Town B is to the north of Town A. Town C is to the east of Town B. Town D is to the north of Town C. Town E is to the west of Town D. What is the position of Town E with respect to Town A? (All positions are arranged in GRID pattern)
North
Analyzing Town Positions in a Grid Pattern
The question asks us to determine the position of Town E relative to Town A, given a series of directional relationships between several towns arranged in a grid pattern. We will break down the information step-by-step to map out the relative locations of each town.
Step-by-Step Analysis of Town Locations
- Town B is to the north of Town A. This means if you start at A and move north, you reach B. We can represent this movement vertically upwards on a map or grid.
- Town C is to the east of Town B. Starting from B and moving east, you arrive at C. This is a horizontal movement to the right.
- Town D is to the north of Town C. From C, moving north leads to D. This is another vertical movement upwards.
- Town E is to the west of Town D. Starting from D and moving west brings you to E. This is a horizontal movement to the left.
Mapping the Relative Positions
Let's visualize these movements starting from Town A:
- Start at Town A.
- Move North to reach Town B.
- From B, move East to reach Town C.
- From C, move North to reach Town D.
- From D, move West to reach Town E.
Since the arrangement is in a grid pattern, moving North or South changes only the vertical position, and moving East or West changes only the horizontal position. Also, moving North then South by the same 'distance' brings you back to the original vertical line. Similarly, moving East then West by the same 'distance' brings you back to the original horizontal line.
Let's trace the path from A to E:
A → (North) → B → (East) → C → (North) → D → (West) → E
Notice the horizontal movements: B is reached from A (North, no East/West). C is East of B. E is West of D. Since C is East of B and D is North of C, and E is West of D, the West movement from D to E effectively cancels out the East movement from B to C, placing E back on the same vertical line as B. Since B is North of A, E which is on the same vertical line as B and is North of B (as seen from the moves C → D is North, and D → E is West, so E is North of C and West of D), must be North of A.
Alternatively, consider a coordinate system. Let Town A be at (0,0).
- Town B is North of A: B is at (0, y1) where y1 > 0.
- Town C is East of B: C is at (x1, y1) where x1 > 0.
- Town D is North of C: D is at (x1, y2) where y2 > y1.
- Town E is West of D: E is at (x2, y2) where x2 < x1.
In a strict grid pattern with equal steps (though not specified, it helps visualize), assume one unit per step:
- A = (0, 0)
- B = (0, 1) (North of A)
- C = (1, 1) (East of B)
- D = (1, 2) (North of C)
- E = (0, 2) (West of D - returning to the x-coordinate of 0)
Comparing the coordinates of E (0, 2) and A (0, 0), the x-coordinate is the same, and the y-coordinate of E is greater than A. This indicates that E is directly North of A.
Conclusion: Position of Town E with respect to Town A
Based on the sequence of movements and the grid pattern, Town E is located directly to the north of Town A.
| Reference Town | Relative Position | Destination Town |
|---|---|---|
| A | North | B |
| B | East | C |
| C | North | D |
| D | West | E |
Revision Table: Key Directional Concepts
| Direction | Movement | Effect on Grid Coordinates (e.g., from (x,y)) |
|---|---|---|
| North | Towards the top | Increases y-coordinate (x, y+Δy), Δy > 0 |
| South | Towards the bottom | Decreases y-coordinate (x, y-Δy), Δy > 0 |
| East | Towards the right | Increases x-coordinate (x+Δx, y), Δx > 0 |
| West | Towards the left | Decreases x-coordinate (x-Δx, y), Δx > 0 |
Additional Information on Directional Reasoning
Directional reasoning questions test your ability to understand and follow instructions involving directions (North, South, East, West, and sometimes intermediate directions like Northeast, Southwest). These questions often involve a series of movements or the relative positions of objects or places.
- Visualisation is key: Try to imagine or sketch the path or positions described.
- Grid patterns simplify things: In grid patterns, movements are typically along cardinal directions, making it easier to track horizontal and vertical displacements.
- Relative vs. Absolute Positions: Understand whether you are asked for the position of one point from another (relative) or a specific direction/distance from a fixed origin (absolute).
- Net Displacement: Sometimes you can calculate the net displacement by summing up movements in opposite directions (e.g., 3 steps East and 2 steps West result in 1 step East from the starting point). In this problem, the East movement from B to C and the West movement from D to E cancel out horizontally, leaving only a net vertical movement from A to E.
Similar Questions
A lies to the north-west of C and north of D. If B is to the east of A, what is the position of D with respect to B?
Town B is to the east of Town A. Town C is to the north of Town B. Town D is to the east of Town C. Town E is to the south of Town D. What is the position of Town E with respect to Town A? (All positions are arranged in GRID pattern)
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Important Questions from Direction and Distance Stops
The area of a square is 4096 sq cm. Find the ratio of the breadth and the length of a rectangle whose length is twice the side of the square and breadth is 24 cm less than the side of the square.
What should come in place of the question mark (?) in the given series?
28 39 53 70 90 ?Pranay starts from Point A and drives 8 km towards east. He then takes a right turn, drives 11 km, turns right and drives 12 km. He then takes a right turn and drives 13 km. He takes a final right turn, drives 4 km and stops at Point P. How far (shortest distance) and towards which direction should he drive in order to reach Point A again? (All turns are 90° turns only unless specified.)
A child went 90 feet in the west to look for his father, then he turned right and went 20 feet. After this, he turned right and walked 30 feet to reach his uncle's house. His father was NOT there. From there he went 100 feet to his south and met his father. How far did he meet his father from the starting point?
Four friends live in a locality. A's house is to the west of B. B 's house is to the south of C and C's house is to the east of D. In which direction is B's house as to D?
