Question No 1 to 4: There are exactly ten stores and no other building 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 of the street, also from West to east, are stores 2, 4, 6, 8 and 10. The stores on the northern side are located directly across the street from those on the southern side, facing each other in pairs, as follows: 1 and 2; 3 and 4; 5 and 6; 7 and 8; 9 and 10. Each store is decorated with lights in exactly one of the following colours: Gray, Royalblue, and Yellowgreen. The stores have been ecorated with lights according to the following conditions:
No store is decorated with lights of the same colour as those of any store adjacent to it.
No store is decorated with lights of the same colour as those of the store directly cross the street from it.
Yellowgreen lights decorate exactly one store on each side of the street.
Royalblue lights decorate store 4.
Yellowgreen lights decorate store 5.

Question 1 : Suppose that Yellowgreen 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. Gray lights decorate store 1
B. Royalblue lights decorate store 7
C. Royalblue lights decorate store 10
D. Yellowgreen lights decorate store 2
E. Yellowgreen light decorate store 8

Question 2: Which one of the following could be an accurate list of the colours of the lights that decorate stores 2, 4, 6, 8 and 10, respectively?
A. Gray, Royalblue, Gray, Royalblue, Gray
B. Gray, Royalblue, Gray, Yellowgreen, Royalblue
C. Gray, Royalblue, Yellowgreen, Royalblue, Gray
D. Yellowgreen, Gray, Royalblue, Gray, Royalblue
E. Yellowgreen, Royalblue, Gray, Royalblue, Yellowgreen

Question 3 : If Gray lights decorate store 7, then each of the following statements could be false
EXCEPT:
A. Gray lights decorate store 2
B. Gray lights decorate store 10
C. Royalblue lights decorate store 8
D. Yellowgreen lights decorate store 2
E. Royalblue lights decorate store 9

Question4 : Which one of the following statements MUST be true?
A. Royalblue lights decorate store 1
B. Gray lights decorate store 10
C. Royalblue lights decorate store 8
D. Yellowgreen lights decorate store 8
E. Yellowgreen lights decorate store 10

Answers and Explanations

Answer 1 : (D)

We can easily see that for stores 2, 4, 6, 8 and 10, lights used to decorate are Gray, Royalblue, Gray, Yellowgreen and Royalblue respectively. Hence, option (B) is the correct choice

Answer 2 : (B)

For question 2, we can have the following arrangements

Answer 3 : (E)

Answer 4 : (A)

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