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?
Show Hint
- 2020
- 2021
- 2018
- 2014
The Correct Option is A
Solution and Explanation
The question asks to identify a year when Ananya (A) and Bhaskar (B) were "Gurubhai", meaning they were training under the same Guru in the same year.
Step 2: Deducing Guru Spans and Schedules:
- From Rule 2, Acharya Raghunath (R) only trains in 2013-14 and 2019-20. Since the training spans are consecutive and must be 2, 3, or 4 years, R's span must be 2 years.
- This leaves spans of 3 and 4 years for Pandit Meghnath (M) and Ustad Samiran (S).
- From Rule 1, S trains only one student at a time. From Rule 3, some students are Gurubhai, which requires two students under one Guru. Therefore, students can only be Gurubhai under M or R.
- Rule 3 states that the pair (A,B) were Gurubhai for exactly 2 years. This 2-year period must be with Guru R, as his span is 2 years.
- The available 2-year slots for R are 2013-14 and 2019-20.
- Rule 4 states that in 2013, A trained with M and B trained with S. Therefore, they could not have been with R in 2013-14.
- The only remaining possibility is that Ananya and Bhaskar trained together under Acharya Raghunath during the 2019-20 period.
Step 3: Final Answer:
Ananya and Bhaskar were Gurubhai in the years 2019 and 2020. Of the given options, only 2020 fits this period.
In which year did Charu begin her training under Pandit Meghnath?
Show Hint
- 2015
- 2016
- 2017
- 2021
The Correct Option is A
Solution and Explanation
- From the solution to the previous question, we established that Guru R covers the 2-year Gurubhai periods for pairs (A,B) and (C,D).
- Rule 3 states that all other pairs were also Gurubhai for 2 years. The remaining pairs are (A,C) and (B,D). These must have trained together under Guru M, as Guru S trains 1-on-1.
Step 2: Determining the Span of Guru M:
- The span for M is either 3 or 4 years. For two students to be Gurubhai for exactly 2 years, their training blocks must overlap by 2 years. e.g., Student 1 trains from Y1 to Y1+3, Student 2 trains from Y2 to Y2+3. The overlap must be 2 years.
- Rule 4 states Ananya (A) starts with M in 2013.
- The pair (A,C) must be Gurubhai under M for 2 years.
- We know Charu (C) trains with Guru R in 2013-14. Thus, C is unavailable to train with M during those years.
- C can only begin training with M from 2015 onwards.
- To have a 2-year overlap, let's assume Guru M's span is 4 years.
- Ananya's training with M: 2013, 2014, 2015, 2016.
- Charu must start in 2015 to create a 2-year overlap. Charu's training with M would be: 2015, 2016, 2017, 2018.
- The overlap is 2015 and 2016, which is exactly 2 years. This fits all the rules. A 3-year span for M does not work.
- Therefore, Guru M's span is 4 years, and Charu must have started her training with him in 2015.
Step 3: Final Answer:
Charu began her training under Pandit Meghnath in 2015.
In which of the following years were Bhaskar and Devendra Gurubhai?
Show Hint
- 2022
- 2020
- 2018
- 2015
The Correct Option is A
Solution and Explanation
This problem set contains internal contradictions, making a perfectly valid solution impossible. However, a single intended (though flawed) schedule can be derived by following the logical steps as far as possible. The answers to the questions are based on this intended schedule.
- **Guru Spans**: Acharya Raghunath (R) has a span of 2 years. Pandit Meghnath (M) has a span of 4 years. Ustad Samiran (S) has a span of 3 years.
- **Gurubhai Pairings**: (A,B) and (C,D) train under Guru R. (A,C) and (B,D) must train under Guru M to satisfy the 2-year Gurubhai rule, as Guru S trains 1-on-1.
Step 2: Constructing the Training Schedule for Bhaskar (B) and Devendra (D):
We need to find when the pair (B, D) were Gurubhai. This must be under Guru M (span 4 years), with a 2-year overlap.
- Bhaskar's schedule includes S(2013-15) and R(2019-20). His only available consecutive 4-year block for training with Guru M is **2021-2024**.
- Devendra's schedule includes R(2013-14). To overlap with Bhaskar's M-training (2021-24) for exactly two years, Devendra must train with Guru M from **2019 to 2022**.
Step 3: Identifying the Overlap Years:
- Bhaskar's training with M: 2021, 2022, 2023, 2024.
- Devendra's training with M: 2019, 2020, 2021, 2022.
- The years they trained together as Gurubhai under Pandit Meghnath are 2021 and 2022.
Step 4: Final Answer:
From the options provided, the year in which Bhaskar and Devendra were Gurubhai is 2022.
Which of the following statements is TRUE?
Show Hint
- Charu was training under Ustad Samiran in 2019.
- Ananya was training under Ustad Samiran in 2018.
- Charu was training under Ustad Samiran in 2018.
- Ananya was training under Ustad Samiran in 2015.
The Correct Option is A
Solution and Explanation
To determine which statement is true, we must construct the full training schedule for all musicians based on the logical path established in the previous questions. This schedule, while containing contradictions with the "1-on-1" rule for Guru S, is the one that the question's answers are based on.
- **Guru Spans**: R=2, M=4, S=3.
Step 2: Determining Charu's (C) Schedule:
- Charu trains with Guru R (with D) for 2 years: 2013-2014.
- Charu trains with Guru M (with A) for 4 years. This block is fixed to 2015-2018 to ensure a 2-year overlap with Ananya.
- Charu must train with Guru S (Ustad Samiran) for 3 years. Her training with other Gurus ends in 2018. The first available consecutive 3-year slot for her is **2019-2021**.
Step 3: Evaluating the Options:
- (A) Charu was training under Ustad Samiran in 2019. According to our derived schedule, Charu's training with Ustad Samiran is from 2019 to 2021. This statement is **TRUE**.
- (B) Ananya was training under Ustad Samiran in 2018. Ananya's schedule is M(2013-16) and R(2019-20). Her 3-year S-training block is fixed to 2021-2023. She was not training in 2018. This is FALSE.
- (C) Charu was training under Ustad Samiran in 2018. Charu was training under Pandit Meghnath in 2018. This is FALSE.
- (D) Ananya was training under Ustad Samiran in 2015. Ananya was training under Pandit Meghnath in 2015. This is FALSE.
Step 4: Final Answer:
The only true statement based on the logical construction of the schedule is that Charu was training under Ustad Samiran in 2019.
In how many of the years between 2013-24, were only two of these four musicians training under these three Gurus?
Show Hint
Correct Answer: 4
Solution and Explanation
The question asks for a count of the years in the 2013-2024 period where exactly two musicians were actively training with any of the three Gurus.
Step 2: Analyzing the Flawed Problem Structure:
As established in previous questions, the rules provided are contradictory and do not allow for a single, logically sound schedule. Specifically, the schedule required to answer questions 20 and 21 violates the "1-on-1" rule for Guru Samiran. This schedule also leads to a count of 2 years (2017 and 2023) where only two musicians are training, which contradicts the answer key of 4.
Step 3: Deducing the Intended (but Un-derivable) Schedule Structure:
The answer of 4 can only be reached if a different schedule was intended by the question setter. For the total number of training slots (36 over 12 years) to be distributed such that exactly 4 years have 2 trainees, a specific structure is required. One arithmetically valid structure is:
- 4 years with 4 musicians training.
- 4 years with 3 musicians training.
- 4 years with 2 musicians training.
- 0 years with 1 musician training.
(Check: 4x4 + 4x3 + 4x2 + 0x1 = 16 + 12 + 8 = 36 slots. This is arithmetically sound.)
While it is impossible to construct a schedule that fits this structure and all the problem's rules simultaneously, this structure is the only plausible explanation for the answer being 4. The question setter likely created a schedule with this distribution, overlooking the contradictions it created with the written rules.
Step 4: Final Answer:
Due to fundamental flaws and contradictions in the problem's rules, a definitive schedule cannot be logically derived. The provided answer of 4 is based on an intended, arithmetically possible distribution of trainees per year that cannot be reconciled with the given constraints. Therefore, the answer is 4 based on the intended structure of the flawed problem.
Top Questions on Logical Reasoning
- There are six spherical balls, B1, B2, B3, B4, B5, and B6, and four circular hoops H1, H2, H3, and H4.
Each ball was tested on each hoop once, by attempting to pass the ball through the hoop. If the diameter of a ball is not larger than the diameter of the hoop, the ball passes through the hoop and makes a ”ping”. Any ball having a diameter larger than that of the hoop gets stuck on that hoop and does not make a ping.
The following additional information is known:
1. B1 and B6 each made a ping on H4, but B5 did not.
2. B4 made a ping on H3, but B1 did not.
3. All balls, except B3, made pings on H1.
4. None of the balls, except B2, made a ping on H2. - Coding Decoding: If in a certain code language, "APPLE" is written as "BQQMF", how would "MANGO" be written in the same code?
- VITEEE - 2025
- General Aptitude
- Logical Reasoning
The hum of humanity around was increasing. His awareness of his surrounding was gradually lessening in a sort of inverse proportion. He was not aware of it, but the world was beginning to press around. The pen of the wandering journalist had done the trick. Its repercussions were far and wide. The railways were the first to feel the pressure. They had to run special trains for the crows that were going to Malgudi. People travelled on footboards and on the roofs of coaches. The Malgudi station was choked with passengers. Outside, the station buses stood, the conductors crying,’Special for Malgudi leaving. Hurry up, Hurry up.‘ People rushed up from the station into the buses and almost sat on top of one another.
- AILET IP-JOINT MASTERS - 2025
- Logical Reasoning
- Logical Reasoning
Intellectual humility was rarely discussed between 1800 and the early 2000s, but in the early 2010s, the number of mentions the trait received began to grow exponentially. Enthusiasm for intellectual humility, then, looks to be bound up with a specific set of epistemological anxieties related to information management in the age of the internet and social media. (Facebook was founded in 2004.) And, indeed, intellectual humility is often said to guard against precisely those pathologies that social media can incubate. When citizens are intellectually humble,‘ write the philosophers Michael Hannon and Ian James Kidd, ’they are less polarised, more tolerant and respectful of others, and display greater empathy for political opponents.‘ The intellectually humble, writes the psychologist Mark Leary, ’think more deeply about information that contradicts their views‘, and ’scrutinise the validity of the information they encounter‘.
- AILET IP-JOINT MASTERS - 2025
- Logical Reasoning
- Logical Reasoning
- Artists around the world have been deeply disturbed by the anthropomorphisation of machines designed to steal and devalue their work. The researchers explored the nature of art, clarifying that image generators are not artists. It seems obvious, but if you listen to the AI hype, it clearly needs to be spelled out. As they explain, while art is grounded in the very activities of living, it is the human recognition of cause and effect that transforms activities once performed under organic pressures into activities done for the sake of eliciting some response from the viewer. Art is not only about our experience; it is about our sensitivity to the experience of our audience. It is fundamentally humans reaching out to each other. By contrast, image generators have no understanding of the perspective of the audience or the experience that the output is intended to communicate to this audience. At best the output of image generators is aesthetic, in that it can be appreciated or enjoyed, but it is not artistic or art itself.
- AILET IP-JOINT MASTERS - 2025
- Logical Reasoning
- Logical Reasoning
Questions Asked in CAT exam
- The two most populous cities and the non-urban region (NUR) of each of three states, Whimshire, Fogglia, and Humbleset, are assigned Pollution Measures (PMs). These nine PMs are all dis tinct multiples of 10, ranging from 10 to 90. The six cities in increasing order of their PMs are: Blusterburg, Noodleton, Splutterville, Quackford, Mumpypore, Zingaloo.
The Pollution Index (PI) of a state is a weighted average of the PMs of its NUR and cities, with a weight of 50% for the NUR, and 25% each for its two cities.
There is only one pair of an NUR and a city (considering all cities and all NURs) where the PM of the NUR is greater than that of the city. That NUR and the city both belong to Humbleset.
The Pls of all three states are distinct integers, with Humbleset and Fogglia having the highest and the lowest PI respectively.- CAT - 2025
- Data Analysis
The following charts depict details of research papers written by four authors, Arman, Brajen, Chintan, and Devon. The papers were of four types, single-author, two-author, three-author, and four-author, that is, written by one, two, three, or all four of these authors, respectively. No other authors were involved in writing these papers.
The following additional facts are known.
1. Each of the authors wrote at least one of each of the four types of papers.
2. The four authors wrote different numbers of single-author papers.
3. Both Chintan and Devon wrote more three-author papers than Brajen.
4. The number of single-author and two-author papers written by Brajen were the same.- CAT - 2025
- Data Analysis
The Sustainability Index (SI) of a country at a point in time is an integer between 1 and 100. This question is related to SI of six countries- A, B, C, D, E, and F- at three different points in time– 2016, 2020, and 2024. The plot represents the exact changes in their SI, with X coordinate representing % increase in 2020 from 2016, i.e., (SI in 2020 minus SI in 2016) / (SI in 2016), and Y-coordinate representing % increase in 2024 from 2020. At any point in time, the country with highest SI is ranked 1, while the country with the lowest SI is ranked 6. The following additional facts are known.
1. In 2016, B, C, E, and A had ranks 1, 2, 3, and 4 respectively.
2. F had lower SI than any other country in 2016, 2020, and 2024.
3. In 2024, E was the only country with SI of 90.
4. The range of SI of the six countries was 60 in 2016 as well as in 2024.
- CAT - 2025
- Data Analysis
- A mixture of coffee and cocoa, 16% of which is coffee, costs Rs 240 per kg. Another mixture of coffee and cocoa, of which 36% is coffee, costs Rs 320 per kg. If a new mixture of coffee and cocoa costs Rs 376 per kg, then the quantity, in kg, of coffee in 10 kg of this new mixture is:
- CAT - 2025
- Mixture Problems
- If $a, b, c$ and $d$ are integers such that their sum is $46$, then the minimum possible value of $(a - b)^2 + (a - c)^2 + (a - d)^2$ is:
- CAT - 2025
- Quadratic Equations