EXPECTED CET SOLUTION (PUZZLE)

Q1   D From additional information (4) we know that C is not in group Y and D is not in group Z. Given that C and D are in the same group, which means that both C and D are in group X. A, C, D, H and I are in group X. Since, we need to find the friend who cannot be in the group that has exactly three friends; it means that group X will have only five friends. From additional information (1) we know that B and J are in the same group. Also from additional information (2), D, E and F are in different groups. So, it is clear that in a group which has exactly three friends; B and J will be accompanied by either E or F. So, G will be in the group that has exactly two friends along with either E or F. Q2 B Given that F is in group X and G is not in group Y Since D, E and F are in different groups and D is not in group Z, therefore D is in group Y and E is in group Z. Since, C is not in group Y and C, I and H are in the same group, therefore C, I and H are either in group X or group Z. Also, G is either in group X or Z. Since each group has at least two friends and B and J are in the same group, therefore in group Y, there are exactly three friends namely B, J and D. Therefore, out of the pairs mentioned the following four pairs of friends cannot be in the same group; (J, F); (D, G); (B, E) and (D, I). Q3  D Let us first form a group that has exactly six friends. Since, in one group there are six friends, therefore in each of the two other groups there are two friends. Also, we know that D, E and F are in different groups, B and J are in the same group and so are C, I and H. This means that in a group which has six friends, the following five friends namely B, J, H, I and C must be there. Since, C cannot be in group Y and in group X there is A along with one out of D, E and F, we can conclude that it is only group Z that can have six friends. The sixth friend in group Z could be either E or F as D cannot be in group Z. So, neither A nor G nor D can be in the group that has six friends. Q4  A Since there are exactly five friends in group Z, so it can be concluded that H, I and C are definitely in group Z. Since A is in group X, and D, E and F are in different groups, therefore B and J who are in the same group are in group Y. So, G is also in group Z. The fifth friend in group Z could be either E or F. The third friend in group Y and second friend in group X could be either D or E or F. Therefore, J is definitely in group Y