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Test Level 1: Critical Path - CAT MCQ


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20 Questions MCQ Test Level-wise Tests for CAT - Test Level 1: Critical Path

Test Level 1: Critical Path for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 1: Critical Path questions and answers have been prepared according to the CAT exam syllabus.The Test Level 1: Critical Path MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 1: Critical Path below.
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Test Level 1: Critical Path - Question 1
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Directions: Study the following information and answer the questions that follows.
Seven playrooms (P1, P2, P3, P4, P5, P6 and P7) of a play-way school are connected to each other through different routes. Distances between these playrooms are shown with the help of a diagram. All the students first go for assembly, which will be held in the main hall, that is P1.

What could be the shortest distance a child needs to cover if he wants to go from P4 to P7?

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

The shortest route would be P4-P5-P7 that would add up to give 25 m.

Test Level 1: Critical Path - Question 2
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Directions: Study the following information and answer the questions that follows.
Seven playrooms (P1, P2, P3, P4, P5, P6 and P7) of a play-way school are connected to each other through different routes. Distances between these playrooms are shown with the help of a diagram. All the students first go for assembly, which will be held in the main hall, that is P1.

What could be the longest possible route from P4 to P3?

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

(1) P4-P5-P3 = 25 m
(2) P4-P2-P1-P3 = 36 m
(3) P4-P2-P5-P3 = 38 m
(4) P4-P6-P7-P3 = 57 m
Hence, the longest possible route among the options is given by option 4.

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Test Level 1: Critical Path - Question 3
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Directions: Study the following information and answer the questions that follows.
Seven playrooms (P1, P2, P3, P4, P5, P6 and P7) of a play-way school are connected to each other through different routes. Distances between these playrooms are shown with the help of a diagram. All the students first go for assembly, which will be held in the main hall, that is P1.

Which of the following routes would add up to a distance of 23 m?

Detailed Solution for Test Level 1: Critical Path - Question 3

(1) P5-P4-P6 = 22 m
(2) P2-P5-P3 = 28 m
(3) P1-P2-P4 = 20 m
(4) P4-P2-P5 = 23 m
Hence, option 4 is the correct option.

Test Level 1: Critical Path - Question 4
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Directions: Study the following information and answer the questions that follows.
Seven playrooms (P1, P2, P3, P4, P5, P6 and P7) of a play-way school are connected to each other through different routes. Distances between these playrooms are shown with the help of a diagram. All the students first go for assembly, which will be held in the main hall, that is P1.

How many maximum number of playrooms does a child need to cross to go from P2 to P3, if he can go around any classroom just once?
Detailed Solution for Test Level 1: Critical Path - Question 4

A child needs to cross a maximum of 4 playrooms to go from P2 to P3.
The route would be P2-P4-P6-P7-P5-P3.

Test Level 1: Critical Path - Question 5
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Directions: Study the following information and answer the questions that follows.
Kiran, Piya and Amar are going to take a round of a city following different or same pathways. All of them can take any means of transportation (car, two wheeler, or public transport). Charges for all of them are different. They have to pay Rs. 200/hr, if they are taking a car on rent. While the charges for a two wheeler are Rs. 50/hr. However, they just need to pay Rs. 20 to go through a public transport for an hour. Their route will start from point K and will end at point P. O is the place where they can sit and relax. M, L and N are places to get different means of transport. M is the place where cars are parked. L is a bus stand, while at place N, two wheelers are parked. The charges of going to car parking, two wheeler parking or bus stand are fixed and are Rs. 30, Rs. 10 and Rs. 40, respectively. The different pathways are as follows and the distance between them is given in km.

How much minimum distance does Kiran need to cover if she prefers to go by a car?
Detailed Solution for Test Level 1: Critical Path - Question 5

As she prefers to go by a car, we have to take route through M.
The minimum distance she needs to cover is 9 km, that is K-M-P.
K to M = 4 km
M to P = 5 km
Total distance = 9 km

Test Level 1: Critical Path - Question 6
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Directions: Study the following information and answer the questions that follows.
Kiran, Piya and Amar are going to take a round of a city following different or same pathways. All of them can take any means of transportation (car, two wheeler, or public transport). Charges for all of them are different. They have to pay Rs. 200/hr, if they are taking a car on rent. While the charges for a two wheeler are Rs. 50/hr. However, they just need to pay Rs. 20 to go through a public transport for an hour. Their route will start from point K and will end at point P. O is the place where they can sit and relax. M, L and N are places to get different means of transport. M is the place where cars are parked. L is a bus stand, while at place N, two wheelers are parked. The charges of going to car parking, two wheeler parking or bus stand are fixed and are Rs. 30, Rs. 10 and Rs. 40, respectively. The different pathways are as follows and the distance between them is given in km.

What amount does Amar need to pay in total, if he wants to travel through the route K-L-O-P and his whole journey takes three and a half hours in total whereas it takes half an hour to travel from the starting point till the bus stand?
Detailed Solution for Test Level 1: Critical Path - Question 6

Charges from K to L = Rs. 40
L is a bus stand; the charges for a bus are Rs. 20 per hour.
He spends half an hour to travel from point K to L.
So he used a bus for 3 hours and the charges would be Rs. 20 x 3 = Rs. 60.
Total amount = Rs. (40 + 60) = Rs. 100
Hence, answer option 4 is correct.

Test Level 1: Critical Path - Question 7
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Directions: Study the following information and answer the questions that follows.
Kiran, Piya and Amar are going to take a round of a city following different or same pathways. All of them can take any means of transportation (car, two wheeler, or public transport). Charges for all of them are different. They have to pay Rs. 200/hr, if they are taking a car on rent. While the charges for a two wheeler are Rs. 50/hr. However, they just need to pay Rs. 20 to go through a public transport for an hour. Their route will start from point K and will end at point P. O is the place where they can sit and relax. M, L and N are places to get different means of transport. M is the place where cars are parked. L is a bus stand, while at place N, two wheelers are parked. The charges of going to car parking, two wheeler parking or bus stand are fixed and are Rs. 30, Rs. 10 and Rs. 40, respectively. The different pathways are as follows and the distance between them is given in km.

What would be the distance travelled by Priya, if she wants to travel through the path K-N-L-P?
Detailed Solution for Test Level 1: Critical Path - Question 7

Distance from K to N = 2 km
Distance from N to L = 5 km
Distance from L to P = 5 km
Total distance = 5 + 5 + 2 = 12 km

Test Level 1: Critical Path - Question 8
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Directions: Study the following information and answer the questions that follows.
Kiran, Piya and Amar are going to take a round of a city following different or same pathways. All of them can take any means of transportation (car, two wheeler, or public transport). Charges for all of them are different. They have to pay Rs. 200/hr, if they are taking a car on rent. While the charges for a two wheeler are Rs. 50/hr. However, they just need to pay Rs. 20 to go through a public transport for an hour. Their route will start from point K and will end at point P. O is the place where they can sit and relax. M, L and N are places to get different means of transport. M is the place where cars are parked. L is a bus stand, while at place N, two wheelers are parked. The charges of going to car parking, two wheeler parking or bus stand are fixed and are Rs. 30, Rs. 10 and Rs. 40, respectively. The different pathways are as follows and the distance between them is given in km.

How much amount does Priya need to pay, if she first goes by a car, then by a bus and finally reaches her destination, given that she spends an hour on each vehicle?
Detailed Solution for Test Level 1: Critical Path - Question 8

Priya's route would be K-M-L-P.
Charges from K to M = Rs. 30
M to L = Rs. (200 + 40)
L to P = Rs. 20
Total amount = 30 + 240 + 20 = 290

Test Level 1: Critical Path - Question 9
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Directions: Study the given information and answer the question that follows.
Some athletes are riding bicycles in a playground and they are at different places, which is shown in the diagram given below. Each of them has started their journey from the entry gate, which is at the start point and their final destination is the end point. It is not necessary that all of them will reach their final destination. Their direction of movement is shown with the help of an arrow. Distance between them is given in metres.

How much distance Ankit has to cover to reach point A if he can go only from uni-directional way?
Detailed Solution for Test Level 1: Critical Path - Question 9

Ankit can only follow one pathway that is = Start - B - A
Distance covered by Ankit through a uni-directional way = 8 + 7 = 15 m
He cannot follow: Start - D - A path because from D to A, the pathway is bi-directional.

Test Level 1: Critical Path - Question 10
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Directions: Study the given information and answer the question that follows.
Some athletes are riding bicycles in a playground and they are at different places, which is shown in the diagram given below. Each of them has started their journey from the entry gate, which is at the start point and their final destination is the end point. It is not necessary that all of them will reach their final destination. Their direction of movement is shown with the help of an arrow. Distance between them is given in metres.

Karan, an athlete, has started from the 'start' point and is going towards point D from the shortest route. If the shortest distance between the starting point and D is reduced to half and his pathway towards A is blocked, then how much distance will have to be covered by Karan to reach its final destination?
Detailed Solution for Test Level 1: Critical Path - Question 10

Shortest distance between the starting point and D = 10 m
From question, half of 10 = 5 m
Distance from D to E = 3 m
E to final point = 10 m
Required distance to be covered to reach the destination = 5 + 3 + 10 = 18 m

Test Level 1: Critical Path - Question 11
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Directions: Study the given information and answer the question that follows.
Some athletes are riding bicycles in a playground and they are at different places, which is shown in the diagram given below. Each of them has started their journey from the entry gate, which is at the start point and their final destination is the end point. It is not necessary that all of them will reach their final destination. Their direction of movement is shown with the help of an arrow. Distance between them is given in metres.

If there is one athlete standing at every place (A, B, C, D, E and G), as shown in the diagram, then how many maximum number of athletes can Ankit meet on his way from the starting point till the end point, as he has to go through place A?
Detailed Solution for Test Level 1: Critical Path - Question 11

There are three possible ways for Ankit to go from the starting till end point, which are as follows:
Start - B - A - End
Start - B - A - D - E - End
Start - D - A - End
So, he can meet maximum 4 athletes (at places - B, A, D, and E) on his way.

Test Level 1: Critical Path - Question 12
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Directions: Study the following information carefully and answer the question that follows.
Six levels of a game – A through F – are connected by a few two-way paths, as shown below. To travel along any path directly connecting any two ways, a person has to collect some points. In the figure below, the length of each path (in m) is indicated by the number, and the points a person can collect are written inside the square adjacent to the path. Direction of the arrow is representing the different paths they can follow.

If two players are playing a game and want to score equal points but both cannot take same route, then which routes should they follow such that the total distance covered remains more than 10 m for each of them?
Detailed Solution for Test Level 1: Critical Path - Question 12

If they take routes A-B-F and A-C-D-F, they will have equal points.
(i) A-B-F
A to B = 150 points
B to F = 100 points
Total = 100 + 150 = 250 points
Distance from A to B = 6 m and from B to F = 5 m
Total distance = 6 + 5 = 11 m
(ii) A-C-D-F
A to C = 60 points
C to D = 70 points
D to F = 120 points
Total = 60 + 70 + 120 = 250 points
Distance from A to C = 4 m, from C to D = 3 m, and from D to F = 4 m
Total distance = 4 + 3 + 4 = 11 m

Test Level 1: Critical Path - Question 13
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Directions: Study the following information carefully and answer the question that follows.
Six levels of a game – A through F – are connected by a few two-way paths, as shown below. To travel along any path directly connecting any two ways, a person has to collect some points. In the figure below, the length of each path (in m) is indicated by the number, and the points a person can collect are written inside the square adjacent to the path. Direction of the arrow is representing the different paths they can follow.

If points at all the pathways are reduced to half and distance has been doubled, then what would be the pathway between A and F with highest points but not with the shortest distance?
Detailed Solution for Test Level 1: Critical Path - Question 13

(i) A-B-F
Points = 150 + 100 = 250, Half of 250 = 125
Distance = 6 + 5 = 11, Double of 11 = 2
(ii) A-C-E-D-F
Points = 60 + 40 + 100 + 120 = 320, Half of 320 = 160
Distance = 4 + 2 + 3 + 4 = 13, Double of 13 = 26
(iii) A-C-D-F
Points = 60 + 70 + 120 = 250, Half of 250 = 125
Distance = 4 + 3 + 4 = 11, Double of 11 = 22
(iv) A-C-B-F
Points = 60 + 50 + 100 = 210, Half of 210 = 105
Distance = 4 + 5 + 5 = 14, Double of 14 = 28

Test Level 1: Critical Path - Question 14
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Directions: Study the given information and answer the question that follows.
There are different ways to travel from point K to P in a garden, where point K is the entry gate and point P is the place where rides are available. L, M, Q and S are the four other places located in the garden, and the distance between these places is shown with the help of the diagram given below. L is the point where canteen is available, while at point Q, anyone can park their vehicles (which is free of cost). Toilets are at point M, and S is the place where people can sit and enjoy music. The charges per ride are Rs. 40 and the price per eatable is Rs. 10. Persons who want to enjoy music need to pay Rs. 100 per head. Entry charges are Rs. 50 per head for adults and Rs. 20 per head for children.

Which of the following is the shortest distance to reach point P from the entry gate?
Detailed Solution for Test Level 1: Critical Path - Question 14

(1) K-M-Q-P
Distance = 5 + 2 + 3 = 10 m
(2) K-S-Q-P
Distance = 5 + 4 + 3 = 12 m
(3) K-L-M-Q-P
Distance = 4 + 2 + 2 + 3 = 11
(4) K-S-Q-M-P
Direction of pathway from Q to M is not there. Hence, we cannot determine this distance.

Test Level 1: Critical Path - Question 15
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Directions: Study the following information and answer the questions that follows.
Few friends (A, B, D, E and F) are playing ludo and their tokens (same as their names) are at different places on the board. The distances between the tokens are given in steps in the following diagram. All of the tokens will be started at green point, which is C in the following diagram, and they can cross the point C again on their way to reach at different locations.

How many minimum number of steps would be required to reach point B from point E?
Detailed Solution for Test Level 1: Critical Path - Question 15

To take minimum number of steps, the route would be E-C-B = 13 + 9 = 22.

Test Level 1: Critical Path - Question 16
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Directions: Study the following information and answer the questions that follows.
Few friends (A, B, D, E and F) are playing ludo and their tokens (same as their names) are at different places on the board. The distances between the tokens are given in steps in the following diagram. All of the tokens will be started at green point, which is C in the following diagram, and they can cross the point C again on their way to reach at different locations.

If F's final destination is point A and he has to take the longest route and can cross the point C only once, then how many total steps would be required by F?
Detailed Solution for Test Level 1: Critical Path - Question 16

The route followed by F would be F-B-D-C-E-A.
Number of steps taken by F = 13 + 20 + 15 + 13 + 5 = 66.

Test Level 1: Critical Path - Question 17
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Directions: Study the following information and answer the questions that follows.
Few friends (A, B, D, E and F) are playing ludo and their tokens (same as their names) are at different places on the board. The distances between the tokens are given in steps in the following diagram. All of the tokens will be started at green point, which is C in the following diagram, and they can cross the point C again on their way to reach at different locations.

Which of the following combinations has distance of steps more than the first multiple of 5 but less than the third multiple of 5?
Detailed Solution for Test Level 1: Critical Path - Question 17

First multiple of 5 = 5
Third multiple of 5 = 15
So, the number of steps should be between 5 and 15.
(1) D-B = 20 steps
(2) C-B = 9 steps
(3) A-E = 5 steps
(4) E-D = 5 steps

Test Level 1: Critical Path - Question 18
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Directions: Study the following information and answer the questions that follows.
Few friends (A, B, D, E and F) are playing ludo and their tokens (same as their names) are at different places on the board. The distances between the tokens are given in steps in the following diagram. All of the tokens will be started at green point, which is C in the following diagram, and they can cross the point C again on their way to reach at different locations.

If a new person joins the game and he is at the same point as E, then how many steps would be required by him to reach B when the route taken by him is E-D-C-B?
Detailed Solution for Test Level 1: Critical Path - Question 18

Number of steps required to cover the distance E-D-C-B = 5 + 15 + 9 = 29

Test Level 1: Critical Path - Question 19
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Directions: Study the given information and answer the question that follows.
There are different ways to travel from point K to P in a garden, where point K is the entry gate and point P is the place where rides are available. L, M, Q and S are the four other places located in the garden, and the distance between these places is shown with the help of the diagram given below. L is the point where canteen is available, while at point Q, anyone can park their vehicles (which is free of cost). Toilets are at point M, and S is the place where people can sit and enjoy music. The charges per ride are Rs. 40 and the price per eatable is Rs. 10. Persons who want to enjoy music need to pay Rs. 100 per head. Entry charges are Rs. 50 per head for adults and Rs. 20 per head for children.

How much does an adult need to pay by taking the longest route possible (in distance) if he wants to travel from the entry gate till the parking and wants to enjoy everything on his way?
Detailed Solution for Test Level 1: Critical Path - Question 19

Entry gate is K and parking point is Q.
Possible routes from K to Q are:
K-M-Q = (5 + 2 = 7)
K-S-Q = (5 + 4 = 9)
K-L-M-Q = (4 + 2 + 2 = 8)
Longest route = K-S-Q = 9 m
Entry charges = Rs. 50
Music = Rs. 100
Parking = Free
Total amount = Rs. 150

Test Level 1: Critical Path - Question 20
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Directions: Study the given information and answer the question that follows.
There are different ways to travel from point K to P in a garden, where point K is the entry gate and point P is the place where rides are available. L, M, Q and S are the four other places located in the garden, and the distance between these places is shown with the help of the diagram given below. L is the point where canteen is available, while at point Q, anyone can park their vehicles (which is free of cost). Toilets are at point M, and S is the place where people can sit and enjoy music. The charges per ride are Rs. 40 and the price per eatable is Rs. 10. Persons who want to enjoy music need to pay Rs. 100 per head. Entry charges are Rs. 50 per head for adults and Rs. 20 per head for children.

How much distance will Arun have to cover if he first wants to go from the entry gate to the music hall, then to parking, and at last for rides?
Detailed Solution for Test Level 1: Critical Path - Question 20

Distance from:
Entry gate to music hall (K to S) = 5 m
From music hall to parking (S to Q) = 4 m
From parking to rides (Q to P) = 3 m
Total distance = 5 + 4 + 3 = 12 m

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