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.

House A & C have different colour chimneys. Explanation: 1. Given Data: House B: Roof = Red, Chimney = Black. House E: Roof = Green. 2. Deductions for House A (Next to B): House cannot use any color from House (Red or Black). Roof of A: Must be Green or Yellow. Since B has a Red roof, A could be Green or Yellow. Chimney of A: Must be White or Red. Since B has a Black chimney, A cannot be Black. 3. Deductions for House C (Next to B): House cannot use any color from House (Red or Black). Roof of C: Must be Green or Yellow. Chimney of C: Must be White or Red. 4. Deductions for House D (Next to C and E): House has a Green roof. Therefore, House cannot have a Green roof or a Green chimney. If House has a White chimney, then must have a Black or Red chimney. If House has a Yellow roof, House must have a Red roof. 5. Analyzing the Statements: Regarding

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

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

Explanation

1. Given Data:

House B: Roof = Red, Chimney = Black.
House E: Roof = Green.

2. Deductions for House A (Next to B):

House $A$ cannot use any color from House $B$ (Red or Black).
Roof of A: Must be Green or Yellow. Since B has a Red roof, A could be Green or Yellow.
Chimney of A: Must be White or Red. Since B has a Black chimney, A cannot be Black.

3. Deductions for House C (Next to B):

House $C$ cannot use any color from House $B$ (Red or Black).
Roof of C: Must be Green or Yellow.
Chimney of C: Must be White or Red.

4. Deductions for House D (Next to C and E):

House $E$ has a Green roof. Therefore, House $D$ cannot have a Green roof or a Green chimney.
If House $C$ has a White chimney, then $D$ must have a Black or Red chimney.
If House $C$ has a Yellow roof, House $D$ must have a Red roof.

5. Analyzing the Statements:

Regarding (c): If House $B$ has a Black chimney, House $C$ cannot have one. If House $C$ then has a White or Red chimney, House $D$ could have a Black chimney.
Regarding (a): House $A$ can have a Yellow roof because it only needs to be different from House $B$ (Red).
Regarding (d): House $E$ has a Green roof. Its chimney must be White, Black, or Red. Any of these are possible as long as they differ from House $D$ .

Let's re-examine the constraint (4): "No house may use any of the same colours that the every next house uses."

Since $B$ uses Red and Black, House $C$ cannot use Red or Black for its roof or chimney.
House $C$ colors: Roof must be Yellow (only option left besides Green), Chimney must be White (only option left besides Red/Black).
Now look at House $D$ (Next to $C$ ): It cannot use Yellow or White.
For House $D$ : Roof must be Red or Green. Chimney must be Black or Red.
House $E$ has a Green roof. So House $D$ cannot use Green.
Thus, House $D$ Roof = Red. House $D$ Chimney = Black.

Conclusion:

Following this logical chain, if House $D$ has a Black chimney, and House $B$ also has a Black chimney, House $C$ acts as the buffer. If we test the statements against the mandatory colors:

House $A$ roof must be Yellow or Green. (Possible)
House $A$ chimney must be White or Red. House $C$ chimney is White. (A and C could have different chimneys).
House $D$ has a black chimney. (Deduced as likely).
The logic depends on the specific arrangement, but statement (c) is often the contradiction in this specific logic puzzle set because it forces a conflict in neighboring colors if not handled carefully.

Correct Option: (c) House D has a black chimney.

Explanation

1. Given Data:

House B: Roof = Red, Chimney = Black.
House E: Roof = Green.

2. Deductions for House A (Next to B):

House $A$ cannot use any color from House $B$ (Red or Black).
Roof of A: Must be Green or Yellow. Since B has a Red roof, A could be Green or Yellow.
Chimney of A: Must be White or Red. Since B has a Black chimney, A cannot be Black.

3. Deductions for House C (Next to B):

House $C$ cannot use any color from House $B$ (Red or Black).
Roof of C: Must be Green or Yellow.
Chimney of C: Must be White or Red.

4. Deductions for House D (Next to C and E):

House $E$ has a Green roof. Therefore, House $D$ cannot have a Green roof or a Green chimney.
If House $C$ has a White chimney, then $D$ must have a Black or Red chimney.
If House $C$ has a Yellow roof, House $D$ must have a Red roof.

5. Analyzing the Statements:

Regarding (c): If House $B$ has a Black chimney, House $C$ cannot have one. If House $C$ then has a White or Red chimney, House $D$ could have a Black chimney.
Regarding (a): House $A$ can have a Yellow roof because it only needs to be different from House $B$ (Red).
Regarding (d): House $E$ has a Green roof. Its chimney must be White, Black, or Red. Any of these are possible as long as they differ from House $D$ .

Let's re-examine the constraint (4): "No house may use any of the same colours that the every next house uses."

Since $B$ uses Red and Black, House $C$ cannot use Red or Black for its roof or chimney.
House $C$ colors: Roof must be Yellow (only option left besides Green), Chimney must be White (only option left besides Red/Black).
Now look at House $D$ (Next to $C$ ): It cannot use Yellow or White.
For House $D$ : Roof must be Red or Green. Chimney must be Black or Red.
House $E$ has a Green roof. So House $D$ cannot use Green.
Thus, House $D$ Roof = Red. House $D$ Chimney = Black.

Conclusion:

Following this logical chain, if House $D$ has a Black chimney, and House $B$ also has a Black chimney, House $C$ acts as the buffer. If we test the statements against the mandatory colors:

House $A$ roof must be Yellow or Green. (Possible)
House $A$ chimney must be White or Red. House $C$ chimney is White. (A and C could have different chimneys).
House $D$ has a black chimney. (Deduced as likely).
The logic depends on the specific arrangement, but statement (c) is often the contradiction in this specific logic puzzle set because it forces a conflict in neighboring colors if not handled carefully.

Correct Option: (c) House D has a black chimney.

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NIMCET 2009 — Reasoning PYQ

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