CAT 2025 Slot 2 · DILR · Set 1: Musicians and Their Gurus
The full set and all 5 questions (Q1–Q5) from CAT 2025 Slot 2, with answers and solutions.
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.
Question 1 · Quant Based Puzzles and Optimisation
In which of the following years were Ananya and Bhaskar Gurubhai?
- A
2020
- B
2018
- C
2021
- D
2014
Answer & solution
Answer: Option A
Acharya Raghunath (AR) can teach only in 2013, 2014, 2019 and 2020 (fact 2). His span must fit inside one of the windows 2013–14 or 2019–20, so AR's span is 2 years.
AR must train all four musicians, and at most two at a time, so two musicians take 2013–14 and the other two take 2019–20.
In 2013 Ananya was with Pandit Meghnath and Bhaskar with Ustad Samiran (fact 4), so neither can be with AR in 2013–14. Ananya and Bhaskar therefore both train under AR in 2019–20, and Charu and Devendra in 2013–14.
So Ananya and Bhaskar are Gurubhai in 2019 and 2020. Of the options, only 2020 fits.
Shortcut: AR has only two usable 2-year windows. The two musicians already busy elsewhere in 2013 must share the later window.
Hence, the answer is option 1.
Question 2 · Quant Based Puzzles and Optimisation
In which year did Charu begin her training under Pandit Meghnath?
- A
2017
- B
2015
- C
2021
- D
2016
Answer & solution
Answer: Option B
AR's span is 2 years, so Ustad Samiran (US) and Pandit Meghnath (PM) have spans of 3 and 4 years.
US teaches only one musician at a time (fact 1). Four separate US spans must fit within 12 years, so 4 × span ≤ 12, giving span = 3. Hence US = 3 years and PM = 4 years, and the four US spans fill the 12 years exactly: 2013–15, 2016–18, 2019–21 and 2022–24.
Ananya: PM from 2013, so PM 2013–16. Her AR span is 2019–20 (from the previous question). Her US span cannot be 2016–18 (clashes with PM in 2016) or 2019–21 (clashes with AR), so it is 2022–24.
Ananya and Charu must be Gurubhai for exactly 2 years (fact 3). US is solo and their AR windows differ, so the 2 years must come from PM. Charu's 4-year PM span must overlap Ananya's 2013–16 by exactly 2 years, and Charu is with AR in 2013–14, so her PM span is 2015–18.
Shortcut: US must be the 3-year Guru because he is solo across 12 years. A 4-year PM span overlapping 2013–16 by exactly 2 years can only start in 2015.
Hence, the answer is option 2.
Question 3 · Quant Based Puzzles and Optimisation
In which of the following years were Bhaskar and Devendra Gurubhai?
- A
2022
- B
2015
- C
2020
- D
2018
Answer & solution
Answer: Option A
Spans: AR = 2, US = 3, PM = 4; US slots are 2013–15, 2016–18, 2019–21 and 2022–24.
Bhaskar: US 2013–15 and AR 2019–20. His 4-year PM span must avoid both, so it is 2021–24.
Charu: AR 2013–14 and PM 2015–18, so of the free US slots (2016–18 and 2019–21) she must take 2019–21. Devendra takes US 2016–18.
Devendra: AR 2013–14 and US 2016–18, so his PM span lies in 2019–24: 2019–22, 2020–23 or 2021–24.
Bhaskar and Devendra must be Gurubhai for exactly 2 years, and PM is the only Guru they can share. The overlaps with Bhaskar's 2021–24 are 2, 3 and 4 years respectively, so Devendra's PM span is 2019–22 and they are Gurubhai in 2021 and 2022.
Of the options, only 2022 fits.
Shortcut: Bhaskar's PM span is forced to the very end (2021–24), so a 2-year overlap with Devendra can only be 2021–22.
Hence, the answer is option 1.
Question 4 · Quant Based Puzzles and Optimisation
Which of the following statements is TRUE?
- A
Charu was training under Ustad Samiran in 2018.
- B
Ananya was training under Ustad Samiran in 2015.
- C
Ananya was training under Ustad Samiran in 2018.
- D
Charu was training under Ustad Samiran in 2019.
Answer & solution
Answer: Option D
The complete schedule is:
Ananya: PM 2013–16, AR 2019–20, US 2022–24.
Bhaskar: US 2013–15, AR 2019–20, PM 2021–24.
Charu: AR 2013–14, PM 2015–18, US 2019–21.
Devendra: AR 2013–14, US 2016–18, PM 2019–22.
Option 1 is false: in 2018 Charu was with PM.
Options 2 and 3 are false: Ananya was with US only in 2022–24.
Option 4 is true: Charu was with US in 2019–21.
Shortcut: once the four US slots are fixed as 2013–15, 2016–18, 2019–21 and 2022–24, each option is a quick lookup.
Hence, the answer is option 4.
Question 5 · Quant Based Puzzles and Optimisation
In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?
Answer & solution
Answer: 4
From the schedule, the years each musician trains are:
Ananya: 2013–16, 2019–20, 2022–24.
Bhaskar: 2013–15, 2019–24.
Charu: 2013–21.
Devendra: 2013–14, 2016–22.
Number training each year: 2013: 4, 2014: 4, 2015: 3, 2016: 3, 2017: 2, 2018: 2, 2019: 4, 2020: 4, 2021: 3, 2022: 3, 2023: 2, 2024: 2.
Only two are training in 2017, 2018, 2023 and 2024, that is, in 4 years.
Shortcut: each musician trains 2 + 3 + 4 = 9 years, a total of 36 musician-years. With four years at 4 and four years at 3 (28 musician-years), the remaining four years hold 8 musician-years, i.e. 2 each.
Hence, the answer is 4.
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