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Question 06

Venkatesan S
IIM Bangalore Alumni | Cleared CAT 2015 | Cleared IIM B, C, L, K & I

U
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  1. CAT 2017: Data Interpretation Question 6 Venkatesan S IIMB Alumnus


  2. A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule. The underlying principle that they are working on is the following: Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.


  3. Question No.:1 If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is: A) 45 B) 90 C) 180 D) 135


  4. Question No.: 2 Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and/or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is: A) 54 B) 120 C) 96 D) 60


  5. Question No.:3 Suppose the 10 cities are divided into 4 distinct groups G1,G2,G3,G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following: 1. Both cities are in G1 2. Between A and any city in G2 3. Between B and any city in G3 4. Between C and any city in G4 A) 40 B) 54 C) 60 D) 84


  6. Question No.: 4 Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following. 1. Both cities are in G1 2. Between A and any city in G2 3. Between B and any city in G3 4. Between C and any city in G4 However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4.


  7. What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose? A) 4 B) 0 C) 6 D) Cannot be determined


  8. A new airlines company is planning to start operations in a country. The company has identified ten different cities which they plan to connect through their network to start with. The flight duration between any pair of cities will be less than one hour. To start operations, the company has to decide on a daily schedule. The underlying principle that they are working on is the following: Any person staying in any of these 10 cities should be able to make a trip to any other city in the morning and should be able to return by the evening of the same day.


  9. Question No.:1 If the underlying principle is to be satisfied in such a way that the journey between any two cities can be performed using only direct (non-stop) flights, then the minimum number of direct flights to be scheduled is: A) 45 B) 90 C) 180 D) 135 Between A & B- 2 flights in Morning and 2 in Evening. Thus, 4 flights between 2 cities. Total such pairs is, (10 X 9)/2 45. Total Flights 45 X 4 180


  10. Question No.: 2 Suppose three of the ten cities are to be developed as hubs. A hub is a city which is connected with every other city by direct flights each way, both in the morning as well as in the evening. The only direct flights which will be scheduled are originating and/or terminating in one of the hubs. Then the minimum number of direct flights that need to be scheduled so that the underlying principle of the airline to serve all the ten cities is met without visiting more than one hub during one trip is: A) 54 B) 120 C) 96 D) 60 HubHub HubNon-Hub 3 Hubs 3X 4 12 1 Non Hub to Hub 4 1 Non-Hub to 3 Hubs 4 X 3-12 Total Non-Hubs 7 Total Non-Hub flights 12 X7 84 Total Flights 84+12 96


  11. Question No.:3 Suppose the 10 cities are divided into 4 distinct groups G1,G2,G3,G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following: 1. Both cities are in G1 2. Between A and any city in G2 3. Between B and any city in G3 4. Between C and any city in G4 A) 40 B) 54 C) 60 D) 84 Between G1 3 X 4 12 G2 to G1 3 X4- 12 G3 to G1 2 X4 8 Total 40


  12. Question No.: 4 Suppose the 10 cities are divided into 4 distinct groups G1, G2, G3, G4 having 3, 3, 2 and 2 cities respectively and that G1 consists of cities named A, B and C. Further, suppose that direct flights are allowed only between two cities satisfying one of the following. 1. Both cities are in G1 2. Between A and any city in G2 3. Between B and any city in G3 4. Between C and any city in G4


  13. However, due to operational difficulties at A, it was later decided that the only flights that would operate at A would be those to and from B. Cities in G2 would have to be assigned to G3 or to G4. What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose? A) 4 B) 0 C) 6 D) Cannot be determined Previous: Between G1 3 X 4 12 G2 to G1 (A) 3X4 12 G3 to G1 (B) 2 X4 8 G4 to G1 (C) 2 X4 8 Total 40 Current: Between G1 2 X 4 8 G2 to G3 3 X 4 12 G3 to G1 (B) 2 X4 8 G4 to G1 (C) 2 X4 8 Total 36


  14. CAT 2017: Data Interpretation Question 7 Venkatesan S IIMB Alumnus


  15. Four cars need to travel from Akala (A) to Bakala (B). Two routes are available, one via Mamur (M) and the other via Nanur (N). The roads from A to M, and from N to B, are both short and narrow. In each case, one car takes 6 minutes to cover the distance, and each additional car increases the travel time per car by 3 minutes because of congestion. (For example, if only two cars drive from A to M, each car takes 9 minutes.) On the road from A to N, one car takes 20 minutes, and each additional car increases the travel time per car by 1 minute. On the road from M to B, one car takes 20 minutes, and each additional car increases the travel time per car by 0.9 minute The police department orders each car to take a particular route in such a manner that it is not possible for any car to reduce its travel time by not following the order, while the other cars are following the order.


  16. How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department? A) 2 B) C) D)


  17. If all the cars follow the police order, what is the difference in travel time (in minutes) between a car which takes the route A-NB and a car that takes the route A-M-B? A) 1 B) 0.1 C) 0.2 D) 0.9


  18. A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-MN-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A-M- N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the A-N-B route. How many cars would the police department order to take the A-M-N-B route so that it is not possible for any car to reduce its travel time by not following the order while the other cars follow the order? (Assume that the police department would never order all the cars to take the same route.) A) 2 B) C) D)


  19. A new one-way road is built from M to N. Each car now has three possible routes to travel from A to B: A-M-B, A-N-B and A-MN-B. On the road from M to N, one car takes 7 minutes and each additional car increases the travel time per car by 1 minute. Assume that any car taking the A M-N-B route travels the A-M portion at the same time as other cars taking the A-M-B route, and the N-B portion at the same time as other cars taking the - A-N-B route. If all the cars follow the police order, what is the minimum travel time (in minutes) from A to B? (Assume that the police department would never order all the cars to take the same route.) A) 26 B) 32 C) 29.9 D) 30


  20. CAT 2017: Data Interpretation Question 7 Venkatesan S IIMB Alumnus


  21. Question No.:1 A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence. The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence. The lab has decided to allow a variation in the sequence of scans of the five fingers so that at most two scans (out of five) are out of place. For example, if the original sequence is Thumb (T), index finger (I), middle finger (M), ring finger (R) and little finger (L) then TLMRI is also allowed, but TMRLI is not. How many different sequences of scans are allowed for any given person's original scan? A) 11 B) C) D)


  22. Question No.: 2 A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence. The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence. The lab has decided to allow variations of the original sequence so that input of the scanned sequence of five fingers is allowed to vary from the original sequence by one place for any of the fingers. Thus, for example, if TIMRL is the original sequence, then ITRML is also allowed, but LIMRT is not. How many different sequences are allowed for any given person's original scan? A) 7 B) 5 C) 8 D) 13


  23. Question No.:3 A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in an order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence. The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence. The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. Suppose the lab allows a variation of the original sequence (of six inputs) where at most two scans (out of six) are out of place, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed for any given person's original scan? A) 15 B) C) D)


  24. Question No.: 4 A high security research lab requires the researchers to set a pass key sequence based on the scan of the five fingers of their left hands. When an employee first joins the lab, her fingers are scanned in arn order of her choice, and then when she wants to re-enter the facility, she has to scan the five fingers in the same sequence. The lab authorities are considering some relaxations of the scan order requirements, since it is observed that some employees often get locked-out because they forget the sequence The lab has now decided to require six scans in the pass key sequence, where exactly one finger is scanned twice, and the other fingers are scanned exactly once, which can be done in any order. For example, a possible sequence is TIMTRL. Suppose the lab allows a variation of the original sequence (of six inputs) so that input in the form of scanned sequence of six fingers is allowed to vary from the original sequence by one place for any of the fingers, as long as the finger originally scanned twice is scanned twice and other fingers are scanned once. How many different sequences of scans are allowed if the original scan sequence is LRLTIM? A) 8 B) 11 C) 13 D) 14


  25. CAT 2017: Logical Reasoning Question 7 Venkatesan S IIMB Alumnus


  26. Applicants for the doctoral programme of Ambi Institute of Engineering (AIE) and Bambi Institute of Engineering (BIE) have to appear for a Common Entrance Test (CET). The test has three sections: Physics (P), Chemistry (C), and Maths (M). Among those appearing for CET, those at or above the 80th percentile in at least two sections, and at or above the 90th percentile overall, are selected for Advanced Entrance Test (AET) conducted by AIE. AET is used by AIE for final selection. For the 200 candidates who are at or above the 90th percentile overall based on CET, the following are known about their performance in CET: 1. No one is below the 80th percentile in all 3 sections. 2. 150 are at or above the 80th percentile in exactly two sections. 3. The number of candidates at or above the 80th percentile only in P is the same as the number of candidates at or above the 80th percentile only in C. The same is the number of candidates at or above the 80th percentile only in M. 4. Number of candidates below 80th percentile in P: Number of candidates below 80th percentile in C: Number of candidates below 80th percentile in M 4:2:1.


  27. BIE uses a different process for selection. If any candidate is appearing in the AET by AIE, BIE considers their AET score for final selection provided the candidate is at or above the 80th percentile in P. Any other candidate at or above the 80th percentile in P in CET, but who is not eligible for the AET, is required to appear in a separate test to be conducted by BIE for being considered for final selection. Altogether, there are 400 candidates this year who are at or above the 80th percentile in P.


  28. Question No.:1 What best can be concluded about the number of candidates sitting for the separate test for BIE who were at or above the 90th percentile overall in CET? A) 3 or 10 B) 10 C) 5 D) 7 or 10


  29. Question No.: 2 If the number of candidates who are at or above the 90th percentile overall and also at or above the 80th percentile in all three sections in CET is actually a multiple of 5, what is the number of candidates who are at or above the 90th percentile overall and at or above the 80th percentile in both P and M in CET? A) 60 B) C) D)


  30. Question No.:3 If the number of candidates who are at or above the 90 th percentile overall and also at or above the 80 th percentile in all three sections in CET is actually a multiple of 5, then how many candidates were shortlisted for the AET for AIE? A) 170 B) C) D)


  31. Question No.: 4 If the number of candidates who are at or above the 90th percentile overall and also are at or above the 80th percentile in P in CET, is more than 100, how many candidates had to sit for the separate test for BIE? A) 299 B) 310 C) 321 D) 330