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Previous Year Question (PYQs)



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 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.
  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?





Solution

Fixed data:

B = Red roof + Black chimney

E = Green roof

Since A and C are adjacent to B, they cannot use Red or Black colour. Therefore, A and C must have White chimney, and their roof can be Green or Yellow.

Case House A House B House C House D House E
1 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Red roof, Black chimney Green roof, White chimney
2 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, White chimney
3 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, Red chimney
4 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, White chimney
5 Green roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, Black chimney
6 Green roof, White chimney Red roof, Black chimney Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney
7 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Red roof, Black chimney Green roof, White chimney
8 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, White chimney
9 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Black chimney Green roof, Red chimney
10 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, White chimney
11 Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney Yellow roof, Red chimney Green roof, Black chimney
12 Yellow roof, White chimney Red roof, Black chimney Yellow roof, White chimney Red roof, Black chimney Green roof, White chimney


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