Step-by-step Solution:

Logical Deduction

The clearest way to solve this is to place the parallel roads on a number line (representing the West-East axis) with road B at a reference point of 0.

1. 
   Establish the Main Road Positions:
   
   
   
   • Road B is at position 0.
   
   
   • "A is 1 km East of B" places road A at position 1.
   
   
   • "B is 0.5 km West of C" places road C at position 0.5.
   
   
   
   


2. 
   Determine the Position of E and D:
   
   
   
   • "E is between B and C" means E's position is somewhere between 0 and 0.5.
   
   
   • "D is 1 km West of E" means D's position is E - 1. Since E is between 0 and 0.5, D's position must be between -1 and -0.5.
   
   
   
   


3. 
   Calculate the Distance between A and D:
   

   The distance is the difference between their positions: Distance = A - D = 1 - D.

   
   
   
   
   • If D were at its easternmost possible point (-0.5), the distance would be 1 - (-0.5) = 1.5 km.
   
   
   • If D were at its westernmost possible point (-1), the distance would be 1 - (-1) = 2 km.
   
   
   
   

This means the distance between road A and road D must be greater than 1.5 km and less than 2 km.

Final Answer: The option stating the distance is between 1 km and 2 km is correct, as the actual range (1.5 km to 2 km) falls entirely within it.