Question 76

Logical Reasoning Data Sufficiency / Interpretation Easy

All the roads of a city are either perpendicular or parallel to one another. The roads are all straight. Roads A, B, C, D and E are parallel to one another. Roads F, G, H, I, J, K, L and M are parallel to one another.

Road A is 1 km East of road B.

Road B is 1/2 km West of road C.

Road D is 1 km West of road E.

Road G is 1/2 km South of road L.

Road I is 1 km North of road J.

Road K is 1/2 km North of road L.

Road K is 1 km South of road M.

Which of the following is necessarily true?

(A) E and B intersect
(B) D is 2 km West of B
(C) D is atleast 2 km West of A
(D) M is 1.5 km North of L
View Dynamic Solution & Explanation
Correct Solution: Option D

Step-by-step Solution:

Analysis of the Road Systems



The problem describes two independent sets of parallel roads.




  • East-West Roads (A, B, C, D, E): The relative positions of A, B, C are fixed with respect to each other, and the relative positions of D, E are fixed. However, there is no information linking these two subgroups, so we cannot know the distance between a road from the first group (e.g., A) and a road from the second (e.g., D).


  • North-South Roads (F, G, ... M): The relationships between these roads are clearly defined, allowing us to build a definite map of their positions.

    • L is 0.5 km North of G.

    • K is 0.5 km North of L.

    • M is 1 km North of K.


    This creates a fixed order from South to North: G → L → K → M.




Evaluation of the Options




  • A. E and B intersect: False. The roads in the East-West set are all parallel to one another and cannot intersect.


  • B. D is 2 km West of B: Not necessarily true. As established, we cannot determine the distance between D and B.


  • C. D is at least 2 km West of A: Not necessarily true. We cannot determine the distance between D and A.


  • D. M is 1.5 km North of L: True. Based on our map, the distance from L to K is 0.5 km, and the distance from K to M is 1 km. The total distance is 0.5 km + 1 km = 1.5 km.





Final Answer: The correct option is D. M is 1.5 km North of L.