NIMCET 2012 — Reasoning PYQ

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Question

NIMCET 2012 — Reasoning PYQ

NIMCET | Reasoning | 2012

Directions : Read the following passage carefully and answer the questions.
Five houses lettered A, B, C, D and E are built in a row next to each other. The houses are lined up in the order A, B, C, D and E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each houses must be painted as follows.
1. The roof must be painted either green, red or yellow.
2. The chimney must be painted either white, black or red.
3. No house may have the same colour chimney as the colour of roof.
4. No house may use any of the same colours that adjacent house uses.
5. House E has a green roof.
6. House B has a red roof and a black chimney.
What is the maximum number of green roofs?

Choose the correct answer:

Explanation

Step 1: Fixed constraints

House $E$ : Green Roof (Rule 5).
House $B$ : Red Roof (Rule 6).

Step 2: Check adjacent houses

Since House $E$ has a green roof, the adjacent House $D$ cannot have a green roof (Rule 4).
Since House $B$ is red/black, the adjacent House $A$ and House $C$ can potentially have green roofs.

Step 3: Test the maximum possibility

Let's see if $A, C,$ and $E$ can all have Green roofs:

House A: Green Roof. (Valid, as $B$ is Red).
House B: Red Roof. (Fixed).
House C: Green Roof. (Valid, as $B$ is Red and $D$ is not yet assigned).
House D: Cannot be Green (because $C$ and $E$ would be Green). Let's say Yellow Roof.
House E: Green Roof. (Fixed).

Step 4: Verify with chimney rules

We must ensure chimneys can be painted without matching the green roof or the neighbor's colors:

House $A$ (Green Roof): Chimney can be White.
House $B$ (Red Roof): Chimney is Black.
House $C$ (Green Roof): Chimney can be White.
House $D$ (Yellow Roof): Chimney can be Red.
House $E$ (Green Roof): Chimney can be White (since $D$ is using Yellow/Red).

In this configuration, houses $A, C,$ and $E$ all have Green roofs. This does not violate any rules because no two green-roofed houses are next to each other.

Conclusion:

The maximum number of green roofs possible is $3$ .

Correct Option: (c) $3$