CAT 2019 DILR Slot 2 Question Paper(Available):Download Solutions with Answer Key

CAT Questions

• 1.

  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.
  

  ---

• 2.

  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.

  ---

• 3.

  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.

  ---

• 4.

  Anu, Bijay, Chetan, Deepak, Eshan, and Faruq are six friends. Each of them uses a mobile number from exactly one of the two mobile operators- Xitel and Yocel. During the last month, the six friends made several calls to each other. Each call was made by one of these six friends to another. The table below summarizes the number of minutes of calls that each of the six made to (outgoing minutes to) and received from (incoming minutes from) these friends, grouped by the operators. Some of the entries are missing.  
  Operator Xitel Operator Yocel
  

  It is known that the duration of calls from Faruq to Eshan was 200 minutes. Also, there were no calls from:
  • Bijay to Eshan,
  • Chetan to Anu and Chetan to Deepak,
  • Deepak to Bijay and Deepak to Faruq,
  • Eshan to Chetan and Eshan to Deepak.

  ---

• 5.

  A round table has seven chairs around it. The chairs are numbered 1 through 7 in a clockwise direction. Four friends, Aslam (A), Bashir (B), Chhavi (C), and Davies (D), sit on four of the chairs. In the starting position, Aslam and Chhavi are sitting next to each other, while for Bashir as well as Davies, there are empty chairs on either side of the chairs they are sitting on.
  The friends take turns moving either clockwise or counterclockwise from their chair. The friend who has to move in a turn occupies the first empty chair in whichever direction they choose to move. Aslam moves first (Turn 1), followed by Bashir, Chhavi, and Davies (Turns 2, 3, and 4, respectively). Then Aslam moves again followed by Bashir, and Chhavi (Turns 5, 6, and 7, respectively).
  The following information is known: 1. The four friends occupy adjacent chairs only at the end of Turn 2 and Turn 6. 2. Davies occupies Chair 2 after Turn 1 and Chair 4 after Turn 5, and Chhavi occupies Chair 7 after Turn 2.

  ---

• 6.

  A train travels from Station A to Station E, passing through stations B, C, and D, in that order. The train has a seating capacity of 200. A ticket may be booked from any station to any other station ahead on the route, but not to any earlier station. A ticket from one station to another reserves one seat on every intermediate segment of the route. For example, a ticket from B to E reserves a seat in the intermediate segments B– C, C– D, and D–E. The occupancy factor for a segment is the total number of seats reserved in the segment as a percentage of the seating capacity. The total number of seats reserved for any segment cannot exceed 200. The following information is known. 1. Segment C– D had an occupancy factor of 952. Exactly 40 tickets were booked from B to C and 30 tickets were booked from B to E. 3. Among the seats reserved on segment D– E, exactly four-sevenths were from stations before C. 4. The number of tickets booked from A to C was equal to that booked from A to E, and it was higher than that from B to E. 5. No tickets were booked from A to B, from B to D and from D to E. 6. The number of tickets booked for any segment was a multiple of 10.