CAT 2022 Slot 1 DILR Question Paper (Available): Download Solutions with Answer Key

CAT Questions

• 1.

  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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• 2.

  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.

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• 3.

  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.

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• 4.

  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.

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• 5.

  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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• 6.

  Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means “Yes”, two taps mean “No”, and three taps mean “Maybe”. A total of 40 taps were heard across the five questions. Each question received at least one “Yes”, one “No”, and one “Maybe.” The following information is known. 1. Alia tapped a total of 6 times and received 9 taps to her question. She responded “Yes” to the questions asked by both Clive and Dilshan. 2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded “No” to Badal. 3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions. 4. No one responded “Yes” more than twice. 5. No one’s answer to Alia’s question matched the answer that Alia gave to that person’s question. This was also true for Ehsaan. 6. Clive tapped more times in total than Badal.