Civil Services Prep

Prelims 2022 · CSAT / Quantitative Aptitude · Question 27

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?

  1. 10
  2. 13
  3. 15
  4. 36

Answer

15

  • Direct travel from A to C: there are 3 roads, so 3 ways.
  • Travel from A to B to C: choose 1 of 3 roads from A to B and 1 of 4 roads from B to C, so 3 x 4 = 12 ways.
  • Total ways from A to C using these roads = 3 + 12 = 15.

Option check:

  • (a) 10: Incorrect; ignores some valid routes.
  • (b) 13: Incorrect; total is higher.
  • (c) 15: Correct.
  • (d) 36: Incorrect; wrongly multiplies all roads together.
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