CAT 2025 Slot 2 · DILR · Question 3

CAT 2025 Slot 2 previous year question on Quant Based Puzzles and Optimisation, with the answer and a step-by-step solution.

Quant Based Puzzles and OptimisationLOGICAL REASONING - High LevelMultiple choiceHard

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 which of the following years were Bhaskar and Devendra Gurubhai?

  1. A

    2022

  2. B

    2015

  3. C

    2020

  4. D

    2018

Pick an option, then check.
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.

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