- Sequential Output Tracing (Input Output)
- Syllogism
- Critical Reasoning: Assumptions & Conclusions
- Relationships
- Cause & Effect
- Circular Arrangement
- Coding-Decoding
- Complex Arrangements
- Critical Reasoning: Course of Action
- Critical Path
- Direction and Word Puzzle
- Games And Tournaments
- Linear Arrangement
- Team Selection
- Venn Diagram
- Bar Graphs
- Data Sufficiency
- Line Graph
- Pie Chart
- Tables and Caselets

Critical Path: The logical reasoning and data interpretation section in several MBA entrances is an unpredictable section with a wide variety of questions. This is one of the types of questions that is asked in the exams. The data interpretation and logical reasoning section is designed to test the critical thinking skills and decision-making ability of aspirants which is an important requirement for all managers. Such problems also test the analytical, logical, and mathematical ability. A common problem within this LRDI CAT section is routes and networks. Critical path concept is important from the point of view of various MBA entrance exams like CAT, ATMA, SNAP and XAT. This concept requires in- depth understanding of networks and relationships- related problems. It also requires correct understanding of the question and making the required connections so that the concept can be broken down into its simplest possible parts and then solved. These types of questions are included in several MBA entrance exams like CAT, XAT, SNAP and ATMA but the frequency of questions is not very high.

Below are the details about the critical path concept for different MBA competitive exams: –

**CAT:**

CAT | ||||

Year | No of Questions | Good attempts | Difficulty Level | |

Slot 1 | 0 | 0 | – | |

Slot 2 | 1 | 1 | Moderate | |

Slot 3 | 0 | 0 | – | |

Slot 1 | 2 | 2 | Moderate | |

Slot 2 | 2 | 1 | Moderate | |

Slot 1 | 3 | 2 | Easy | |

Slot 2 | 3 | 3 | Moderate |

__XAT:__

XAT | |||

Year | No of Questions | Good attempts | Difficulty Level |

2020 | 3 | 2 | Moderate |

2018 | 2 | 2 | Moderate |

__ATMA:__

ATMA | |||

Year | No of Questions | Good attempts | Difficulty Level |

2020 | 5 | 4 | Easy |

2018 | 4 | 3 | Easy |

__SNAP:__

SNAP | |||

Year | No of Questions | Good attempts | Difficulty Level |

2020 | 2 | 2 | Moderate |

2019 | 3 | 2 | Moderate |

Below you will find certain critical path method example questions and answers for your understanding:

Q.1

The figure below shows the street map for a certain region with the street intersections marked from a through l. A person standing at an intersection can see along straight lines to other intersections that are in her line of sight and all other people standing at these intersections.

For example, a person standing at intersection g can see all people standing at intersections b, c, e, f, h, and k. In particular, the person standing at intersection g can see the person standing at intersection e irrespective of whether there is a person standing at intersection f.

Six people U, V, W, X, Y, and Z, are standing at different intersections. No two people are standing at the same intersection.

The following additional facts are known.

- X, U, and Z are standing at the three corners of a triangle formed by three street segments.
- X can see only U and Z.
- Y can see only U and W.
- U sees V standing in the next intersection behind Z.
- W cannot see V or Z.
- No one among the six is standing at intersection d.

1) Who is standing at intersection a?a) V

b) W

c) No one

d) Y

2) Who can V see?

a) U and Z only

b) Z only

c) U only

d) U, W and Z only

b) Z only

c) U only

d) U, W and Z only

3) What is the minimum number of street segments that X must cross to reach Y?

a) 1

b) 2

c) 3

d) 4

b) 2

c) 3

d) 4

4) Should a new person stand at intersection d, who among the six would she see?

a) W and X only

b) U and W only

c) V and X only

d) U and Z only [CAT 2019]

b) U and W only

c) V and X only

d) U and Z only [CAT 2019]

1.Answer:

1) Option: 3

2) Option: 1

3) Option: 2

4) Option: 1

2) Option: 1

3) Option: 2

4) Option: 1

Explanation:

X,U,Z are at ends of a triangle so they can be at any of b,c,f,g intersections.

Now X cannot be at g since he sees only 2 people.

UZV have to be in a straight line and x sees only U and z thus

X must be at b, V at e, Z at f, U at g.

Since Y can see W and W cannot see either V or Z thus

Y must be at k and W must be at at l.

– V –

X Z –

– U Y

– – W

Now all questions can be answered.

Now X cannot be at g since he sees only 2 people.

UZV have to be in a straight line and x sees only U and z thus

X must be at b, V at e, Z at f, U at g.

Since Y can see W and W cannot see either V or Z thus

Y must be at k and W must be at at l.

– V –

X Z –

– U Y

– – W

Now all questions can be answered.

Q.2.

A significant amount of traffic flows from point S to point T in the one-way street network shown below. Points A, B, C, and D are junctions in the network, and the arrows mark the direction of traffic flow. The fuel cost in rupees for traveling along a street is indicated by the number adjacent to the arrow representing the street. Motorists traveling from point S to point T would obviously take the route for which the total cost of traveling is the minimum. If two or more routes have the same least travel cost, then motorists are indifferent between them. Hence, the traffic gets evenly distributed among all the least cost routes. The government can control the flow of traffic only by levying an appropriate toll at each junction. For example, if a motorist takes the route S-A-T (using junction A alone), then the total cost of travel would be Rs 14 (i.e. Rs 9 + Rs 5) plus the toll charged at junction A.

- If the government wants to ensure that all motorists travelling from S to T pay the same amount (fuel costs and toll combined) regardless of the route they choose and the street from B to C is under repairs (and hence unusable), then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

(1) 2, 5, 3, 2

(2) 0, 5, 3, 1

(3) 1, 5, 3, 2

(4) 2, 3, 5, 1

(5) 1, 3, 5, 1

2) If the government wants to ensure that no traffic flows on the street from D to T, while equal amount of traffic flows through junctions A and C, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

(1) 1, 5, 3, 3

(2) 1, 4, 4, 3

(3) 1, 5, 4, 2

(4) 0, 5, 2, 3

(5) 0, 5, 2, 2

3) If the government wants to ensure that all routes from S to T get the same amount of traffic, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

(1) 0, 5, 2, 2

(2) 0, 5, 4, 1

(3) 1, 5, 3, 3

(4) 1, 5, 3, 2

(5) 1, 5, 4, 2

4) If the government wants to ensure that the traffic at S gets evenly distributed along streets from S to A, from S to B, and from S to D, then a feasible set of toll charged (in rupees) at junctions A, B, C, and D respectively to achieve this goal is:

(1) 0, 5, 4, 1

(2) 0, 5, 2, 2

(3) 1, 5, 3, 3

(4) 1, 5, 3, 2

(5) 0, 4, 3, 2

5) The government wants to devise a toll policy such that the total cost to the commuters per trip is minimized. The policy should also ensure that not more than 70 per cent of the total traffic passes through junction B. The cost incurred by the commuter travelling from point S to point T under this policy will be:

(1) Rs 7

(2) Rs 9

(3) Rs 10

(4) Rs 13

(5) Rs 14

[CAT 2006]

Answer:

No traffic flows on the street from D to T. Now, we have fuel cost on different paths as

SAT : 9 + 5 = Rs. 14 + toll at junction A

SBAT : 2 + 2 + 5 = Rs. 9 + toll at junction B and A

SBCT : 2 3 + 2 = Rs. 7 + toll at junction B and C

SDCT : 7 + 1 + 2 = Rs. 10 + toll at junction D and C

Now, checking the options we find that toll at junction A is 0 or 1.

When toll is 0, fuel cost on SAT = 14 + 0 = Rs. 14

When toll is 1, fuel cost on SAT = 14 + 1 = Rs. 15

The fuel cost on all the paths should be equal.Options (1), (2), (3) can be ruled out as in all these options toll at C and D add up to more than Rs. 5. As fuel cost on SDCT is Rs. 10 without toll, so with toll it cannot exceed Rs. 15 (i.e. toll of path SAT).

Option (4) is ruled out as in this option SAT comes out to be Rs. 14 and SDCT sums up to Rs.15.

So correct answer is option (5).Note: Both the options b and c are correct. Available routes are:

SAT → Rs. 14 SBAT → Rs. 9 SDCT → Rs. 10 SDT → Rs. 13

Now, fuel cost of SAT – fuel of SDT = 14 – 13 = Rs. 1. Hence toll at junction D should be 1 more than the toll at

A. So option (a), (d) and (e) are ruled out.

Now, fuel cost of SAT – fuel cost of SBAT = 14 – 9 = Rs. 5. So toll at junction B should be Rs. 5. So answer could be either (2) or option (3).- Available paths considering no toll are SAT → Rs. 14

SBCT → Rs. 7 SBAT → Rs. 9 SDCT → Rs. 10 SDT → Rs. 13

It is very likely that option (4) is selected. But, if all the five routes have the same cost, then there will be an equal flow on all the five routes i.e., 20% on each route. But, then the percentage of traffic. On

S – A → 20%

S – B → 40% (As there are two routes involving S – B.) S – D → 40% (As there are two routes involving S – D.)

But, it is given that traffic on S – A = traffic on S – B = traffic on S – D. - Available routes are SAT → Rs. 14 SBAT → Rs. 9 SBCT → Rs. 7 SDCT → Rs. 10 SDT → Rs. 13

Fuel cost on path SAT – fuel cost on path SDT = 14 – 13 = Rs. 1.

So the toll at junction D should be 1 more than toll at junction A. So option a and c are ruled out.

Fuel cost on path SAT – fuel cost on path SBCT = 14 – 7 = Rs. 7.

So sum of toll at junction B and C should be 7 more than the toll at A. Hence, only option (d) matches. - We have to find a path on which minimum cost is incurred and such that total traffic through B does not exceed 70%.

So option (5) is ruled out because we can send all the traffic through SDCT or SDT and meet all conditions. Option (1) is also ruled out as in that case all traffic will be passed through SBCT [not possible as traffic at B can’t be more than 70%]

Option (2) is also ruled out as it is possible only when toll at junction C is 2. In that case also all traffic will pass through B.

Option (3) can be the answer, when toll at junction B is 4 and toll at junction C is 0. Then SDCT will have toll equal to Rs. 10.

As Rs. 10 is less than Rs. 13, so option (4) is also ruled out.

Hence, option (3) is the correct choice.

The list of concepts that are covered in the Critical Path Concept is as follows: –

- Usually, the network is given between two cities and there is a complex route.
- The aspirant is required to identify the critical path i.e. distinct routes or the amount a particular product can flow from one place to another through another route like pipelines.
- Other CAT critical Reasoning questions might include more intricate processes like finding the time taken to reach an endpoint based on speed calculations, finding the shortest path, and similar questions.
- To solve such questions, one should attempt to breakdown the network into simpler parts as far as possible.
- Suppose that there are 2 segments of an operation and the 2 segments can be carried out in a and b ways, then that operation can be carried out in a x b ways.
- If using one tool an action can be carried out in a ways, using another tool in b ways, and using yet another tool in c ways, the overall operation can be carried out in (a + b + c) ways.
- When there are product flow-related questions, a clear understanding of the slack concept can be useful in solving questions.

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