Eight persons, A through H, were sitting around a circular table with eight equally spaced chairs. There are exactly four married couples among the eight. Among the eight persons, A, D, E and F are males, while the rest are females. Each person wore a dress of a colour among Red, Blue and Green. it is known that any two persons wearing a dress of the same colour neither sit adjacent to each other nor sit opposite each other. Further, any two persons married to each other do not wear a dress of the same colour, do not sit adjacent to each other and do not sit opposite each other.
Given that A was sitting opposite C and E was sitting opposite G. A's spouse cannot be C (since C is opposite A), H (from (ii)). Hence, A’s spouse can be B or G.
D's spouse cannot be G or H. Hence, D’s spouse can be B or C. E's spouse also can be B or C. Since G cannot be the spouse of D or E, G has to be the spouse of A.
Let the following diagram represent the chairs around the table: Let A be at 1. and C be at 5. From (iii). B will be at 6.
If D's spouse is C. B and E will be married to each other. From (iii). D will be at 7. Since E and G must be opposite each other, they must be at 8 and 4 (G cannot be at 8 as she will be sitting next to his spouse. A). In this case. F and H will have to sit at 2 and 3. This will violate the given information as a married couple cannot sit next to each other. Hence. D’s spouse cannot be C.
If E‘s spouse is C. D will be married to B. in this case, E will be at 7 and G will be at 3 (from (i)). Also, A and B are wearing Green dresses. E is wearing Blue dress. C cannot be wearing a Green dress (since she is opposite A) and cannot be wearing a Blue dress (since she is married to E). Hence. C will be wearing a Red dress. G cannot weat a Blue dress (since she is opposite E) and cannot wear a Green dress (since she is married to A).Hence. G must wear a Red dress.
If D is in 2. F and H will be opposite each other. Hence. D cannot be in 2. If D is in 8, D must be wearing a Red dress (since A and E. who are adjacent to D. are wearing a Green dress and a Blue dress respectively). This will violate (ii) and hence. D must be in 4. wearing a Blue dress (since D’s spouse. B, is wearing a Green dress). F and H will be in 8 and 2 in any order. This is the only possible case.
Q1. Irrespective of where F sits, he will be sitting adjacent to A. Choice (1)
Q2. D's spouse 8. is wearing a Green dress. Choice (3)
Q3. Both the persons sitting adjacent to G will be wearing a Blue dress. Choice (4)
Q4. The spouse of E is wearing a Red dress. Choice (1)Online CAT LRDI Course @ INR 3999 only