
2. 2017
3. 2016
4. 2015
Answer & Explanation
Correct Answer: 2015
Charu must be Gurubhai with Ananya for exactly two years. This overlap cannot occur under Ustad Samiran, and Acharya Raghunath has only limited two‑year windows that are already constrained by other mandatory Gurubhai pairs. Hence, the Ananya–Charu Gurubhai overlap must occur under Pandit Meghnath. Ananya begins training under Pandit Meghnath in 2013, and Pandit Meghnath’s span must be four consecutive years to accommodate all required overlaps. For Charu to overlap with Ananya for exactly two years under Pandit Meghnath, Charu’s start year under Pandit Meghnath must be precisely two years after Ananya’s start, so that their overlap is neither more nor less than two years. If Charu started earlier than 2015, the overlap would exceed two years; if she started later, the overlap would be reduced to one or zero years. Hence, Charu must begin training under Pandit Meghnath in 2015, making this the only viable and forced answer.
Steps to make the table:
Phase 1: Fix training spans and Raghunath slots
1. Each guru trains for a different duration: 2, 3, and 4 continuous years.
2. Acharya Raghunath is available only in two isolated windows: 2013–14 and 2019–20. Hence, his training span must be exactly 2 years.
3. This leaves Pandit Meghnath and Ustad Samiran with spans of 3 years and 4 years respectively.
4. To satisfy the given gurubhai overlap conditions, assign Meghnath a 3-year span and Samiran a 4-year span.
5. From Fact 4, Ananya starts with Meghnath in 2013 and Bhaskar starts with Samiran in 2013.
6. Therefore, neither Ananya nor Bhaskar can take Raghunath’s 2013–14 slot, as that would overlap with their starting guru.
7. Hence, Ananya and Bhaskar must take Raghunath in 2019–20, leaving Charu and Devendra to take Raghunath in 2013–14.
Phase 2: Fix schedules for Ananya and Bhaskar
8. Ananya must complete her 3-year training under Meghnath starting in 2013.
So, Ananya studies under Meghnath from 2013 to 2015.
9. Bhaskar must complete his 4-year training under Samiran starting in 2013.
So, Bhaskar studies under Samiran from 2013 to 2016.
10. Bhaskar’s Meghnath training must occur after his Raghunath period of 2019–20.
The only viable placement is 2022–2024.
11. Ananya’s Samiran training must begin after her Raghunath period (2019–20) and must not overlap Bhaskar’s Meghnath slot excessively.
The consistent placement is 2021–2024.
Phase 3: Fix schedules for Charu and Devendra
12. Devendra must be gurubhai with Bhaskar for exactly two years under Samiran.
13. Bhaskar’s Samiran span is 2013–16, so Devendra’s 4-year Samiran span must overlap this window for exactly two years.
14. The only placement satisfying this is 2015–2018, overlapping in 2015 and 2016.
15. Devendra’s Meghnath training must follow his Samiran period.
16. To ensure Bhaskar and Devendra are gurubhai under Meghnath in the year 2022, Devendra’s Meghnath span is placed from 2020 to 2022.
17. Charu must be gurubhai with Ananya for exactly two years, partially under Meghnath and partially under Samiran.
18. Ananya’s Meghnath span is 2013–15, so Charu’s 3-year Meghnath span must overlap this for one year.
The only placement is 2015–2017.
19. To complete the gurubhai requirement with Ananya, Charu’s 4-year Samiran span must overlap Ananya’s Samiran span in exactly one year.
20. Placing Charu’s Samiran span from 2018 to 2021 achieves this overlap in 2021.
Final Working Table (2013–2024)
Spans: M=3 yrs, S=4 yrs, R=2 yrs.
R Groups:
Group 1 (R=2013–2014): C, D
Group 2 (R=2019–2020): A, B
| Musician | M (3 years) | S (4 years) | R (2 years) |
| Ananya (A) | 2013–2015 | 2021–2024 | 2019–2020 |
| Bhaskar (B) | 2022–2024 | 2013–2016 | 2019–2020 |
| Charu (C) | 2015–2017 | 2018–2021 | 2013–2014 |
| Devendra (D) | 2020–2022 | 2015–2018 | 2013–2014 |
In which of the following years were Bhaskar and Devendra Gurubhai? Moderate
1. 2020
2. 2015
3. 2018
4. 2022
Answer & Explanation
Correct Answer: 2022
Bhaskar and Devendra are required to be Gurubhai for exactly two years. As with other pairs, this cannot happen under Ustad Samiran. Acharya Raghunath’s two‑year blocks can accommodate only one Gurubhai pair per block and are already compelled to host other valid pairs after applying the “never Gurubhai” restrictions. Therefore, Bhaskar and Devendra must overlap under Pandit Meghnath. From the final year‑wise allocation, Bhaskar’s and Devendra’s Pandit Meghnath spans overlap exactly for two years. Among the listed options, 2022 is one of those overlapping years and is the only option that is guaranteed to be part of the Bhaskar–Devendra Gurubhai overlap across all valid configurations. The other years either fall outside their common Pandit Meghnath window or violate other fixed constraints. Hence, 2022 is the correct answer.
Steps to make the table:
Phase 1: Fix training spans and Raghunath slots
1. Each guru trains for a different duration: 2, 3, and 4 continuous years.
2. Acharya Raghunath is available only in two isolated windows: 2013–14 and 2019–20. Hence, his training span must be exactly 2 years.
3. This leaves Pandit Meghnath and Ustad Samiran with spans of 3 years and 4 years respectively.
4. To satisfy the given gurubhai overlap conditions, assign Meghnath a 3-year span and Samiran a 4-year span.
5. From Fact 4, Ananya starts with Meghnath in 2013 and Bhaskar starts with Samiran in 2013.
6. Therefore, neither Ananya nor Bhaskar can take Raghunath’s 2013–14 slot, as that would overlap with their starting guru.
7. Hence, Ananya and Bhaskar must take Raghunath in 2019–20, leaving Charu and Devendra to take Raghunath in 2013–14.
Phase 2: Fix schedules for Ananya and Bhaskar
8. Ananya must complete her 3-year training under Meghnath starting in 2013.
So, Ananya studies under Meghnath from 2013 to 2015.
9. Bhaskar must complete his 4-year training under Samiran starting in 2013.
So, Bhaskar studies under Samiran from 2013 to 2016.
10. Bhaskar’s Meghnath training must occur after his Raghunath period of 2019–20.
The only viable placement is 2022–2024.
11. Ananya’s Samiran training must begin after her Raghunath period (2019–20) and must not overlap Bhaskar’s Meghnath slot excessively.
The consistent placement is 2021–2024.
Phase 3: Fix schedules for Charu and Devendra
12. Devendra must be gurubhai with Bhaskar for exactly two years under Samiran.
13. Bhaskar’s Samiran span is 2013–16, so Devendra’s 4-year Samiran span must overlap this window for exactly two years.
14. The only placement satisfying this is 2015–2018, overlapping in 2015 and 2016.
15. Devendra’s Meghnath training must follow his Samiran period.
16. To ensure Bhaskar and Devendra are gurubhai under Meghnath in the year 2022, Devendra’s Meghnath span is placed from 2020 to 2022.
17. Charu must be gurubhai with Ananya for exactly two years, partially under Meghnath and partially under Samiran.
18. Ananya’s Meghnath span is 2013–15, so Charu’s 3-year Meghnath span must overlap this for one year.
The only placement is 2015–2017.
19. To complete the gurubhai requirement with Ananya, Charu’s 4-year Samiran span must overlap Ananya’s Samiran span in exactly one year.
20. Placing Charu’s Samiran span from 2018 to 2021 achieves this overlap in 2021.
Final Working Table (2013–2024)
Spans: M=3 yrs, S=4 yrs, R=2 yrs.
R Groups:
Group 1 (R=2013–2014): C, D
Group 2 (R=2019–2020): A, B
| Musician | M (3 years) | S (4 years) | R (2 years) |
| Ananya (A) | 2013–2015 | 2021–2024 | 2019–2020 |
| Bhaskar (B) | 2022–2024 | 2013–2016 | 2019–2020 |
| Charu (C) | 2015–2017 | 2018–2021 | 2013–2014 |
| Devendra (D) | 2020–2022 | 2015–2018 | 2013–2014 |
Which of the following statements is TRUE? Moderate
1. Charu was training under Ustad Samiran in 2018.
2. Ananya was training under Ustad Samiran in 2018.
3. Charu was training under Ustad Samiran in 2019.
4. Ananya was training under Ustad Samiran in 2015.
Answer & Explanation
Correct Answer: Charu was training under Ustad Samiran in 2019
Ustad Samiran trains exactly one student per year, so assigning students to him is tightly constrained. Bhaskar must start under Ustad Samiran in 2013, fixing the early part of Samiran’s schedule. Once the required Gurubhai overlaps under Pandit Meghnath and Acharya Raghunath are fixed, the remaining unassigned years for Ustad Samiran get forced. Tracing the only arrangement that satisfies all constraints shows that Charu’s three‑year consecutive span under Ustad Samiran necessarily includes 2019. This placement avoids forbidden Gurubhai overlaps, ensures Charu completes training under all three Gurus, and keeps Samiran restricted to a single student per year. None of the other statements can be guaranteed without violating at least one given condition. Therefore, the statement “Charu was training under Ustad Samiran in 2019” is the only one that is necessarily true.
Steps to make the table:
Phase 1: Fix training spans and Raghunath slots
1. Each guru trains for a different duration: 2, 3, and 4 continuous years.
2. Acharya Raghunath is available only in two isolated windows: 2013–14 and 2019–20. Hence, his training span must be exactly 2 years.
3. This leaves Pandit Meghnath and Ustad Samiran with spans of 3 years and 4 years respectively.
4. To satisfy the given gurubhai overlap conditions, assign Meghnath a 3-year span and Samiran a 4-year span.
5. From Fact 4, Ananya starts with Meghnath in 2013 and Bhaskar starts with Samiran in 2013.
6. Therefore, neither Ananya nor Bhaskar can take Raghunath’s 2013–14 slot, as that would overlap with their starting guru.
7. Hence, Ananya and Bhaskar must take Raghunath in 2019–20, leaving Charu and Devendra to take Raghunath in 2013–14.
Phase 2: Fix schedules for Ananya and Bhaskar
8. Ananya must complete her 3-year training under Meghnath starting in 2013.
So, Ananya studies under Meghnath from 2013 to 2015.
9. Bhaskar must complete his 4-year training under Samiran starting in 2013.
So, Bhaskar studies under Samiran from 2013 to 2016.
10. Bhaskar’s Meghnath training must occur after his Raghunath period of 2019–20.
The only viable placement is 2022–2024.
11. Ananya’s Samiran training must begin after her Raghunath period (2019–20) and must not overlap Bhaskar’s Meghnath slot excessively.
The consistent placement is 2021–2024.
Phase 3: Fix schedules for Charu and Devendra
12. Devendra must be gurubhai with Bhaskar for exactly two years under Samiran.
13. Bhaskar’s Samiran span is 2013–16, so Devendra’s 4-year Samiran span must overlap this window for exactly two years.
14. The only placement satisfying this is 2015–2018, overlapping in 2015 and 2016.
15. Devendra’s Meghnath training must follow his Samiran period.
16. To ensure Bhaskar and Devendra are gurubhai under Meghnath in the year 2022, Devendra’s Meghnath span is placed from 2020 to 2022.
17. Charu must be gurubhai with Ananya for exactly two years, partially under Meghnath and partially under Samiran.
18. Ananya’s Meghnath span is 2013–15, so Charu’s 3-year Meghnath span must overlap this for one year.
The only placement is 2015–2017.
19. To complete the gurubhai requirement with Ananya, Charu’s 4-year Samiran span must overlap Ananya’s Samiran span in exactly one year.
20. Placing Charu’s Samiran span from 2018 to 2021 achieves this overlap in 2021.
Final Working Table (2013–2024)
Spans: M=3 yrs, S=4 yrs, R=2 yrs.
R Groups:
Group 1 (R=2013–2014): C, D
Group 2 (R=2019–2020): A, B
| Musician | M (3 years) | S (4 years) | R (2 years) |
| Ananya (A) | 2013–2015 | 2021–2024 | 2019–2020 |
| Bhaskar (B) | 2022–2024 | 2013–2016 | 2019–2020 |
| Charu (C) | 2015–2017 | 2018–2021 | 2013–2014 |
| Devendra (D) | 2020–2022 | 2015–2018 | 2013–2014 |
In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus? Hard _____
Answer & Explanation
Correct Answer: 4
Each musician trains for a total of 9 years (2 + 3 + 4), so total training‑years across all musicians equals 36. These 36 training‑years are distributed over 12 calendar years, giving an average of 3 musicians training per year. However, due to Ustad Samiran’s restriction of training at most one student per year and Acharya Raghunath’s long inactive stretches, the distribution cannot be uniform. Some years will necessarily have fewer than three musicians training. When the final consistent schedule is examined, exactly four years emerge in which only two musicians are training, with the remaining musicians either between training spells or constrained by inactive Gurus. Any reduction below four would force compensating years with more than four trainees, which is impossible. Hence, the number of years with exactly two musicians training is fixed at four.
Steps to make the table:
Phase 1: Fix training spans and Raghunath slots
1. Each guru trains for a different duration: 2, 3, and 4 continuous years.
2. Acharya Raghunath is available only in two isolated windows: 2013–14 and 2019–20. Hence, his training span must be exactly 2 years.
3. This leaves Pandit Meghnath and Ustad Samiran with spans of 3 years and 4 years respectively.
4. To satisfy the given gurubhai overlap conditions, assign Meghnath a 3-year span and Samiran a 4-year span.
5. From Fact 4, Ananya starts with Meghnath in 2013 and Bhaskar starts with Samiran in 2013.
6. Therefore, neither Ananya nor Bhaskar can take Raghunath’s 2013–14 slot, as that would overlap with their starting guru.
7. Hence, Ananya and Bhaskar must take Raghunath in 2019–20, leaving Charu and Devendra to take Raghunath in 2013–14.
Phase 2: Fix schedules for Ananya and Bhaskar
8. Ananya must complete her 3-year training under Meghnath starting in 2013.
So, Ananya studies under Meghnath from 2013 to 2015.
9. Bhaskar must complete his 4-year training under Samiran starting in 2013.
So, Bhaskar studies under Samiran from 2013 to 2016.
10. Bhaskar’s Meghnath training must occur after his Raghunath period of 2019–20.
The only viable placement is 2022–2024.
11. Ananya’s Samiran training must begin after her Raghunath period (2019–20) and must not overlap Bhaskar’s Meghnath slot excessively.
The consistent placement is 2021–2024.
Phase 3: Fix schedules for Charu and Devendra
12. Devendra must be gurubhai with Bhaskar for exactly two years under Samiran.
13. Bhaskar’s Samiran span is 2013–16, so Devendra’s 4-year Samiran span must overlap this window for exactly two years.
14. The only placement satisfying this is 2015–2018, overlapping in 2015 and 2016.
15. Devendra’s Meghnath training must follow his Samiran period.
16. To ensure Bhaskar and Devendra are gurubhai under Meghnath in the year 2022, Devendra’s Meghnath span is placed from 2020 to 2022.
17. Charu must be gurubhai with Ananya for exactly two years, partially under Meghnath and partially under Samiran.
18. Ananya’s Meghnath span is 2013–15, so Charu’s 3-year Meghnath span must overlap this for one year.
The only placement is 2015–2017.
19. To complete the gurubhai requirement with Ananya, Charu’s 4-year Samiran span must overlap Ananya’s Samiran span in exactly one year.
20. Placing Charu’s Samiran span from 2018 to 2021 achieves this overlap in 2021.
Final Working Table (2013–2024)
Spans: M=3 yrs, S=4 yrs, R=2 yrs.
R Groups:
Group 1 (R=2013–2014): C, D
Group 2 (R=2019–2020): A, B
| Musician | M (3 years) | S (4 years) | R (2 years) |
| Ananya (A) | 2013–2015 | 2021–2024 | 2019–2020 |
| Bhaskar (B) | 2022–2024 | 2013–2016 | 2019–2020 |
| Charu (C) | 2015–2017 | 2018–2021 | 2013–2014 |
| Devendra (D) | 2020–2022 | 2015–2018 | 2013–2014 |
