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.

Suppose that yellow lights decorate exactly two stores on the south side of the street and exactly one store on the north side. If all other conditions remain the same, then which one of the following statements MUST be true?

• A. Green lights decorate store 1
• B. Red lights decorate store 7
• C. Red lights decorate store 10
• D. Yellow lights decorate store 2

Hint:

Only three south-side stores are free to take the two yellow slots; check which pairings among them are actually allowed once you rule out two neighbours both being yellow.

Answer 1

The Correct Option is D

The extra condition here changes only how many stores on the south side get yellow lights, from one to two. Store 4 stays red and store 5 stays yellow as before. The cleanest way to solve this is to list the two possible cases for where the south side's two yellow stores could sit, and see what they have in common.

1. Green lights decorate store 1: this is ruled out immediately, since store 1 sits next to store 3 (which is always green, because it neighbours red store 4 and faces yellow store 5) and store 1 also cannot be yellow (the one yellow slot on the north side already belongs to store 5). With green and yellow both blocked, store 1 has to be red, not green, in every case, so this statement is false to begin with.
2. Red lights decorate store 7: store 7 is not pinned down by anything in this new condition, since the change only affects the south side. Store 7 can be red or green depending on the rest of the layout, so this is not guaranteed.
3. Red lights decorate store 10: consider the two cases for the south side's yellow stores. Case A: yellow stores are store 2 and store 8, leaving store 10 to be red or green (it just needs to differ from store 8 and from store 9). Case B: yellow stores are store 2 and store 10; here store 10 is yellow, not red. Since Case B is a valid possibility where store 10 is not red, this statement is not forced.
4. Yellow lights decorate store 2: we know store 4 is red and store 6 is green, so the only candidates left for the south side's two yellow stores are store 2, store 8, and store 10, and two of these three must be yellow. Store 8 and store 10 sit next to each other, so they cannot both be yellow (neighbouring stores cannot match). That rules out the pairing store 8 with store 10, leaving only two possible pairings: store 2 with store 8, or store 2 with store 10. Store 2 appears in both of the only pairings that work, so store 2 is yellow no matter which case actually holds.

Only the statement about store 2 holds across both possible cases, so "yellow lights decorate store 2" is the one that must be true.

Let's summarize:

• Only three stores, 2, 8, and 10, can carry the south side's two yellow slots, since store 4 is red and store 6 is green.
• Store 8 and store 10 are neighbours, so they cannot both be yellow, which forces store 2 into every valid pairing.

So the correct statement is that yellow lights decorate store 2.