DI - Routes & Networks - Previous Year CAT/MBA Questions
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Read the passage below and answer the questions that follow.
Export cargo of a trader can go through seven cities P, Q, R, S, T, U and V. The following cities have a two way connection i.e., Cargo can move in both directions between them; S and U, P and Q, Q and R, V and T, R and T, V and U. Cargo can move only in one direction from U to Q.
If the trader wants the cargo to move from City S to City T then excluding cities S and T, what is the minimum number of cities that the cargo has to cross in transit?
- (a)
4
- (b)
3
- (c)
2
- (d)
5
Answer: Option C
Text Explanation :
From the figure, Excluding cities S and T cargo can go from city S to city T in 2 ways i.e S-U-Q-R-T and S-U-V-T. The shortest path from S to T is S-U-V-T. Therefore the minimum number of cities that the cargo has to cross in transit is 2.
Hence, option (c).
Workspace:
If the trader wants the cargo to go to City U from City P through the longest route, how many cities will he be required to cross (excluding cities P and U)?
- (a)
2
- (b)
4
- (c)
3
- (d)
5
Answer: Option B
Text Explanation :
From the figure, Cargo can go from city P to city U in only one possible way i.e. P-Q-R-T-V-U. Going through this path, the cargo will have to pass through 4 cities.
Hence, option (b).
Workspace:
To move cargo from City P to City U, which of the following statements will minimise the number of cities to be crossed in transit?
- (a)
Connect cities U to R with a two way connection
- (b)
Connect cities P to S with a one way connection from cities S to P
- (c)
Connect cities U to Q with a two way connection
- (d)
Connect cities R to V with a two way connection
Answer: Option C
Text Explanation :
Consider option A. The path is P-Q-R-U. We have to cross 2 intermediate cities in it.
Consider option B. If we connect cities from P to S with a one way connection from cities S to P. The path formed will be P-Q-R-T-V-U. It becomes a longer path than option A.
Using option C, the path formed is the shortest path. The path formed is P-Q-U. This smaller than that in option A.
Consider option D. The path formed using option D is longer compared to the path formed using option C. Hence options A, B, and D are eliminated.
Hence, option (c).
Workspace:
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