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: –
Below you will find certain critical path method example questions and answers for your understanding:
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.
1) Who is standing at intersection a?a) V
c) No one
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.
(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
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).
The list of concepts that are covered in the Critical Path Concept is as follows: –
While practicing these problems for MBA entrance exams, the first step is to identify the variables and the number of instances of the variables in the data. Also, identify the respective relationships among the variables. Make the table required and add the data given in the question in the table. Now as the basic framework is ready to identify the required solution and solve it to get the answer based on the question given. MBA entrances are usually speeding tests as much as a test to assess the aspirant’s skills. Ample practice needs to be done to do calculations with speed and do calculations mentally as far as possible. Also, the different tips and tricks should be customized to individual students’ needs as no two students are identical and need their ways to carry out calculations. Use MBAP CAT E-book (Concept theory) study material for practicing critical path method examples.
After the basic level, the aspirant should solve problems with accuracy and without looking at the solutions. Don’t focus on the time taken to complete the questions but that the questions should be done correctly. Maintain an Excel sheet to monitor the progress in the questions by the student. The questions where difficulty was faced should be revised after a week again and if the difficulty is faced again, then the concept should be revised. For the intermediate level, watch MBAP live lecture Recording (Basic). You can also find some examples in MBAP Previous year CAT question paper.
After completing the previous levels, the aspirant should move on to solving sectional tests and giving mocks in a timed environment. This is the most important stage as it will help in preparing for the real exam. The mocks should be given diligently and, in any environment, similar to that of the test center. A mixture of different levels of difficulty should be attempted through section-wise tests. Attempting too many easy or too many difficult questions is not advised. Taking up a mock test series from a coaching institute will be beneficial. They can find out more examples of critical path in the logical reasoning puzzles section from MBAP CAT E-book (Practice Questions). The art of selecting which questions to attempt and which to leave should be instilled at this stage, a very important part of the DILR section. All the questions can’t and shouldn’t be attempted.