Logical Reasoning – Set – Four cars need to travel from Akala to Bakala

DILR – Logical Reasoning – Set

The following set contains four questions related to Logical Reasoning. Choose the best answer to each question.

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.

Questions

Q1) How many cars would be asked to take the route A-N-B, that is Akala-Nanur-Bakala route, by the police department?

Q2) 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

Q3) 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.)

Q4) 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

Q1: 2
Q2: Option (B)
Q3: 2
Q4: Option (B)

Solutions

Q1
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When two cars go from the route A – N – B

Total time taken = 30 minutes
When two cars go from the route A – M – B

Total time taken = 29.9 minutes
So, the number of cars that can go from the route A-N-B are 2

Q2
From CAT 2017 – Logical Reasoning – Set, we can infer that,

As we can see from the above question, the difference in time will be 30-29.9 = 0.1 minutes
Option (B)

Q3
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When only one care takes the route A – N –B

Total time = 26 minutes
When only one car takes the route A – M – B

Total time = 26 minutes
So, police department will ask 2 cars to take the route A – M – N – B

Q4
From CAT 2017 – Logical Reasoning – Set, we can infer that,

When all cars follow the police order the time taken would be A-M-B (1 car) = 12 + 20 = 32 minutes.
A-M-N-B (2cars) = 12 + 8 + 12 = 32 minutes. A-N-B (1 car) = 20 + 12 =32 minutes.
Option (B)

CAT 2017 Questions from Logical Reasoning

Logical Reasoning – Set 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.
Logical Reasoning – Set 2: Eight friends: Ajit, Byomkesh, Gargi, Jayanta, Kikira, Manik, Prodosh and Tapesh are going to Delhi from Kolkata by a flight operated by Cheap Air.
Logical Reasoning – Set 3: In an 8 X 8 chessboard a queen placed anywhere can attack another piece if the piece is present in the same row, or in the same column or in any diagonal position in any possible 4 directions, provided there is no other piece in between in the path from the queen to that piece.
Logical Reasoning – Set 4: A tea taster was assigned to rate teas from six different locations – Munnar, Wayanad, Ooty, Darjeeling, Assam and Himachal.
Logical Reasoning – Set 5: A new airlines company is planning to start operations in a country.
Logical Reasoning – Set 6: In a square layout of size 5m × 5m, 25 equal sized square platforms of different heights are built.
Logical Reasoning – Set 7: There are 21 employees working in a division, out of whom 10 are special-skilled employees (SE) and the remaining are regular skilled employees (RE).
Logical Reasoning – Set 8: Healthy Bites is a fast food joint serving three items: burgers, fries and ice cream.

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