LR · Arrangements , linear, circular & spatial layouts
Linear & circular arrangements, seating, ordering-in-a-line, and 2-D grid/layout sets. Fix a direction, anchor the most constrained entity, then place the rest cell by cell.
Approach Sheet, Arrangements
How to set up linear, circular and grid arrangements cleanly.
- People in a row / seats / queue / floors. Fix a direction (left→right, bottom→top) and stick to it.
- Anchor the most constrained person first; place "immediately next to / between / ends" clues early.
- Use a blank slot diagram and pencil tentative placements; branch only when forced.
- Watch "left of" vs "immediately left of", gaps are allowed in the former.
- Note whether people face centre or outward, it flips left/right.
- Fix one person's seat to kill rotational symmetry, then place neighbours.
- "Opposite" only works cleanly when the count is even.
- For mixed in/out facing, mark each person's facing direction next to them.
- Spatial sets: m×n grid of heights/beads, line-of-sight "can reach" rules.
- Re-state each rule as a cell-by-cell condition; then scan systematically row by row.
- Build a parallel "reachability count" or colour grid rather than re-deriving each time.
- Adjacency & "between" rules (e.g. one Green between two Blues) cap the pattern density.
Real CAT LR Sets, Arrangements
Actual CAT previous-year arrangement/layout sets from the book. Difficulty: Easy Moderate Hard. Click any question to reveal the solution.
CAT 2017
Directions (Q. 28 to 31): Answer the questions on the basis of following information.
In a square layout of size 5 m × 5 m, 25 equal-sized square platforms of different heights are built. The heights (in metre) of individual platforms are as shown below:
| 6 | 1 | 2 | 4 | 3 |
| 9 | 5 | 3 | 2 | 8 |
| 7 | 8 | 4 | 6 | 5 |
| 3 | 9 | 5 | 1 | 2 |
| 1 | 7 | 6 | 3 | 9 |
Individuals (all of same height) are seated on these platforms. We say an individual A can reach individual B, if all the three following conditions are met:
(a) A and B are in the same row or column.
(b) A is at a lower height than B.
(c) If there is/are any individual(s) between A and B, such individual(s) must be at a height lower than that of A.
Thus in the table given above, consider the individual seated at height 8 on 3rd row and 2nd column. He can be reached by four individuals. He can be reached by the individual on his left at height 7, by the two individuals on his right at heights of 4 and 6 and by the individual above at height 5.
Rows in the layout are numbered from top to bottom and columns are numbered from left to right.
28. How many individuals in this layout can be reached by just one individual?
- (1) 3
- (2) 5
- (3) 7
- (4) 8
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29. Which of the following is true for any individual at a platform of height 1 m in this layout?
- (1) They can be reached by all the individuals in their own row and column.
- (2) They can be reached by at least 4 individuals.
- (3) They can be reached by at least one individual.
- (4) They cannot be reached by anyone.
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30. We can find two individuals who cannot be reached by anyone in
- (1) the last row.
- (2) the fourth row.
- (3) the fourth column.
- (4) the middle column.
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31. Which of the following statements is true about this layout?
- (1) Each row has an individual who can be reached by 5 or more individuals.
- (2) Each row has an individual who cannot be reached by anyone.
- (3) Each row has at least two individuals who can be reached by an equal number of individuals.
- (4) All individuals at the height of 9 m can be reached by at least 5 individuals.
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CAT 2020
Directions (Q. 62 to 65): Read the following passage carefully and answer the questions that follow.
Twenty five coloured beads are to be arranged in a grid comprising of five rows and five columns. Each cell in the grid must contain exactly one bead. Each bead is coloured either Red, Blue or Green.
While arranging the beads along any of the five rows or along any of the five columns, the rules given below are to be followed:
(1) Two adjacent beads along the same row or column are always of different colours.
(2) There is at least one Green bead between any two Blue beads along the same row or column.
(3) There is at least one Blue and at least one Green bead between any two Red beads along the same row or column.
Every unique, complete arrangement of twenty five beads is called a configuration.
62. The total number of possible configurations using beads of only two colours is: TITA
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63. What is the maximum possible number of Red beads that can appear in any configuration? TITA
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64. What is the minimum number of Blue beads in any configuration? TITA
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65. Two Red beads have been placed in 'second row, third column' and 'third row, second column'. How many more Red beads can be placed so as to maximise the number of Red beads used in the configuration? TITA