UPSC Prelims 2017 · CSAT
Question 77: Logical Reasoning and Mental Ability
Eight railway stations A, B, C, D, E, F, G and H are connected either by two-way passages or one-way passages. One-way passages are from C to A, E to G, B to F, D to H, G to C, E to C and H to G. Two-way passages are between A and E, G and B, F and D, and E and D. In how many different ways can a train travel from F to A without passing through any station more than once?
AnswerUPSC’s answer is (d).
From F the only road out is to D (the B to F road runs into F). From D one can go to E or to H. The simple routes to A are F-D-E-A, F-D-E-C-A, F-D-E-G-C-A and F-D-H-G-C-A. Branches through B lead back to F, which is not allowed, or to a dead end. That gives 4 routes. List routes systematically by branching at each junction.
How you could have got this
No shortcut here: in a “how many” question, ruling out options doesn’t help. Every statement has to be judged.
Which options go is worked out from UPSC’s key and the options, not by a model.
Why each option is right or wrong
- (a) More than one route exists.
- (b) Two routes undercounts: four are possible.
- (c) Three misses one of the four routes.
- (d) Correct: F-D-E-A, F-D-E-C-A, F-D-E-G-C-A and F-D-H-G-C-A.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2017, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.