# Practice Questions on Critical PathLogical Reasoning

Common Information

The flow of energy from Generator (G) to Motor (M) in a power distribution network is as shown. Points P, Q, R and S are capacitor banks (denoted by CB) in the network. The arrows mark the direction of the energy flow. The energy loss (in Rs. ’00) in the power lines during the flow is indicated by the numbers adjacent to the arrows.

An energy analyst has to make sure that when the energy flows from G to M, it flows through a path where the total energy loss (in Rs. ’00) is minimal. There is an additional energy loss (in Rs. ’00) at the capacitor banks. This loss can be regulated. For example, if the energy analyst selects a path G – P – M (using CB P) then the total energy loss would be Rs. 1,000 + Rs. 600 + the regulated energy loss at the CB P.

## Section-1: Critical Path Question - 16

 Q16. Common Information Question: 3/4 Due to overheating, the energy loss in the power line connecting G and Q has doubled. What is a feasible set of the energy loss values (in Rs. ’00) that have to be regulated at the capacitor banks P, Q, R and S respectively so that the energy loss from G to M across all paths is the same?
 A. 1, 3, 2, 3 B. 0, 4, 2, 4 C. 0, 1, 2, 1 D. 1, 0, 2, 5 E. None of these

## Section-1: Critical Path Question - 17

 Q17. Common Information Question: 4/4 If the power line between R and M is not working, then which capacitor bank has the highest regulated energy loss such that the energy loss from G to M across all the paths is the same?
 A. Q only B. P only C. S D. Q or P E. Insufficient information

Common Information

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 travelling along a street is indicated by the number adjacent to the arrow representing the street.

Motorists travelling from point S to point T would obviously take the route for which the total cost of travelling 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 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.

## Section-1: Critical Path Question - 18

 Q18. Common Information Question: 1/5 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:
 A. 2, 5, 3, 2 B. 0, 5, 3, 1 C. 1, 3, 5, 2 D. 2, 3, 5, 1 E. 1, 3, 5, 1

## Section-1: Critical Path Question - 19

 Q19. Common Information Question: 2/5 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:
 A. 1, 5, 3, 3 B. 1, 4, 4, 3 C. 1, 5, 4, 2 D. 0, 5, 2, 3 E. 0, 5, 2, 2

## Section-1: Critical Path Question - 20

 Q20. Common Information Question: 3/5 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:
 A. 0, 5, 2, 2 B. 0, 5, 4, 1 C. 1, 5, 3, 3 D. 1, 5, 3, 2 E. 1, 5, 4, 2
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