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 E is between B and C, which of the following is false?

• A. D is 2 km west of A.
• B. C is less than 1.5 km from D.
• C. Distance from E to B added to distance of E to C is $\frac{1}{2}$ km.
• D. E is less than 1 km from A.
• E. D is less than 1 km from B.

Answer 1

The correct option is A D is 2 km west of A.

We can analyze the data as follows

Clearly from statements (1) and (2), figure 1 follows; from statement (3), figure 2 follows; from statment (4), figure 3 follows; and from statement (5), figure 4 follows; and from statement (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 will be less than 2 km.

Thus, first statement is false.