Multiple choice

Directions: Study the following information carefully to answer the question: 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 the roof.
  4. No house may use any of the same colours that the next house on each side uses.
  5. House E has a green roof.
  6. House B has a red roof and a black chimney.

Which statement is false?

  1. A house has a yellow roof.

  2. House A & C have different colour chimneys.

  3. House D has a black chimney.

  4. House E has a white chimney.
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If all houses must have different roof colors, we need 5 colors but only 3 are available (green, red, yellow). So roof colors must repeat. However, house B has red roof and house E has green roof. If we try green for A, yellow for C, red for D, we have roof colors: A-green, B-red, C-yellow, D-red, E-green. Check chimney constraints: A's chimney cannot be white (E has white), cannot be red (A has green), cannot be black (B has black). This is impossible, making the statement 'House A & C have different colour chimneys' necessarily false.

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