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Test Level 2: Critical Path - CAT MCQ


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20 Questions MCQ Test - Test Level 2: Critical Path

Test Level 2: Critical Path for CAT 2024 is part of CAT preparation. The Test Level 2: Critical Path questions and answers have been prepared according to the CAT exam syllabus.The Test Level 2: Critical Path MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 2: Critical Path below.
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Test Level 2: Critical Path - Question 1
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Directions: Read the given information carefully and answer the question that follows.
The architectural map below shows the hallways connecting six rooms – R1, R2, R3, R4, R5 and R6 of a certain guest house. However, all the hallways in the map below are not opened to walk at the same time because some maintenance work is going at different hallways during different time of month. Any guest can travel along any hallway only after the hallway is open to walk. The hallways R1R3, R1R2, R2R4, R3R5 and R2R6 are open to walk on week-1, the hallways R1R4 and R5R6 are open to walk on week-2 and the remaining hallways are open to walk on week-3.

After the opening of all the hallways, in how many ways can a person can go from room R1 to room R6 without passing through any room twice ?

Detailed Solution for Test Level 2: Critical Path - Question 1

The various routes that can be followed are:
R1 - R3 - R5 - R6;
R1 - R3 - R5 - R2 - R6;
R1 - R3 - R4 - R2 - R6;
R1 - R3 - R4 - R2 - R5 - R6;
R1 - R4 - R3 - R5 - R2 - R6;
R1 - R4 - R3 - R5 - R6;
R1 - R4 - R2 - R5 - R6;
R1 - R4 - R2 - R6;
R1 - R2 - R4 - R3 - R5 - R6;
R1 - R2 - R5 - R6;
R1 - R2 - R6.
Thus, there are 11 ways in all.
Hence, answer option 2 is correct.

Test Level 2: Critical Path - Question 2
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Directions: Read the given information carefully and answer the question that follows.
The architectural map below shows the hallways connecting six rooms – R1, R2, R3, R4, R5 and R6 of a certain guest house. However, all the hallways in the map below are not opened to walk at the same time because some maintenance work is going at different hallways during different time of month. Any guest can travel along any hallway only after the hallway is open to walk. The hallways R1R3, R1R2, R2R4, R3R5 and R2R6 are open to walk on week-1, the hallways R1R4 and R5R6 are open to walk on week-2 and the remaining hallways are open to walk on week-3.

If, in the 1st week, a person travelled from room R4 to room R5, what is the minimum number of rooms that he must have passed through?

Detailed Solution for Test Level 2: Critical Path - Question 2

To travel from room R4 to room R5, a person must take the route - R4 - R2 - R1 - R3 - R5.
Thus, the person must pass through 3 rooms.
Hence, answer option 3 is correct.

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Test Level 2: Critical Path - Question 3
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Directions: Read the given information carefully and answer the question that follows.
The architectural map below shows the hallways connecting six rooms – R1, R2, R3, R4, R5 and R6 of a certain guest house. However, all the hallways in the map below are not opened to walk at the same time because some maintenance work is going at different hallways during different time of month. Any guest can travel along any hallway only after the hallway is open to walk. The hallways R1R3, R1R2, R2R4, R3R5 and R2R6 are open to walk on week-1, the hallways R1R4 and R5R6 are open to walk on week-2 and the remaining hallways are open to walk on week-3.

What is the difference between the number of ways that a person can travel from room R1 to room R6 without passing through any room twice in week-2 and that in week-3?

Detailed Solution for Test Level 2: Critical Path - Question 3

In week-2, number of ways that a person can travel from room R1 to room R6 = 3 (R1R3R5R6, R1R4R2R6, R1R2R6)
In week-3, the possible routes are R1R2R6, R1R2R5R6, R1R2R4R3R5R6, R1R4R2R6, R1R4R2R5R6, R1R4R3R5R6, R1R4R3R5R2R6, R1R3R5R2R6, R1R3R5R6, R1R3R4R2R6, R1R3R4R2R5R6, i.e. 11 ways.
Required difference = 11 - 3 = 8

Test Level 2: Critical Path - Question 4
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Directions: Read the given information carefully and answer the question that follows.
The architectural map below shows the hallways connecting six rooms – R1, R2, R3, R4, R5 and R6 of a certain guest house. However, all the hallways in the map below are not opened to walk at the same time because some maintenance work is going at different hallways during different time of month. Any guest can travel along any hallway only after the hallway is open to walk. The hallways R1R3, R1R2, R2R4, R3R5 and R2R6 are open to walk on week-1, the hallways R1R4 and R5R6 are open to walk on week-2 and the remaining hallways are open to walk on week-3.

The route taken by which of the following persons would not change in week-3 as compared to that in week-2, if each person passes through the minimum number of rooms and does not pass through any room twice?
Detailed Solution for Test Level 2: Critical Path - Question 4

Option (1): In week-2, a person will take the route R2R6R5 and in week-3, a person will take the route R2R5.
Option (2): In week-2, a person will take the route R4R2R6 and in week-3, a person will take the same route.
Option (3): In week-2, a person will take the route R4R2R6R5/R4R1R3R5 and in week-3, a person will take the route R4R2R5/R4R3R5.
Option (4): In week-2, a person will take the route R3R1R4 and in week-3, a person will take the route R3R4. Hence, the route remains unchanged only in option 2.

Test Level 2: Critical Path - Question 5
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Directions: Read the given information carefully and answer the question that follows.
Six Harbors - H1, H2, H3, H4, H5, and H6 - are connected by waterways, as shown in the map below. The arrows represent the direction in which the boats can travel.

On a particular day, race of one thousand boats was conducted from H1 till H6, passing through different harbors in between. However, no boat passed through the same harbour twice. Further, it is also known that the number of boats which passed through harbour H2 is double the number of boats which passed through H4.
The number of boats which travelled on the waterways connecting harbour H3 and harbour H2 is one-fourth the number of boats which travelled on the waterways connecting harbour H4 and harbour H6.
The number of boats which travelled on the waterways connecting harbour H2 and harbour H5 is double the number of boats which passed through harbour H3. 
Exactly 640 boats passed through harbour H5.

How many boats travelled through harbour H4?
Detailed Solution for Test Level 2: Critical Path - Question 5

Let a, b, c, and d be the number of boats travelling on the routes H1H2, H1H4, H3H2, and H5H4, respectively.
From (i), a + c = 2(b + d)
From (ii), c = 1/4(b + d)
From (iii), a + c = 2(1000 - a - b)
From (iv), a + c = 640 
⇒ b + d = 320
⇒ c = 80
⇒ a = 560
From (iii), 1000 - a - b = 320
⇒ a + b = 680
⇒ b = 120 and d = 200
The following diagram shows the number of boats that travelled along each waterway:

From the above diagram, it is clear that 320 boats travelled through H4.
Hence, answer option 2 is correct.

Test Level 2: Critical Path - Question 6
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Directions: Read the given information carefully and answer the question that follows.
Six Harbors - H1, H2, H3, H4, H5, and H6 - are connected by waterways, as shown in the map below. The arrows represent the direction in which the boats can travel.

On a particular day, race of one thousand boats was conducted from H1 till H6, passing through different harbors in between. However, no boat passed through the same harbour twice. Further, it is also known that the number of boats which passed through harbour H2 is double the number of boats which passed through H4.
The number of boats which travelled on the waterways connecting harbour H3 and harbour H2 is one-fourth the number of boats which travelled on the waterways connecting harbour H4 and harbour H6.
The number of boats which travelled on the waterways connecting harbour H2 and harbour H5 is double the number of boats which passed through harbour H3. 
Exactly 640 boats passed through harbour H5.

Which of the following routes was taken by the maximum number of boats?
Detailed Solution for Test Level 2: Critical Path - Question 6

Let a, b, c, and d be the number of boats travelling on the routes H1H2, H1H4, H3H2, and H5H4, respectively.
From (i), a + c = 2(b + d)
From (ii), c = 1/4(b + d)
From (iii), a + c = 2(1000 - a - b)
From (iv), a + c = 640 
⇒ b + d = 320
⇒ c = 80
⇒ a = 560
From (iii), 1000 - a - b = 320
⇒ a + b = 680
⇒b = 120 and d = 200
The following diagram shows the number of boats that travelled along each waterway:

The number of boats which travelled along H1H2H5H6 is at least 440 - 80 = 360 (because 80 boats joined in at H2). 
The number of boats which travelled along H1H4H6 will be 120 (since the 120 boats which travelled from H1 to H4, must have gone to H6 from H4).
Similarly, the number of boats which travelled along H1H3H2H5H4H6 lies between 0 and 80.
The number of boats which travelled along H1H3H6 will be 240.
Thus, the maximum number of boats travelled through H1H2H5H6.
Hence, answer option 1 is correct.

Test Level 2: Critical Path - Question 7
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Directions: Read the given information carefully and answer the question that follows.
Six Harbors - H1, H2, H3, H4, H5, and H6 - are connected by waterways, as shown in the map below. The arrows represent the direction in which the boats can travel.

On a particular day, race of one thousand boats was conducted from H1 till H6, passing through different harbors in between. However, no boat passed through the same harbour twice. Further, it is also known that the number of boats which passed through harbour H2 is double the number of boats which passed through H4.
The number of boats which travelled on the waterways connecting harbour H3 and harbour H2 is one-fourth the number of boats which travelled on the waterways connecting harbour H4 and harbour H6.
The number of boats which travelled on the waterways connecting harbour H2 and harbour H5 is double the number of boats which passed through harbour H3. 
Exactly 640 boats passed through harbour H5.

Among the following waterways, on which waterway did the maximum number of boats travel?
Detailed Solution for Test Level 2: Critical Path - Question 7

Let a, b, c, and d be the number of boats travelling on the routes H1H2, H1H4, H3H2, and H5H4, respectively.
From (i), a + c = 2(b + d)
From (ii), c = 1/4(b + d)
From (iii), a + c = 2(1000 - a - b)
From (iv), a + c = 640 
⇒ b + d = 320
⇒ c = 80
⇒ a = 560
From (iii), 1000 - a - b = 320
⇒ a + b = 680
⇒ b = 120 and d = 200
The following diagram shows the number of boats that travelled along each waterway:

Out of the waterways given in the options, the highest number of boats travelled on the waterways connecting harbour H5 and harbour H6. 
Hence, answer option 1 is correct.

Test Level 2: Critical Path - Question 8
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Directions: Read the given information carefully and answer the question that follows.
Six Harbors - H1, H2, H3, H4, H5, and H6 - are connected by waterways, as shown in the map below. The arrows represent the direction in which the boats can travel.

On a particular day, race of one thousand boats was conducted from H1 till H6, passing through different harbors in between. However, no boat passed through the same harbour twice. Further, it is also known that the number of boats which passed through harbour H2 is double the number of boats which passed through H4.
The number of boats which travelled on the waterways connecting harbour H3 and harbour H2 is one-fourth the number of boats which travelled on the waterways connecting harbour H4 and harbour H6.
The number of boats which travelled on the waterways connecting harbour H2 and harbour H5 is double the number of boats which passed through harbour H3. 
Exactly 640 boats passed through harbour H5.

What is the number of boats which travelled on the waterways connecting harbour H4 and harbour H6?
Detailed Solution for Test Level 2: Critical Path - Question 8

Let a, b, c, and d be the number of boats travelling on the routes H1H2, H1H4, H3H2, and H5H4, respectively.
From (i), a + c = 2(b + d)
From (ii), c = 1/4(b + d)
From (iii), a + c = 2(1000 - a - b)
From (iv), a + c = 640 
⇒ b + d = 320
⇒ c = 80
⇒ a = 560
From (iii), 1000 - a - b = 320
⇒ a + b = 680
⇒ b = 120 and d = 200
The following diagram shows the number of boats that travelled along each waterway:

320 boats travelled on the waterways connecting harbour H4 and harbour H6.
Hence, answer option 3 is correct.

Test Level 2: Critical Path - Question 9
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Directions: Read the given information carefully and answer the question that follows.
Six check-points, CP1, CP2, CP3, CP4, CP5, and CP6, are connected by two-way racing tracks, as shown below.

Seven cars, Car-A, Car-B, Car-C, Car-D, Car-E, Car-F, and Car-G, are racing from check-point CP1 to check-point CP6, such that each car passes any check-point at most once. Also, no two cars pass through the same set of check-points when travelling from check-point CP1 to check-point CP6. Further, it is also known that
(i) Car-A and Car-D are the only cars to pass through the track connecting check-point CP4 and check-point CP6.
(ii) While both, Car-B and Car-C, pass through check-point CP3, Car-E does not. 
(iii) Car-B is the only car which passes through both, check-point CP2 and check-point CP4, while Car-C does not pass through check-point CP5.
(iv) While Car-F passes from the track connecting check-point CP5 and check-point CP6, it does not pass through check-point CP4.

What is the route followed by Car-F?
Detailed Solution for Test Level 2: Critical Path - Question 9

The possible routes from CP1 to CP6 are:
CP1CP2CP5CP6, CP1CP2CP5CP4CP6, CP1CP2CP5CP4CP3CP6, CP1CP4CP6, CP1CP4CP5CP6, CP1CP4CP3CP6, CP1CP3CP6, CP1CP3CP4CP6, CP1CP3CP4CP5CP6
From (iii), Car-B is the only car which passes through both, check-point CP2 and check-point CP4, and from (ii), it also passes through check-point CP3. Hence, Car-B pass along CP1CP2CP5CP4CP3CP6.
From (i), Car-A and Car-D pass through CP1CP2CP5CP4CP6, CP1CP4CP6, or CP1CP3CP4CP6. No other car passes through these three routes. However, since we have already seen that only Car-B passes through both CP2 and CP4, Car-A and Car-D pass along CP1CP4CP6 and CP1CP3CP4CP6, not necessarily in the same order, while no other car passes along CP1CP2CP5CP4CP6. From (iv), since Car-F passes through CP5 and CP6 but not CP4, the only possibility for it is CP1CP2CP5CP6.
Since, one of Car-A and Car-D pass along CP1CP3CP4CP6, the other route with the same set of check-points, i.e. CP1CP4CP3CP6, cannot be taken by anyone else.
The remaining routes are CP1CP3CP6, CP1CP3CP4CP5CP6 and CP1CP4CP5CP6. But from (ii), Car-E does not travel through CP3, which means that the only possibility left for it is CP1CP4CP5CP6. Further from (iii), Car-C does not travel through CP5, which leaves CP1CP3CP6 as the only possibility for it. This leaves CP1CP3CP4CP5CP6 as the only possibility for Car-G.
The following table presents the possible routes that each car could pass along:

Car-F drives along CP1CP2CP5CP6.
Hence, answer option 1 is correct.

Test Level 2: Critical Path - Question 10
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Directions: Read the given information carefully and answer the question that follows.
A newly-launched metro line in a certain city has started two metros as per a trial test. Each metro travels to various parts of the city, starting from MS–1, as shown in the map given below. In the map, MS–2 through MS–9 represent the metro stations at which the passengers are being dropped–off. The arrows represent the routes (along with the directions) that the metros take while traveling between metro stations. The metros do not necessarily travel along the same routes, but each route (represented by an arrow) is taken by at least one metro on a given day.
Each metro stops at every location that it comes across on and at least 10 passengers are dropped–off by each metro at every metro station that it stops at. Further, the metros return to the MS–1 after they drop–off all the passengers that they carry from MS–1.
The numbers given in the boxes, at some of the metro stations, represent the total number of passengers being dropped–off at the respective metro stations by the metro(s) that visit that location. The numbers mentioned alongside some of the arrows represent the total number of passengers, being carried by the metro(s), who travel along the respective routes.
It is given that no passenger enters the metros once they start the journey from MS–1.

How many passengers are dropped-off at MS-4?
Detailed Solution for Test Level 2: Critical Path - Question 10

The total number of passengers that the metros have when leaving MS-1 is 210 (100 + 110). When they reach MS-5, the total number of passengers they have is 150 (70 + 80). Therefore, they drop-off 60 passengers at MS-2, MS-3 and MS-4. Since they drop-off at least 10 passengers at each location, they must drop-off 10 passengers at MS-2 and 10 at MS-4.
Therefore, the answer is option 1.

Test Level 2: Critical Path - Question 11
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Directions: Read the given information carefully and answer the question that follows.
A newly-launched metro line in a certain city has started two metros as per a trial test. Each metro travels to various parts of the city, starting from MS–1, as shown in the map given below. In the map, MS–2 through MS–9 represent the metro stations at which the passengers are being dropped–off. The arrows represent the routes (along with the directions) that the metros take while traveling between metro stations. The metros do not necessarily travel along the same routes, but each route (represented by an arrow) is taken by at least one metro on a given day.
Each metro stops at every location that it comes across on and at least 10 passengers are dropped–off by each metro at every metro station that it stops at. Further, the metros return to the MS–1 after they drop–off all the passengers that they carry from MS–1.
The numbers given in the boxes, at some of the metro stations, represent the total number of passengers being dropped–off at the respective metro stations by the metro(s) that visit that location. The numbers mentioned alongside some of the arrows represent the total number of passengers, being carried by the metro(s), who travel along the respective routes.
It is given that no passenger enters the metros once they start the journey from MS–1.

What is the total number of passengers who travel between MS-3 and MS-4?
Detailed Solution for Test Level 2: Critical Path - Question 11

The total number of passengers that the metros have when leaving MS-1 is 210 (100 + 110). When they reach MS-5, the total number of passengers they have is 150 (70 + 80). Therefore, they drop-off 60 passengers at MS-2, MS-3 and MS-4. Since they drop-off at least 10 passengers at each location, they must drop-off 10 passengers at MS-2 and 10 at MS-4.
Since 10 passengers are dropped-off at MS-2, the two metros must carry 200 passengers to MS-3. They drop-off 40 passengers at MS-3, and carry 160 passengers in total from MS-3 to MS-4 and MS-3 to MS-5. Since 80 passengers are being carried from MS-3 to MS-5, 80 passengers must be carried from MS-3 to MS-4.
Hence, answer option 2 is correct.

Test Level 2: Critical Path - Question 12
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Directions: Read the given information carefully and answer the question that follows.
A newly-launched metro line in a certain city has started two metros as per a trial test. Each metro travels to various parts of the city, starting from MS–1, as shown in the map given below. In the map, MS–2 through MS–9 represent the metro stations at which the passengers are being dropped–off. The arrows represent the routes (along with the directions) that the metros take while traveling between metro stations. The metros do not necessarily travel along the same routes, but each route (represented by an arrow) is taken by at least one metro on a given day.
Each metro stops at every location that it comes across on and at least 10 passengers are dropped–off by each metro at every metro station that it stops at. Further, the metros return to the MS–1 after they drop–off all the passengers that they carry from MS–1.
The numbers given in the boxes, at some of the metro stations, represent the total number of passengers being dropped–off at the respective metro stations by the metro(s) that visit that location. The numbers mentioned alongside some of the arrows represent the total number of passengers, being carried by the metro(s), who travel along the respective routes.
It is given that no passenger enters the metros once they start the journey from MS–1.

What is the maximum number of passengers that can be dropped-off at MS-8?
Detailed Solution for Test Level 2: Critical Path - Question 12

The metros have a total of 130 passengers with them between MS5 and MS6. If the maximum number of passengers are to be dropped-off at MS-8, only ten passengers each must be dropped-off at MS-7 and MS-9. Therefore, the maximum number of passengers that can be dropped-off at MS-8 can be:
130 - 70 - 10 - 10 = 40 passengers
Hence, answer option 4 is correct.

Test Level 2: Critical Path - Question 13
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Directions: Read the given information carefully and answer the question that follows.
Six check-points, CP1, CP2, CP3, CP4, CP5, and CP6, are connected by two-way racing tracks, as shown below.

Seven cars, Car-A, Car-B, Car-C, Car-D, Car-E, Car-F, and Car-G, are racing from check-point CP1 to check-point CP6, such that each car passes any check-point at most once. Also, no two cars pass through the same set of check-points when travelling from check-point CP1 to check-point CP6. Further, it is also known that
(i) Car-A and Car-D are the only cars to pass through the track connecting check-point CP4 and check-point CP6.
(ii) While both, Car-B and Car-C, pass through check-point CP3, Car-E does not. 
(iii) Car-B is the only car which passes through both, check-point CP2 and check-point CP4, while Car-C does not pass through check-point CP5.
(iv) While Car-F passes from the track connecting check-point CP5 and check-point CP6, it does not pass through check-point CP4.

Which of the following tracks did Car-E pass along?
Detailed Solution for Test Level 2: Critical Path - Question 13

The possible routes from CP1 to CP6 are:
CP1CP2CP5CP6, CP1CP2CP5CP4CP6, CP1CP2CP5CP4CP3CP6, CP1CP4CP6, CP1CP4CP5CP6, CP1CP4CP3CP6, CP1CP3CP6, CP1CP3CP4CP6, CP1CP3CP4CP5CP6
From (iii), Car-B is the only car which passes through both, check-point CP2 and check-point CP4, and from (ii), it also passes through check-point CP3. Hence, Car-B pass along CP1CP2CP5CP4CP3CP6.
From (i), Car-A and Car-D pass through CP1CP2CP5CP4CP6, CP1CP4CP6, or CP1CP3CP4CP6. No other car passes through these three routes. However, since we have already seen that only Car-B passes through both CP2 and CP4, Car-A and Car-D pass along CP1CP4CP6 and CP1CP3CP4CP6, not necessarily in the same order, while no other car passes along CP1CP2CP5CP4CP6. From (iv), since Car-F passes through CP5 and CP6 but not CP4, the only possibility for it is CP1CP2CP5CP6.
Since, one of Car-A and Car-D pass along CP1CP3CP4CP6, the other route with the same set of check-points, i.e. CP1CP4CP3CP6, cannot be taken by anyone else.
The remaining routes are CP1CP3CP6, CP1CP3CP4CP5CP6 and CP1CP4CP5CP6. But from (ii), Car-E does not travel through CP3, which means that the only possibility left for it is CP1CP4CP5CP6. Further from (iii), Car-C does not travel through CP5, which leaves CP1CP3CP6 as the only possibility for it. This leaves CP1CP3CP4CP5CP6 as the only possibility for Car-G.
The following table presents the possible routes that each car could pass along:

Car-E passes along CP1CP4CP5CP6.
Hence, answer option 2 is correct.

Test Level 2: Critical Path - Question 14
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Directions: Read the given information carefully and answer the question that follows.
Six check-points, CP1, CP2, CP3, CP4, CP5, and CP6, are connected by two-way racing tracks, as shown below.

Seven cars, Car-A, Car-B, Car-C, Car-D, Car-E, Car-F, and Car-G, are racing from check-point CP1 to check-point CP6, such that each car passes any check-point at most once. Also, no two cars pass through the same set of check-points when travelling from check-point CP1 to check-point CP6. Further, it is also known that
(i) Car-A and Car-D are the only cars to pass through the track connecting check-point CP4 and check-point CP6.
(ii) While both, Car-B and Car-C, pass through check-point CP3, Car-E does not. 
(iii) Car-B is the only car which passes through both, check-point CP2 and check-point CP4, while Car-C does not pass through check-point CP5.
(iv) While Car-F passes from the track connecting check-point CP5 and check-point CP6, it does not pass through check-point CP4.

What is the number of check-points, including CP1 and CP6, through which Car-G passes?
Detailed Solution for Test Level 2: Critical Path - Question 14

The possible routes from CP1 to CP6 are:
CP1CP2CP5CP6, CP1CP2CP5CP4CP6, CP1CP2CP5CP4CP3CP6, CP1CP4CP6, CP1CP4CP5CP6, CP1CP4CP3CP6, CP1CP3CP6, CP1CP3CP4CP6, CP1CP3CP4CP5CP6
From (iii), Car-B is the only car which passes through both, check-point CP2 and check-point CP4, and from (ii), it also passes through check-point CP3. Hence, Car-B pass along CP1CP2CP5CP4CP3CP6.
From (i), Car-A and Car-D pass through CP1CP2CP5CP4CP6, CP1CP4CP6, or CP1CP3CP4CP6. No other car passes through these three routes. However, since we have already seen that only Car-B passes through both CP2 and CP4, Car-A and Car-D pass along CP1CP4CP6 and CP1CP3CP4CP6, not necessarily in the same order, while no other car passes along CP1CP2CP5CP4CP6. From (iv), since Car-F passes through CP5 and CP6 but not CP4, the only possibility for it is CP1CP2CP5CP6.
Since, one of Car-A and Car-D pass along CP1CP3CP4CP6, the other route with the same set of check-points, i.e. CP1CP4CP3CP6, cannot be taken by anyone else.
The remaining routes are CP1CP3CP6, CP1CP3CP4CP5CP6 and CP1CP4CP5CP6. But from (ii), Car-E does not travel through CP3, which means that the only possibility left for it is CP1CP4CP5CP6. Further from (iii), Car-C does not travel through CP5, which leaves CP1CP3CP6 as the only possibility for it. This leaves CP1CP3CP4CP5CP6 as the only possibility for Car-G.
The following table presents the possible routes that each car could pass along:

Thus, car-G passes through a total of 5 check-points.
Hence, answer option 4 is correct.

Test Level 2: Critical Path - Question 15
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Directions: Read the given information carefully and answer the question that follows.
Six check-points, CP1, CP2, CP3, CP4, CP5, and CP6, are connected by two-way racing tracks, as shown below.

Seven cars, Car-A, Car-B, Car-C, Car-D, Car-E, Car-F, and Car-G, are racing from check-point CP1 to check-point CP6, such that each car passes any check-point at most once. Also, no two cars pass through the same set of check-points when travelling from check-point CP1 to check-point CP6. Further, it is also known that
(i) Car-A and Car-D are the only cars to pass through the track connecting check-point CP4 and check-point CP6.
(ii) While both, Car-B and Car-C, pass through check-point CP3, Car-E does not. 
(iii) Car-B is the only car which passes through both, check-point CP2 and check-point CP4, while Car-C does not pass through check-point CP5.
(iv) While Car-F passes from the track connecting check-point CP5 and check-point CP6, it does not pass through check-point CP4.

Which of the following is a correct combination of check-point and the number of cars which pass through that check-point?
Detailed Solution for Test Level 2: Critical Path - Question 15

The possible routes from CP1 to CP6 are:
CP1CP2CP5CP6, CP1CP2CP5CP4CP6, CP1CP2CP5CP4CP3CP6, CP1CP4CP6, CP1CP4CP5CP6, CP1CP4CP3CP6, CP1CP3CP6, CP1CP3CP4CP6, CP1CP3CP4CP5CP6
From (iii), Car-B is the only car which passes through both, check-point CP2 and check-point CP4, and from (ii), it also passes through check-point CP3. Hence, Car-B pass along CP1CP2CP5CP4CP3CP6.
From (i), Car-A and Car-D pass through CP1CP2CP5CP4CP6, CP1CP4CP6, or CP1CP3CP4CP6. No other car passes through these three routes. However, since we have already seen that only Car-B passes through both CP2 and CP4, Car-A and Car-D pass along CP1CP4CP6 and CP1CP3CP4CP6, not necessarily in the same order, while no other car passes along CP1CP2CP5CP4CP6. From (iv), since Car-F passes through CP5 and CP6 but not CP4, the only possibility for it is CP1CP2CP5CP6.
Since, one of Car-A and Car-D pass along CP1CP3CP4CP6, the other route with the same set of check-points, i.e. CP1CP4CP3CP6, cannot be taken by anyone else.
The remaining routes are CP1CP3CP6, CP1CP3CP4CP5CP6 and CP1CP4CP5CP6. But from (ii), Car-E does not travel through CP3, which means that the only possibility left for it is CP1CP4CP5CP6. Further from (iii), Car-C does not travel through CP5, which leaves CP1CP3CP6 as the only possibility for it. This leaves CP1CP3CP4CP5CP6 as the only possibility for Car-G.
The following table presents the possible routes that each car could pass along:

The correct combinations are CP5-4, CP4-5, CP3-4, and CP2-2. Only choice 4 is correct.

Test Level 2: Critical Path - Question 16
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Directions: Read the given information carefully and answer the question that follows.
Six check-points, CP1, CP2, CP3, CP4, CP5, and CP6, are connected by two-way racing tracks, as shown below.

Seven cars, Car-A, Car-B, Car-C, Car-D, Car-E, Car-F, and Car-G, are racing from check-point CP1 to check-point CP6, such that each car passes any check-point at most once. Also, no two cars pass through the same set of check-points when travelling from check-point CP1 to check-point CP6. Further, it is also known that
(i) Car-A and Car-D are the only cars to pass through the track connecting check-point CP4 and check-point CP6.
(ii) While both, Car-B and Car-C, pass through check-point CP3, Car-E does not. 
(iii) Car-B is the only car which passes through both, check-point CP2 and check-point CP4, while Car-C does not pass through check-point CP5.
(iv) While Car-F passes from the track connecting check-point CP5 and check-point CP6, it does not pass through check-point CP4.

What is the route followed by Car-C?
Detailed Solution for Test Level 2: Critical Path - Question 16

The possible routes from CP1 to CP6 are:
CP1CP2CP5CP6, CP1CP2CP5CP4CP6, CP1CP2CP5CP4CP3CP6, CP1CP4CP6, CP1CP4CP5CP6, CP1CP4CP3CP6, CP1CP3CP6, CP1CP3CP4CP6, CP1CP3CP4CP5CP6
From (iii), Car-B is the only car which passes through both, check-point CP2 and check-point CP4, and from (ii), it also passes through check-point CP3. Hence, Car-B pass along CP1CP2CP5CP4CP3CP6.
From (i), Car-A and Car-D pass through CP1CP2CP5CP4CP6, CP1CP4CP6, or CP1CP3CP4CP6. No other car passes through these three routes. However, since we have already seen that only Car-B passes through both CP2 and CP4, Car-A and Car-D pass along CP1CP4CP6 and CP1CP3CP4CP6, not necessarily in the same order, while no other car passes along CP1CP2CP5CP4CP6. From (iv), since Car-F passes through CP5 and CP6 but not CP4, the only possibility for it is CP1CP2CP5CP6.
Since, one of Car-A and Car-D pass along CP1CP3CP4CP6, the other route with the same set of check-points, i.e. CP1CP4CP3CP6, cannot be taken by anyone else.
The remaining routes are CP1CP3CP6, CP1CP3CP4CP5CP6 and CP1CP4CP5CP6. But from (ii), Car-E does not travel through CP3, which means that the only possibility left for it is CP1CP4CP5CP6. Further from (iii), Car-C does not travel through CP5, which leaves CP1CP3CP6 as the only possibility for it. This leaves CP1CP3CP4CP5CP6 as the only possibility for Car-G.
The following table presents the possible routes that each car could pass along:

Car-C passes along CP1CP3CP6.
Hence, answer option 3 is correct.

Test Level 2: Critical Path - Question 17
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Directions: Read the given information carefully and answer the question that follows.
A newly-launched metro line in a certain city has started two metros as per a trial test. Each metro travels to various parts of the city, starting from MS–1, as shown in the map given below. In the map, MS–2 through MS–9 represent the metro stations at which the passengers are being dropped–off. The arrows represent the routes (along with the directions) that the metros take while traveling between metro stations. The metros do not necessarily travel along the same routes, but each route (represented by an arrow) is taken by at least one metro on a given day.
Each metro stops at every location that it comes across on and at least 10 passengers are dropped–off by each metro at every metro station that it stops at. Further, the metros return to the MS–1 after they drop–off all the passengers that they carry from MS–1.
The numbers given in the boxes, at some of the metro stations, represent the total number of passengers being dropped–off at the respective metro stations by the metro(s) that visit that location. The numbers mentioned alongside some of the arrows represent the total number of passengers, being carried by the metro(s), who travel along the respective routes.
It is given that no passenger enters the metros once they start the journey from MS–1.

At which location are the maximum number of passengers dropped-off by both the metros together?
Detailed Solution for Test Level 2: Critical Path - Question 17

At MS-7, MS-8 and MS-9, the maximum number of passengers that can be dropped-off will be less than 70. Hence, the maximum number of passengers are dropped-off at MS-6, which is 70.

Test Level 2: Critical Path - Question 18
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Directions: Read the given information carefully and answer the question that follows.
The famous VIP club of a particular city has five doors. The manager of club has hired some bouncers in order to prevent any type of chaos inside the club. All the bouncers are always present inside the club, unless ordered to move to a door. A competitor club's manager hired some bouncers to damage the club property and enter inside. The bouncers of the competitor club are gathered outside the club, sitting inside buses which are parked in the given pattern, M–1 to M–7. Each bus has a certain number of bouncers. The bouncers from a given bus can attack only some of the doors of the club, as indicated in the diagram below. However, all the bouncers from a single bus of the competitor club need not necessarily attack the same door. The manager has come to know about this and is planning to send his bouncers to the doors.
The following diagram shows the club doors (B–1 to B–5) and the competitor club's buses with bouncers (M–1 to M–7). The solid lines in the figure represent the respective club doors to which the bouncers can be deployed from the club. The dotted lines from each competitor bus represent the doors that the bouncers from that competitor club can attack. The numbers inside each competitor bus represent the number of bouncers inside the bus.

Assume that all the competitor club bouncers attack the club doors that they are assigned to at the same time and that each competitor club bouncer attacks exactly one club door. Also, a higher numerical strength in terms of bouncers will assure victory to any side in such a manner that, if say, 10 competitor club bouncers attack a club door with 11 bouncers, all the competitor club bouncers will be beaten and the club door will remain safe, but with only 1 bouncer remaining. If the number of competitor club bouncers attacking a club door is equal to the number of bouncers at the club door, all the bouncers belonging to both the sides will be beaten, but the club door will remain safe. In a similar manner, if the number of competitor club bouncers attacking is in excess of the number of bouncers, the club door will be destroyed, but with only the excess number of competitor club bouncers remaining not beaten.

What is the minimum number of bouncers that the manager must deploy to all the club doors put together, in order to ensure that none of the club doors is destroyed?
Detailed Solution for Test Level 2: Critical Path - Question 18

In order to protect all the club doors from being destroyed, each door must have enough bouncers to fight against all the competitor club bouncers that can attack that club door.
Number of bouncers at B-1 = 38 + 69 + 42 + 51 = 200
Number of bouncers at B-2 = 69 + 42 + 51 + 33 = 195
Number of bouncers at B-3 = 51 + 33 + 48 = 132
Number of bouncers at B-4 = 33 + 48 + 28 = 109
Number of bouncers at B-5 = 69 + 28 + 38 = 135
Total number of bouncers across all club doors = 200 + 195 + 132 + 109 + 135 = 771

Test Level 2: Critical Path - Question 19
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Directions: Read the given information carefully and answer the question that follows.
The famous VIP club of a particular city has five doors. The manager of club has hired some bouncers in order to prevent any type of chaos inside the club. All the bouncers are always present inside the club, unless ordered to move to a door. A competitor club's manager hired some bouncers to damage the club property and enter inside. The bouncers of the competitor club are gathered outside the club, sitting inside buses which are parked in the given pattern, M–1 to M–7. Each bus has a certain number of bouncers. The bouncers from a given bus can attack only some of the doors of the club, as indicated in the diagram below. However, all the bouncers from a single bus of the competitor club need not necessarily attack the same door. The manager has come to know about this and is planning to send his bouncers to the doors.
The following diagram shows the club doors (B–1 to B–5) and the competitor club's buses with bouncers (M–1 to M–7). The solid lines in the figure represent the respective club doors to which the bouncers can be deployed from the club. The dotted lines from each competitor bus represent the doors that the bouncers from that competitor club can attack. The numbers inside each competitor bus represent the number of bouncers inside the bus.

Assume that all the competitor club bouncers attack the club doors that they are assigned to at the same time and that each competitor club bouncer attacks exactly one club door. Also, a higher numerical strength in terms of bouncers will assure victory to any side in such a manner that, if say, 10 competitor club bouncers attack a club door with 11 bouncers, all the competitor club bouncers will be beaten and the club door will remain safe, but with only 1 bouncer remaining. If the number of competitor club bouncers attacking a club door is equal to the number of bouncers at the club door, all the bouncers belonging to both the sides will be beaten, but the club door will remain safe. In a similar manner, if the number of competitor club bouncers attacking is in excess of the number of bouncers, the club door will be destroyed, but with only the excess number of competitor club bouncers remaining not beaten.

If the manager wants to save just three club doors from being destroyed, what is the minimum number of bouncers that he must deploy?
Detailed Solution for Test Level 2: Critical Path - Question 19

If three club doors are to be saved from destruction, minimum number of bouncers will be required to protect B-3, B-4, and B-5.
Thus, total number of bouncers required = 132 + 109 + 135 = 376
Hence, answer option 4 is correct.

Test Level 2: Critical Path - Question 20
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Directions: Read the given information carefully and answer the question that follows.
The famous VIP club of a particular city has five doors. The manager of club has hired some bouncers in order to prevent any type of chaos inside the club. All the bouncers are always present inside the club, unless ordered to move to a door. A competitor club's manager hired some bouncers to damage the club property and enter inside. The bouncers of the competitor club are gathered outside the club, sitting inside buses which are parked in the given pattern, M–1 to M–7. Each bus has a certain number of bouncers. The bouncers from a given bus can attack only some of the doors of the club, as indicated in the diagram below. However, all the bouncers from a single bus of the competitor club need not necessarily attack the same door. The manager has come to know about this and is planning to send his bouncers to the doors.
The following diagram shows the club doors (B–1 to B–5) and the competitor club's buses with bouncers (M–1 to M–7). The solid lines in the figure represent the respective club doors to which the bouncers can be deployed from the club. The dotted lines from each competitor bus represent the doors that the bouncers from that competitor club can attack. The numbers inside each competitor bus represent the number of bouncers inside the bus.

Assume that all the competitor club bouncers attack the club doors that they are assigned to at the same time and that each competitor club bouncer attacks exactly one club door. Also, a higher numerical strength in terms of bouncers will assure victory to any side in such a manner that, if say, 10 competitor club bouncers attack a club door with 11 bouncers, all the competitor club bouncers will be beaten and the club door will remain safe, but with only 1 bouncer remaining. If the number of competitor club bouncers attacking a club door is equal to the number of bouncers at the club door, all the bouncers belonging to both the sides will be beaten, but the club door will remain safe. In a similar manner, if the number of competitor club bouncers attacking is in excess of the number of bouncers, the club door will be destroyed, but with only the excess number of competitor club bouncers remaining not beaten.

If it is known that the competitor club is planning to send, from each bus, an equal number of bouncers to all the possible club doors, what is the minimum number of bouncers that will be injured during the attack if no club door should be destroyed?
Detailed Solution for Test Level 2: Critical Path - Question 20

The total number of enemy bouncers that will attack the club door is 309.
Since the number of bouncers attacking each club door is already known, the number of defending bouncers will also be 309.Hence, a minimum of 618 bouncers will be injured if no club door is to be destroyed.

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