NIMCET 2014 — Reasoning PYQ

Step 1: Recap of Road Positions (West to East)

Based on previous logic:

• $B$ is the westernmost point in the first group.

• $C$ is $0.5\text{ km}$ East of $B$.

• $A$ is $0.5\text{ km}$ East of $C$ (total $1\text{ km}$ East of $B$).

• $E$ is located between $B$ and $C$.

• $D$ is $1\text{ km}$ West of $E$.

Step 2: Testing the Options

• Option 1 ($D$ is $2\text{ km}$ West of $A$): Distance $A$ to $E$ is $0.5\text{ km}$ (A to C) + some distance (C to E). Since the gap $B-C$ is only $0.5\text{ km}$, the max distance from $A$ to $E$ is $1\text{ km}$. Since $D$ is $1\text{ km}$ from $E$, the maximum distance from $A$ to $D$ is $2\text{ km}$. This could be a limit, but let's look for a definite mathematical impossibility.

• Option 3 (Distance from $E$ to $B$ and $E$ to $C$ is $1/2\text{ km}$): The total distance between $B$ and $C$ is already given as $1/2\text{ km}$ ($0.5\text{ km}$). If $E$ is between them, the sum of distances $(E\text{ to }B)+(E\text{ to }C)$ must equal $0.5\text{ km}$. It is mathematically impossible for both individual segments to be $0.5\text{ km}$ each, as that would make the total distance $1\text{ km}$.

Conclusion:

Option 3 is definitely false because it contradicts the established distance between roads $B$ and $C$.

Correct Option: 3