Question

Directions for questions 49 to 52: There are exactly ten stores and no other buildings on a straight street in Bistupur Market. On the northern side of the street, from west to east, are stores 1, 3, 5, 7, and 9. On the southern side, also from west to east, are stores 2, 4, 6, 8, and 10. The stores on the northern side sit directly across the street from the stores on the southern side, facing each other in pairs: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10.

Each store is decorated with lights in exactly one colour: green, red, or yellow. The lighting follows these rules:
1. No store has the same light colour as a store next to it on the same side of the street.
2. No store has the same light colour as the store directly across the street from it.
3. Yellow lights decorate exactly one store on each side of the street.
4. Store 4 has red lights.
5. Store 5 has yellow lights.

If green lights decorate store 7, then each of the following statements could be false EXCEPT:

• A. Green lights decorate store 2
• B. Green lights decorate store 10
• C. Red lights decorate store 8
• D. Red lights decorate store 9

Hint:

If store 7 is green, look at what colours are still open for its neighbour, store 9, once yellow is already used up on the north side.

Answer 1

The Correct Option is D

Step 1: Recall what is already fixed from the base rules.
From the shared setup, store 3 and store 6 must both be green, because each of them sits next to a red store and faces a yellow store, leaving green as the only option. Store 1 must be red, because it cannot be green (it neighbours green store 3) and cannot be yellow (the one yellow slot on the north side already belongs to store 5).

Step 2: Apply the new condition, store 7 is green.
Store 7 sits between store 5 and store 9 on the north side, so it is next to both. Store 7 being green does not clash with store 5 being yellow, so that is fine. But store 7 also neighbours store 9, and rule 1 says neighbouring stores cannot share a colour, so store 9 cannot be green.

Step 3: Narrow down store 9.
We already know only one store on the north side can be yellow, and that slot is taken by store 5. So store 9 cannot be yellow either. Store 9 cannot be green (step 2) and cannot be yellow (rule 3), which leaves only one colour available: red. So store 9 must be red, and this is forced no matter how the rest of the street is coloured.

Step 4: Check the four statements against this forced fact.
Option 4 says "red lights decorate store 9", which is exactly what we just proved must be true in every valid arrangement, so option 4 can never be false.
Option 1 says "green lights decorate store 2". Store 2 is not fixed by any of the rules used so far; it only needs to differ from store 4 (red) and from store 1 (red, since they face each other), so store 2 could be green or yellow depending on how the rest of the puzzle is filled in. It does not have to be green, so this statement could be false.
Option 2 says "green lights decorate store 10". Store 10 is free to be green, red, or yellow depending on the rest of the arrangement, as long as it differs from store 8 and from store 9 (red, its facing store). Since store 10 does not have to be green, this statement could be false too.
Option 3 says "red lights decorate store 8". Store 8 differs from store 6 (green) and from store 7 (green, its facing store), so it could be red or yellow. It does not have to be red, so this statement could also be false.

Final Answer:
Store 9 being red is the only fact that is forced in every valid case, so it is the one statement that could not be false. \[ \boxed{\text{Option 4}} \]