Discussion
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 G, H, I, J, K, L and M are parallel to one another.
(i). Road A is 1 km east of road B.
(ii). Road B is ½ km west of road C.
(iii). Road D is 1 km west of road E.
(iv). Road G is ½ km south of road H.
(v). Road I is 1 km north of road J.
(vi). Road K is ½ km north of road L.
(vii). Road K is 1 km south of road M. Which is necessarily true ?
Answer: D
Clearly from statements (1) and (2), figure 1 follows; from statement (3), figure 2 follows; from statement (4), figure 3 follows; and from statement (5), figure 4 follows; and from statements (6) and (7), figure 5 follows.
It follows from figure 5 that distance of M from L = LK + KM = ½ + 1 = 1.5 km and M is to the north of L.