Question

A, B, C, D, E, and F are the six police stations in an area, which are connected by streets as shown below. Four teams - Team 1, Team 2, Team 3 and 
Team 4 patrol these streets continuously between 09:00 hrs. and 12:00 hrs. each day.

The teams need 30 minutes to cross a street connecting one police station to another. All four teams start from Station A at 09:00 hrs. and must return to Station A by 12:00 hrs. They can also pass via Station A at any point on their journeys.
The following facts are known.
1. None of the streets has more than one team traveling along it in any direction at any point in time. 
2. Teams 2 and 3 are the only ones in stations E and D respectively at 10:00 hrs. 
3. Teams 1 and 3 are the only ones in station E at 10:30 hrs. 
4. Teams 1 and 4 are the only ones in stations B and E respectively at 11:30 hrs. 
5. Team 1 and Team 4 are the only teams that patrol the street connecting stations A and E. 
6. Team 4 never passes through Stations B, D or F.
How many times does Team 4 pass through Station E in a day? [This Question was asked as TITA]

• A. 2 times
• B. 5 times
• C. 4 times
• D. 3 times

Answer 1

The Correct Option is A

The goal is to determine how many times Team 4 passes through Station E based on the given constraints.

Step 1: Analyze the facts and constraints:

1. Facts provided:
   • Teams start at A at 09:00 hrs and return by 12:00 hrs.
   • Team 2 is at Station E and Team 3 is at Station D at 10:00 hrs.
   • Teams 1 and 3 are at Station E at 10:30 hrs.
   • Teams 1 and 4 are at Stations B and E at 11:30 hrs.
   • Team 1 and 4 are the only teams on Street A-E.
   • Team 4 does not pass through Station B, D, or F.
2. Team 4's route options are limited due to constraint 6 (does not pass through B, D, or F).

Step 2: Inferences from the facts:

1. Teams start from A and must plan routes within 3 hours (6 segments of 30 minutes each).
2. With only Station E as a mid-point and not passing through B, D, F, Team 4's journey must involve Station E.
3. At 11:30 hrs, Team 4 is at E and since it starts and ends at A, it must have passed through E both going and coming back.

Step 3: Calculate Team 4's occurrences at Station E:

• Leave A to E: 1 time.
• Return to A from E: 1 additional time.

Since Team 4 must return to A by 12:00 hrs and spends the rest of its time patrolling A to E, it passes through Station E exactly 2 times (once towards E, and once back to A).

Thus, the answer is 2 times.