CAT 2025 Slot 2 · DILR · Question 5
CAT 2025 Slot 2 previous year question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.
Set 1: Musicians and Their Gurus — this question belongs to a set. Read the full set with all 5 questions →
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 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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