Question

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 km west of road C.

(iii) Road D is 1 km west of road E.

(iv) Road G is km south of road H.

(v) Road I is 1 km north of road J.

(vi) Road K is km north of road L.

(vii) Road K is 1 km south of road M.

If road E is between B and C, then distance between A and D is

• A. $\frac{1}{2}$ km
• B. $1$ km
• C. $1.5$ km
• D. $1.5-2$ km
• E. $2-2.5$ km

Answer 1

Answer: (D)

$1.5-2$ km

We can analyze the data as follows,

Clearly, from statements (1) and (2), figure 1 follows; from statement (3), figure 2 follows; from statement (4), figure 3 follow; and from statement (5), figure 4 follows; and from statements (6) and (7), figure 5 follows.

If E is between B and C and D is 1 km west of E, then distance of C from D will be less than 1.5 km.

Distance of E and B + Distance of E and $C=\frac{1}{2}$ km.

Since distance between A and B is 1 km and E is between B and C, hence distance of E and A will be less than 1 km.

Since Distance of E and D is 1 km, then D is less than 1 km from B.

Clearly, distance of D and A $=AB+ED-BE=(1+1-\frac{1}{4})=2-.25$ i.e. between $1.5to2km$.

|Thus, distance of A and D is $1.5-2km$.