CAT 2025 Slot 2 · DILR · Question 1

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 choiceMedium

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 Ananya and Bhaskar Gurubhai?

  1. A

    2020

  2. B

    2018

  3. C

    2021

  4. D

    2014

Pick an option, then check.
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.

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