Instructions: Amit was driving in New Town, where all roads run either north-south or east-west, forming a grid. Roads are at a distance of 1 km from each other and are parallel.

Amit started at the intersection of streets no. 7 and 8. He drove 3 km north, 3 km west, and then 4 km south. Which further route could bring him back to his starting point?
I. 3 km east, then 2 km south
II. 1 km north, then 3 km east
III. 1 km north, then 2 km west

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.

Answer 1

Instead of coordinates, this can be tracked as a running balance of north-south and east-west distance, which must both return to zero.

North-south balance after the first three moves: $+3$ (north) $-4$ (south) $= -1$, meaning he ends up 1 km south of the start line.
East-west balance after the first three moves: $-3$ (west), meaning he ends up 3 km west of the start line.
To reach zero on both balances, the next moves must add exactly $+1$ to the north-south balance and $+3$ to the east-west balance.
Route I adds $+3$ east and $-2$ south (i.e. $-2$ to north-south), giving a north-south balance of $-1-2=-3$, not zero.
Route II adds $+1$ north and $+3$ east, giving a north-south balance of $-1+1=0$ and an east-west balance of $-3+3=0$: both zero, so this route returns him exactly to start.
Route III adds $+1$ north and $-2$ west, giving a north-south balance of $0$ but an east-west balance of $-3-2=-5$, not zero.

Only route II clears both balances to zero at the same time.

So the correct answer is option B, II only.

Answer 2

Instead of coordinates, this can be tracked as a running balance of north-south and east-west distance, which must both return to zero.

North-south balance after the first three moves: $+3$ (north) $-4$ (south) $= -1$, meaning he ends up 1 km south of the start line.
East-west balance after the first three moves: $-3$ (west), meaning he ends up 3 km west of the start line.
To reach zero on both balances, the next moves must add exactly $+1$ to the north-south balance and $+3$ to the east-west balance.
Route I adds $+3$ east and $-2$ south (i.e. $-2$ to north-south), giving a north-south balance of $-1-2=-3$, not zero.
Route II adds $+1$ north and $+3$ east, giving a north-south balance of $-1+1=0$ and an east-west balance of $-3+3=0$: both zero, so this route returns him exactly to start.
Route III adds $+1$ north and $-2$ west, giving a north-south balance of $0$ but an east-west balance of $-3-2=-5$, not zero.

Only route II clears both balances to zero at the same time.

So the correct answer is option B, II only.

Show Hint

The Correct Option is B

Solution and Explanation

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