Directions: Read the following information carefully and answer the given questions accordingly. Eighteen students are divided into six different groups viz., Red, Violet, Brown, Orange, Purple and Olive. They are sitting in a linear row and facing north direction. Each group consists of three students. A, B, C, D, E and F are captains of their groups. The distance between any two adjacent groups is equal. Other group members are G, H, I, J, K, L, M, N, O, P, Q and R. G, C and P belong to Violet group. Two groups are sitting between Brown and Purple groups. Neither Brown nor Purple group sits at either end. Orange group sits between Brown and Violet groups. Red group is third to the left of Olive group. A and D belong to Olive and Orange group, respectively. D sits to the left of C. Nine members are sitting between B and E, who belongs to Purple group. F is captain of O and M. K and I belong to the same group, but neither Orange nor Purple group. H and L belong to the group that is to the left of D. R is not a member of Purple group. J and E do not belong to the same group. B doesn't belong to Brown group. Which of the following group/groups is/are seated between Red group and Violet group?

### Concept & Linear Arrangement This problem evaluates your ability to determine the sequence of independent entities (groups) positioned in a linear row using absolute and relative clues. ### Step-by-Step Solution * **Group Positions:** * Let the positions be 1 to 6 from left to right. * Brown and Purple are separated by two groups and neither is at an end, so they must occupy positions 2 and 5. * Red is third to the left of Olive. The only available pair with a distance of 3 (excluding 2 and 5) is 1 and 4. Thus, Red is at 1 and Olive is at 4. * Positions 3 and 6 remain. Orange is between Brown and Violet. If Violet is at 1, it conflicts with Red. Thus, Violet is at 6, Orange is at 3, and Brown must be at 2 to be adjacent to Orange. Consequently, Purple is at 5. * **Group Sequence Deducted:** 1 - Red 2 - Brown 3 - Orange 4 - Olive 5 - Purple 6 - Violet * **Answering the Question:** * The Red group is located at Position 1 (the extreme left). * The Violet group is located at Position 6 (the extreme right). * The groups situated between them occupy positions 2, 3, 4, and 5. * These correspond to the Brown, Orange, Olive, and Purple groups respectively. * Therefore, all the groups listed in options (a), (b), and (c) are seated between the Red and Violet groups. ### Exam Strategy & Shortcut Notice that Red is placed at Position 1 and Violet is placed at Position 6. By definition, every other group in the arrangement (Brown, Orange, Olive, Purple) must lie between the two extremes. This makes the "All three" option the only logical conclusion once the extremes are confirmed. ### Common Pitfall Confusing "between" with "exactly adjacent". In standard logical reasoning puzzles, asking what is "between" two boundary endpoints includes everything inside that range unless "immediately between" is specified. ### Final Answer Therefore, the correct answer is **All three (a), (b), and (c)**.