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CAT 2025 Lesson : DILR: Mar '25 to Apr '25 - Non Standard Cases - 05 Mar 2025
Read the following and answer the questions that follow
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
1) If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?
Answer:
2) What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?
(1) 7.56%
(2) 33.33%
(3) 10.80%
(4) 17.64%
3) If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?
(1) 3.24%
(2) 30%
(3) 18%
(4) 5.4%
4) If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?
(1) 220
(2) 250
(3) 200
(4) 210
Details for Questions 5 to 8 are provided below
In a square layout of size 5m x 5m, 25 equal-sized square platforms of different heights are built.
The heights (in metres) of individual platforms are as shown below:
Individuals (all of same height) are seated on these platforms. We say an individual A can reach individual B, if all the three following conditions are met:
(i) A and B are in the same row or column
(ii) A is at a lower height than B
(iii) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5.
Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
5) How many individuals in this layout can be reached by just one individual?
(1) 3
(2) 5
(3) 7
(4) 8
6) Which of the following is true for any individual at a platform of height 1 m in this layout?
(1) They can be reached by all the individuals in their own row and column.
(2) They can be reached by at least 4 individuals.
(3) They can be reached by at least one individual.
(4) They cannot be reached by anyone.
7) We can find two individuals who cannot be reached by anyone in
(1) the last row.
(2) the fourth row.
(3) the fourth column.
(4) the middle column.
8) Which of the following statements is true about this layout?
(1) Each row has an individual who can be reached by 5 or more individuals.
(2) Each row has an individual who cannot be reached by anyone.
(3) Each row has at least two individuals who can be reached by an equal number of individuals.
(4) All individuals at the height of 9 m can be reached by at least 5 individuals.
Details for Questions 9 to 12 are provided below
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) 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:
(1) 45
(2) 90
(3) 180
(4) 135
10) 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:
(1) 54
(2) 120
(3) 96
(4) 60
11) 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
Then the minimum number of direct flights that satisfies the underlying principle of the airline is:
Answer:
12) 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 operated at A would be those to and from B. Cities in G2 would have to be assigned to G3 or G4.
What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?
Answer:
Every day a widget supplier supplies widgets from the warehouse (W) to four locations – Ahmednagar (A), Bikrampore (B), Chitrachak (C), and Deccan Park (D). The daily demand for widgets in each location is uncertain and independent of each other. Demands and corresponding probability values (in parenthesis) are given against each location (A, B, C, and D) in the figure below. For example, there is a 40% chance that the demand in Ahmednagar will be 50 units and a 60% chance that the demand will be 70 units. The lines in the figure connecting the locations and warehouse represent two-way roads connecting those places with the distances (in km) shown beside the line. The distances in both the directions along a road are equal. For example, the road from Ahmednagar to Bikrampore and the road from Bikrampore to Ahmednagar are both 6 km long.
Every day the supplier gets the information about the demand values of the four locations and creates the travel route that starts from the warehouse and ends at a location after visiting all the locations exactly once. While making the route plan, the supplier goes to the locations in decreasing order of demand. If there is a tie for the choice of the next location, the supplier will go to the location closest to the current location. Also, while creating the route, the supplier can either follow the direct path (if available) from one location to another or can take the path via the warehouse. If both paths are available (direct and via warehouse), the supplier will choose the path with minimum distance.
1) If the total number of widgets delivered in a day is 250 units, then what is the total distance covered in the route (in km)?
Answer:
2) What is the chance that the total number of widgets delivered in a day is 260 units and the route ends at Bikrampore?
(1) 7.56%
(2) 33.33%
(3) 10.80%
(4) 17.64%
3) If the first location visited from the warehouse is Ahmednagar, then what is the chance that the total distance covered in the route is 40 km?
(1) 3.24%
(2) 30%
(3) 18%
(4) 5.4%
4) If Ahmednagar is not the first location to be visited in a route and the total route distance is 29 km, then which of the following is a possible number of widgets delivered on that day?
(1) 220
(2) 250
(3) 200
(4) 210
Details for Questions 5 to 8 are provided below
In a square layout of size 5m x 5m, 25 equal-sized square platforms of different heights are built.
The heights (in metres) of individual platforms are as shown below:
Individuals (all of same height) are seated on these platforms. We say an individual A can reach individual B, if all the three following conditions are met:
(i) A and B are in the same row or column
(ii) A is at a lower height than B
(iii) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5.
Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
5) How many individuals in this layout can be reached by just one individual?
(1) 3
(2) 5
(3) 7
(4) 8
6) Which of the following is true for any individual at a platform of height 1 m in this layout?
(1) They can be reached by all the individuals in their own row and column.
(2) They can be reached by at least 4 individuals.
(3) They can be reached by at least one individual.
(4) They cannot be reached by anyone.
7) We can find two individuals who cannot be reached by anyone in
(1) the last row.
(2) the fourth row.
(3) the fourth column.
(4) the middle column.
8) Which of the following statements is true about this layout?
(1) Each row has an individual who can be reached by 5 or more individuals.
(2) Each row has an individual who cannot be reached by anyone.
(3) Each row has at least two individuals who can be reached by an equal number of individuals.
(4) All individuals at the height of 9 m can be reached by at least 5 individuals.
Details for Questions 9 to 12 are provided below
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) 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:
(1) 45
(2) 90
(3) 180
(4) 135
10) 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:
(1) 54
(2) 120
(3) 96
(4) 60
11) 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
Then the minimum number of direct flights that satisfies the underlying principle of the airline is:
Answer:
12) 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 operated at A would be those to and from B. Cities in G2 would have to be assigned to G3 or G4.
What would be the maximum reduction in the number of direct flights as compared to the situation before the operational difficulties arose?
Answer:
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