Direction : Read the following passage to answer the questions Five houses lettered A, B, C, D, & E are built in a row next to each other. The houses are lined up in the order A, B, C, D, & E. Each of the five houses have coloured roofs and chimneys. The roof and chimney of each house 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.

3 Explanation: To find the maximum number of green roofs, we need to test which houses can potentially have a green roof while following all the rules. 1. Analyze Given Fixed Data: House B: Roof = Red (Cannot be Green). House E: Roof = Green. 2. Check Potential for Other Houses (Applying Rule 4 - Neighbor Rule): Rule 4 states that a house cannot share any color (roof or chimney) with its neighbor. House A: Neighbor to B. Since B uses Red (roof) and Black (chimney), A can have a Green roof as long as its chimney is not Green (chimneys are never green anyway) and not Black or Red (to satisfy neighbor rule with B). So, A can have a Green roof and White chimney. House C: Neighbor to B. Since B uses Red and Black, C can have a Green roof (with a White chimney). House D: Neighbor to C and E. If House C has a G

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NIMCET 2009 Reasoning PYQ — Direction : Read the following passage to answer the questions Fi… | Mathem Solvex

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Explanation

To find the maximum number of green roofs, we need to test which houses can potentially have a green roof while following all the rules.

1. Analyze Given Fixed Data:

House B: Roof = Red (Cannot be Green).
House E: Roof = Green.

2. Check Potential for Other Houses (Applying Rule 4 - Neighbor Rule):

Rule 4 states that a house cannot share any color (roof or chimney) with its neighbor.

House A: Neighbor to B. Since B uses Red (roof) and Black (chimney), A can have a Green roof as long as its chimney is not Green (chimneys are never green anyway) and not Black or Red (to satisfy neighbor rule with B). So, A can have a Green roof and White chimney.
House C: Neighbor to B. Since B uses Red and Black, C can have a Green roof (with a White chimney).
House D: Neighbor to C and E.
- If House C has a Green roof, House D cannot have a Green roof.
- If House E has a Green roof, House D cannot have a Green roof.
- Therefore, House D can never have a green roof in any scenario where E is green.

3. Evaluating the Combinations:

House A: Can be Green.
House B: Red (Fixed).
House C: Can be Green.
House D: Cannot be Green (because it is next to E, which is Green).
House E: Green (Fixed).

However, we must check if A and C can both be Green simultaneously.

If A is Green and C is Green, House B is between them. House B is Red/Black, so there is no conflict between A-B or B-C.
Can House E and House C both be Green? No. Because if C is Green, House D must use colors other than Green. But House E is Green, so House D cannot use Green anyway. The conflict is that if House C is Green, House D must pick a different color. If House E is Green, House D must also pick a different color. This is possible.
Wait, check Rule 4 again: "No house may use any of the same colors that the every next house uses". If House C is Green, and House E is Green, House D is the neighbor to both. House D cannot use Green. This is perfectly fine.

4. Final Count:

House A: Green (Possible)
House B: Red (Fixed)
House C: Green (Possible)
House D: Yellow or Red (Possible)
House E: Green (Fixed)

The maximum number of green roofs is $3$ (Houses A, C, and E).

Correct Option:

Explanation

To find the maximum number of green roofs, we need to test which houses can potentially have a green roof while following all the rules.

1. Analyze Given Fixed Data:

House B: Roof = Red (Cannot be Green).
House E: Roof = Green.

2. Check Potential for Other Houses (Applying Rule 4 - Neighbor Rule):

Rule 4 states that a house cannot share any color (roof or chimney) with its neighbor.

House A: Neighbor to B. Since B uses Red (roof) and Black (chimney), A can have a Green roof as long as its chimney is not Green (chimneys are never green anyway) and not Black or Red (to satisfy neighbor rule with B). So, A can have a Green roof and White chimney.
House C: Neighbor to B. Since B uses Red and Black, C can have a Green roof (with a White chimney).
House D: Neighbor to C and E.
- If House C has a Green roof, House D cannot have a Green roof.
- If House E has a Green roof, House D cannot have a Green roof.
- Therefore, House D can never have a green roof in any scenario where E is green.

3. Evaluating the Combinations:

House A: Can be Green.
House B: Red (Fixed).
House C: Can be Green.
House D: Cannot be Green (because it is next to E, which is Green).
House E: Green (Fixed).

However, we must check if A and C can both be Green simultaneously.

If A is Green and C is Green, House B is between them. House B is Red/Black, so there is no conflict between A-B or B-C.
Can House E and House C both be Green? No. Because if C is Green, House D must use colors other than Green. But House E is Green, so House D cannot use Green anyway. The conflict is that if House C is Green, House D must pick a different color. If House E is Green, House D must also pick a different color. This is possible.
Wait, check Rule 4 again: "No house may use any of the same colors that the every next house uses". If House C is Green, and House E is Green, House D is the neighbor to both. House D cannot use Green. This is perfectly fine.

4. Final Count:

House A: Green (Possible)
House B: Red (Fixed)
House C: Green (Possible)
House D: Yellow or Red (Possible)
House E: Green (Fixed)

The maximum number of green roofs is $3$ (Houses A, C, and E).

Correct Option:

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