Multiple choice general knowledge math & puzzles

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 has a colored chimney. The roof and chimney of each housemust be painted as follows. i. The roof must be painted either green,red ,or yellow. ii. The chimney must be painted either white, black, or red. iii. No house may have the same color chimney as the color of roof. iv. No house may use any of the same colors that the every next house uses. v. House E has a green roof. vi. House B has a red roof and a black chimney If house C has a yellow roof. Which must be true.

  1. House E has a red chimney

  2. House C has a black chimney

  3. House E has a black chimney

  4. House E has a white chimney

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given House E has green roof, House B has red roof and black chimney, and House C has yellow roof, we need to determine House E's chimney. House E's chimney cannot be green (same as roof) by rule iii. House D is next to E, so E cannot use colors D uses. Working through the constraints: If House C has yellow roof, its chimney must be white or black (not yellow). If C's chimney is black, then B and C would both have black chimneys, violating rule iv. So C's chimney must be white, meaning E's chimney must be black or white. Further logical deduction shows E must have white chimney to satisfy all constraints.