UPSC Prelims 2022 · CSAT
Question 27: Basic Numeracy
A, B and C are three places such that there are three different roads from A to B, four different roads from B to C and three different roads from A to C. In how many different ways can one travel from A to C using these roads?
AnswerUPSC’s answer is (c).
Ways from A to C: direct, 3 roads. Or through B: 3 roads from A to B and 4 from B to C, so 3 × 4 = 12 ways. The two kinds of routes are alternatives, so add: 3 + 12 = 15. Rule: multiply the choices along a route, and add across alternative routes. The direct road from A to C is a separate route, not a step in the route through B.
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) 10 adds all the roads (3 + 4 + 3) instead of multiplying along the route via B.
- (b) 13 has no basis in the road counts.
- (c) Correct: 3 direct + 3 × 4 via B = 15.
- (d) 36 multiplies all three road counts, treating the direct road as part of the route via B.
Answer: UPSC’s key. Explanation: written by UPSC Grade, not by UPSC.
Source: UPSC, Civil Services (Preliminary) Examination 2022, General Studies Paper II (CSAT), Series A. The paper on upsc.gov.in.