A building has several rooms and doors as shown in the top view of the building given below. The doors are closed initially. What is the minimum number of doors that need to be opened in order to go from the point P to the point Q?
Reconstructed schematic — room/door topology (Q.5). Redrawn from the original top-view figure; door positions and room adjacency preserved, exact wall proportions approximated.
Options:
(A) 4
(B) 3
(C) 2
(D) 1
Official Answer Key:
C
Step-by-Step Solution & Explanation
• The top-view figure shows P and Q in two different enclosed compartments, connected through an intermediate room via two door openings (as redrawn above).
• Tracing the shortest path: from P, the adjoining room is entered through Door 1; from there, the compartment containing Q is entered through Door 2. No shorter path exists since P and Q's compartments share no common wall/door directly.
• Hence the minimum number of doors that must be opened = 2.
• Distractor logic: (A)/(B) overcount via a longer route; (D) would require a direct doorway between P and Q's rooms, which does not exist.
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