Town C is to the south of Town A. Town D is to the west of town A. Town B is to the east of town D. Town E is to the south of town B and south-east of Town C. What is the position of town A with respect to town B?

Question

Prepp Team · Accepted Answer

Understanding Town Positions and Directions

This question asks us to determine the position of one town relative to another based on a series of statements describing their locations. To solve this type of problem, it's helpful to visualize the positions or draw a simple diagram based on the given directional information.

Let's break down the statements one by one:

Statement 1: Town C is to the south of Town A. This means if you are at Town A, Town C is directly below you. Conversely, Town A is to the north of Town C.
Statement 2: Town D is to the west of town A. This means if you are at Town A, Town D is directly to your left. Conversely, Town A is to the east of Town D.

From these first two statements, we can already picture D, A, and C in a relative arrangement:

    D --- A
          |
          C

Statement 3: Town B is to the east of town D. This tells us B is somewhere to the right of D. It could be between D and A, exactly at A, or further east of A.

Let's consider the possibilities for B's position relative to D and A based on Statement 3 and Statement 2 (D is West of A):

B is between D and A (D --- B --- A)
B is at the same position as A (D --- A, B) - Not possible as A and B are distinct towns.
B is East of A (D --- A --- B)

Now let's use the final statement to figure out which possibility is correct:

Statement 4: Town E is to the south of town B and south-east of Town C.

Let's test the possibilities for B's position:

Possibility 1: If B is between D and A (D --- B --- A).
```
    D --- B --- A
              |
              C
        
```
E is South of B. So, E would be below B:
```
    D --- B --- A
        |     |
        E     C
        
```
Now check if E is South-East of C. From C, South-East is down and to the right. In this diagram, E is to the West and South of C (roughly South-West depending on distances). This doesn't match the condition.
Possibility 2: If B is East of A (D --- A --- B).
```
    D --- A --- B
              |
              C
        
```
E is South of B. So, E would be below B:
```
    D --- A --- B
              |     |
              C     E
        
```
Now check if E is South-East of C. From C, South-East is down and to the right. In this diagram, E is indeed located down and to the right relative to C. This configuration fits all the given conditions.

So, the correct relative positions are:

    D --- A --- B
              |     |
              C     E

The question asks for the position of Town A with respect to Town B.

Looking at our diagram, Town A is to the left of Town B.

In terms of direction, "left" corresponds to West.

Therefore, Town A is to the West of Town B.

Revision Table: Town Direction Analysis

Statement	Relative Position
C south of A	A is North of C
D west of A	A is East of D
B east of D	B is somewhere East of D (could be East of A)
E south of B, south-east of C	Helps confirm B is East of A
A with respect to B	A is West of B

Additional Information: Relative Directions

Understanding relative directions is key to solving such problems. When we say Town X is "to the north of" Town Y, it means if you are standing at Town Y, you would travel North to reach Town X. Conversely, Town Y is "to the south of" Town X.

The primary directions are North, South, East, and West. Intermediate directions include North-East, North-West, South-East, and South-West. Combining statements about relative positions helps build a mental map or diagram to answer questions about the position of one point relative to another.