CAT Quant Practice Problems

Question: The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Neelam rides her bicycle from her house at A to her office at B, taking the shortest path. Then the number of possible shortest paths that she can choose is

  1. 60
  2. 75
  3. 45
  4. 90
  5. 72

Correct Option:4

The shortest route from A to B is via the diagonal OQ in the square P. One can travel from A to O in 4!/2!×2! ways. The shortest way from O to Q is through the diagonal only.From Q to B can be travelled in 6!/4!×2! ways.

The total number of ways is, therefore, (4!/2!×2!) × (6!/4!×2!) = 6×15 = 90

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