CAT 2025 Slot 2 · DILR · Question 2

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 year did Charu begin her training under Pandit Meghnath?

  1. A

    2017

  2. B

    2015

  3. C

    2021

  4. D

    2016

Pick an option, then check.
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.

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