CAT 2022 Slot 3 DILR Question Paper(Available) Download Solutions with Answer Key

CAT Questions

• 1.

  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. 

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• 2.

  Seven children, Aarav, Bina, Chirag, Diya, Eshan, Farhan, and Gaurav, are sitting in a circle facing inside (not necessarily in the same order) and playing a game of ’Passing the Buck’.
  The game is played over 10 rounds. In each round, the child holding the Buck must pass it directly to a child sitting in one of the following positions:
  • Immediately to the left;
  • Immediately to the right;
  • Second to the left; 
  • Second to the right.
  The game starts with Bina passing the Buck and ends with Chirag receiving the Buck. The table below provides some information about the pass types and the child receiving the Buck. Some information is missing and labelled as ’?’.v

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• 3.

  Four companies C1, C2, C3, C4 must interview candidates P, Q, R, S over four time slots (T1--T4).
  Each candidate gets one unique slot and each company interviews exactly one candidate per slot.
  Constraints:
  1. P cannot be interviewed by C1 or C3.
  2. Q must be interviewed in either T1 or T4.
  3. R must be interviewed before S.
  4. C4 only interviews in T2 or T3.
  5. No company interviews the same candidate as last year:
  (C1--P), (C2--Q), (C3--R), (C4--S).
  How many valid interview schedules are possible?
  

  • 6
    
  • 8
    
  • 10
    
  • 12
    
  View Solution

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• 4.

  Aurevia, Brelosia, Cyrenia and Zerathania are four countries with their currencies being Aurels, Brins, Crowns, and Zentars, respectively. The currencies have different exchange values. Crown’s currency exchange rate with Zentars = 0.5, i.e., 1 Crown is worth 0.5 Zentars.
  Three travelers, Jano, Kira, and Lian set out from Zerathania visiting exactly two of the countries. Each country is visited by exactly two travelers. Each traveler has a unique Flight Cost, which represents the total cost of airfare in traveling to both the countries and back to Zerathania. The Flight Cost of Jano was 4000 Zentars, while that of the other two travelers were 5000 and 6000 Zentars, not necessarily in that order. When visiting a country, a traveler spent either 1000, 2000 or 3000 in the country’s local currency. Each traveler had different spends (in the country’s local currency) in the two countries he/she visited. Across all the visits, there were exactly two spends of 1000 and exactly one spend of 3000 (in the country’s local currency).
  The total “Travel Cost” for a traveler is the sum of his/her Flight Cost and the money spent in the countries visited.
  The citizens of the four countries with knowledge of these travels made a few observations, with spends measured in their respective local currencies:
  • Aurevia citizen: Jano and Kira visited our country, and their Travel Costs were 3500 and 8000, respectively.
  • Brelosia citizen: Kira and Lian visited our country, spending 2000 and 3000, respectively. Kira’s Travel Cost was 4000.
  • Cyrenia citizen: Lian visited our country and her Travel Cost was 36000.

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• 5.

  In a survey of 250 people about three activities (Reading, Sports, Travel), the following data are given:
  130 like Reading,
  110 like Sports,
  120 like Travel,
  55 like both Reading and Sports,
  50 like both Sports and Travel,
  45 like both Reading and Travel,
  25 like all three.
  How many like only Travel?
  

  • 35
    
  • 40
    
  • 45
    
  • 50
    
  View Solution

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• 6.

  Four teams T1, T2, T3, T4 play a tournament where each team plays exactly two matches.
  Rules:
  1. No match ends in a draw.
  2. T1 defeats T3.
  3. T4 plays exactly one match before it plays T2.
  4. T2 wins exactly one match.
  5. T3 does not defeat T4.
  6. Total matches = 4.
  How many valid sequences of wins/losses across all matches are possible?
  

  • 6
    
  • 8
    
  • 10
    
  • 12
    
  View Solution