🧩 DILR

Arrangements & Ranking

Linear, circular, and order-ranking arrangements from a set of clues.

20%

of DILR

Why This Topic Matters

Total PYQs📊

of 1002 · 2021–2025

Years featured📅

4/5

of recent CAT years

% of DILR📈

~20%

of section questions

Est. hours⏱️

~12h

to master

~2/20

2021

~9/20

2022

5/20

2023

2024

~6/22

2025

Arrangements & Ranking

Put people or objects into positions — a line, a circle, or a ranking — subject to clues. The whole game is choosing the right diagram and locking the fixed clues before the floating ones.

Arrangement flavour	2021	2022	2023	2024	2025	Avg/slot
Matrix / grid arrangements	–	6.7	–	–	3.0	1.9
Arrangement-style DI & LR sets	1.7	–	5.0	–	–	1.3
Scheduling-flavoured arrangements	3.3	–	–	–	1.7	1.0
Routes as arrangements	–	3.3	–	–	–	0.7
Circular seating	–	–	–	–	2.3	0.5

🎯PYQ Evidence

2025 brought circular seating back. After four years without one, CAT 2025 ran a 7-question circular-table set — and a 9-question matrix set besides. 2022 was the heavyweight year (20 matrix questions, incl. the famous TRICCEK-style numbered-constraint sets). Arrangement skills never skip a year; only the costume changes. If you've been skipping circular practice because "CAT stopped asking it" — 2025 just proved that wrong.

Method

Draw the slots (a row of boxes for linear; a ring for circular).
Place absolutes first — "X is at the end", "Y is third". These anchor everything.
Apply relative clues — "P is immediately left of Q", "two people sit between M and N".
Branch only when forced, and carry every clue down each branch.

💡Exam Tip

Circular tip: in a ring, "immediately left/right" depends on which way people face — for someone facing the centre, their right is the next seat clockwise (CAT 2025's set spelled this rule out in the puzzle text itself). And $n$ distinct people seat in $(n-1)!$ ways because rotations repeat.

A worked example

✏️Worked Example

Five books P, Q, R, S, T sit in a row (positions 1–5). (1) P is at one end. (2) Q is exactly in the middle. (3) R is immediately to the right of S.

Clue 2 fixes Q at position 3.
Clue 1 puts P at position 1 or 5. Try P = 1.
The S–R block (clue 3) needs two adjacent free slots. With 1 and 3 taken, the only adjacent pair left is 4–5: S = 4, R = 5.
T takes the last free slot, 2.

Arrangement: P · T · Q · S · R. (Trying P = 5 instead would force the S–R block into 1–2, giving a second valid line — a reminder to check both ends.)

🎯PYQ Evidence

Sequential arrangement sets reward a state you update one step at a time, anchored on what cannot change. : each group of three is rated with the distinct values 1, 2, 3, so fixing one person forces the others; track running scores quarter by quarter while applying the swap rule — promote the top Novice, demote the lowest Elite — and Dolly's unchanging rating gives the fixed point the rest hangs off. : only one friend moves per turn to the first empty chair in their direction, so anyone who has not yet had a turn is still in their starting seat — the "Davies at chair 2 after Turn 1" clue plus the empty-neighbour start rules pin every starting position, after which you just replay the forced moves. Carry the state forward turn by turn and each question is a lookup.

Common traps

⚠️CAT Trap

"Left of" is not "immediately left of." "To the left" allows gaps; "immediately left" does not. CAT's matrix sets bury exactly this distinction inside long numbered constraint lists — misread one adverb and the whole grid collapses two questions in. Read each positional clue twice: once for order, once for adjacency.

Forgetting circular rotation/reflection double-counts.
Ranking direction. "Taller than" builds an order — fix whether position 1 is the top or bottom.

Checklist

Draw slots; place absolute clues first
Treat "immediately adjacent" pairs as a single block
For circles, mind facing and the $(n-1)!$ count
Check both branches when a clue allows two anchors

Sample Questions

26 practice questions

Medium

Eight employees G,H,I,J,K,M,N,O joined a company in years 2001-2008, one per year. Rules: H before N; K before J; N and J both before G; N before O; J before M; G before I.

Which one of the following CANNOT be true?

Context

Seven students P, Q, R, S, T, U and V sit in a single row of seven seats numbered 1 to 7 from left to right, one student per seat. The following conditions hold: (1) Q sits in seat 4. (2) P sits immediately to the left of Q. (3) R and S occupy the two end seats, with R to the left of S. (4) T sits immediately to the right of R. (5) U sits immediately to the right of Q.

Easy

Who sits in seat 2?

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CAT PYQ Spotlight

Actual CAT questions on this topic

Context

At InnovateX, six employees, Asha, Bunty, Chintu, Dolly, Eklavya, and Falguni, were split into two groups of three each: Elite led by Manager Kuku, and Novice led by Manager Lalu. At the end of each quarter, Kuku and Lalu handed out ratings to all members in their respective groups. In each group, each employee received a distinct integer rating from 1 to 3. The score for an employee at the end of a quarter is defined as their cumulative rating from the beginning of the year. At the end of each quarter the employee in Novice with the highest score was promoted to Elite, and the employee in Elite with the minimum score was demoted to Novice. If there was a tie in scores, the employee with a higher rating in the latest quarter was ranked higher.

1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.

2. Dolly and Falguni were the only employees who got the same rating across all the quarters.

3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

CAT 2025 · Slot 1

TITAHard

What was Eklavya's score at the end of Quarter 2?

Your answer

Context

1. Asha, Bunty, and Chintu were in Elite at the beginning of Quarter 1. All of them were in Novice at the beginning of Quarter 4.

2. Dolly and Falguni were the only employees who got the same rating across all the quarters.

3. The following is known about ratings given by Lalu: Bunty received a rating of 1 in Quarter 2. Asha and Dolly received ratings of 1 and 2, respectively, in Quarter 3.

CAT 2025 · Slot 1

TITAHard

How many employees changed groups more than once up to the beginning of Quarter 4?

Your answer

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