Linear Arrangement for CAT 2026 Concepts, Tricks & Practice

Seven people in a row, six clues, five questions. Easy to read, easy to get stuck on. This guide explains Linear Arrangement for CAT 2026 the quick way: a short note on each concept, then questions with answers, so you learn by solving.

Why Linear Arrangement for CAT 2026 Matters

• CAT 2026 is on Sunday, 29 November, conducted by IIM Indore.
• DILR has 22 questions in a 40-minute window. In CAT 2025 they came as five sets: three of four questions and two of five.
• One set is roughly a fifth of the section, and most students solve two to four sets.
• Slot reviews of CAT 2025 mention circular, round-table and grid-based arrangement sets. Linear arrangement is the base skill for all of them.

What Is a Linear Arrangement?

People or things are placed along one straight line, and you find who is where from a set of clues. It is not only about seating: queues, shelves, flats along a corridor and cabins in a row all count.

CAT uses four common formats:

• Single row, same direction: left and right never change.
• Single row, mixed directions: some face north, some south.
• Two rows facing each other: adds “opposite” clues.
• Row plus attribute: each seat also carries a score, city or profession.

Key Concepts Before You Start

Four rules to remember:

• Counting from both ends: position from left + position from right = total people + 1.
• People between two persons: difference of seat numbers − 1.
• Facing direction: a person facing south has their left on your right. Write N or S above each seat.
• Fixed or possible: under each name, list the seats still possible. One seat left means that person is fixed. One candidate left for a seat means that seat is fixed too.

Linear Arrangement Tricks for CAT

1. Draw numbered slots, not a list of names. Put sure placements in the boxes and maybes above them.
2. Scan every clue first, then start with the strongest: fixed seat, immediate neighbours, distance clues, extreme ends, “between” clues, and negative clues last.
3. Glue neighbours into blocks. “D is immediately right of E” becomes one block [E D] that you slide along the row.
4. Open cases only when forced, for example “C is at one of the extreme ends”. Label Case 1 and Case 2 and keep their deductions separate. Four or more cases usually means you missed a stronger clue.
5. Save negative clues for the end. “F is not next to A” is weak early and deadly late.
6. Redraw for “if” questions. Work on a side copy and never overwrite the base arrangement.
7. Verify before answering. Check the arrangement against every clue. One slip affects all four or five questions.

Solved Example: Linear Arrangement Questions with Solutions

Five friends, A, B, C, D and E, sit in a row facing north.

1. B sits at the extreme left end.
2. D sits immediately to the right of E.
3. C sits between D and A.
4. A does not sit next to B.

Question: Who sits in the middle seat?

Solution (seats 1 to 5 from the left):

• Clue 1: B is in seat 1.
• Clue 2: E and D form a block [E D] that fits in seats 2–3, 3–4 or 4–5.
• Clue 3, block in 2–3: C = seat 4, A = seat 5. Possible.
• Clue 3, block in 3–4: A and C take seats 2 and 5, and C is never between D and A. Not possible.
• Clue 3, block in 4–5: A = seat 2, C = seat 3. Possible for now.
• Clue 4 kills the last case, because A in seat 2 is next to B.

Answer: the arrangement is B, E, D, C, A, so the middle seat is D.

Quick-Fire Concept Check

Solve these on a rough sheet. Answers are right below.

1. In a row of 12 people, A is 5th from the left. What is A’s position from the right?
2. P is 4th and Q is 11th from the left in a row. How many people sit between them?
3. A is 7th from the left and 9th from the right. How many people are in the row?
4. In a row of 9 facing north, X sits third to the right of Y. Which seats can Y occupy?
5. In a row of 10, P is 3rd from the left and Q is 4th from the right. How many people sit between P and Q?
6. In an east-west line, Ravi faces south and Sita stands immediately to his left. Is Sita east or west of Ravi?
7. In a row of 15 people, X sits exactly in the middle. What is X’s position from the left?
8. A sits at the extreme left. B sits third to the right of A. C sits immediately to the left of B. Which seat does C take?

Answers

1. 8th from the right (12 + 1 − 5).
2. 6 (11 − 4 − 1).
3. 15 (7 + 9 − 1).
4. Seats 1 to 6, because Y needs three seats to the right.
5. 3. Q is 7th from the left (10 + 1 − 4), so 7 − 3 − 1 = 3.
6. East. Facing south, Ravi’s left hand points east.
7. 8th (14 people, 7 on each side).
8. Seat 3. A = 1, B = 4, so C = 3.

CAT DILR Practice Questions: Five Sets with Answers

Five sets of CAT linear arrangement questions, 19 questions in all. Set a timer, solve, then check the answers under each set. Real CAT sets have more people and more layers, so treat these as warm-ups before you move to previous year papers.

Set 1: Single Row (Easy, about 6 minutes)

Seven friends, P, Q, R, S, T, U and V, sit in a row of seven seats, all facing north. Seats are numbered 1 to 7 from the left end.

1. P sits somewhere between S and T.
2. U sits immediately to the left of V.
3. T sits third to the right of S.
4. S sits at one of the two extreme ends.
5. R sits next to U.
6. Q does not sit next to T.

• Q1. Who sits at the extreme right end?
• Q2. How many people sit between Q and R?
• Q3. Who are the two neighbours of P?

Answers

• Arrangement: S, Q, P, T, R, U, V
• Q1: V
• Q2: 2 (P and T)

• Q3: Q and T

  Key steps: Clues 3 and 4 force S into seat 1 and T into seat 4. P takes seat 2 or 3. The U–V block cannot use seats 2–3, because P needs one of them. If U and V took seats 5–6, R would have no seat next to U. So U = 6, V = 7, R = 5. Clue 6 then puts Q in seat 2 and P in seat 3.

Set 2: Single Row with Cases (Moderate, about 8 minutes)

Six colleagues, A, B, C, D, E and F, sit in six cabins numbered 1 to 6 from left to right, all facing north.

1. C sits at one of the two extreme ends.
2. E sits immediately to the right of D.
3. B does not sit at either extreme end.
4. D sits exactly two cabins away from C.
5. A sits immediately to the left of B.
6. F does not sit next to A.

• Q1. Who sits immediately to the left of D?
• Q2. How many people sit between B and E?
• Q3. If the cabins were numbered from the right end instead, which number would E get?
• Q4. If A and C exchange cabins, who will sit next to B?

Answers

• Arrangement: A, B, F, D, E, C
• Q1: F
• Q2: 2 (F and D)
• Q3: 2 (E is 5th from the left, so 6 + 1 − 5 = 2nd from the right)

• Q4: C and F (the row becomes C, B, F, D, E, A)

  Key steps: Clue 1 gives two cases. If C is in cabin 1, then D = 3 and E = 4. The free cabins are 2, 5 and 6, and the only adjacent pair is 5–6, so A = 5 and B = 6. But B at an end breaks clue 3, so this case dies. If C is in cabin 6, then D = 4 and E = 5. A and B take cabins 1–2 or 2–3. The 2–3 option puts F in cabin 1 next to A, which clue 6 forbids. So A = 1, B = 2, F = 3.

Set 3: Mixed Facing Directions (Moderate, about 9 minutes)

Six people, A, B, C, D, E and F, stand in a line from west to east at positions 1 to 6 (position 1 is the west end). Each person faces either north or south. A person facing north has west on their left. A person facing south has east on their left.

1. B stands immediately to the left of C.
2. A stands at the extreme west end and faces north.
3. E faces the opposite direction to B.
4. D faces the same direction as A.
5. F faces south, and D stands immediately to the right of F.
6. B faces the same direction as A.
7. C stands immediately to the right of A and faces south.
8. E stands immediately to the right of B.

• Q1. Who stands immediately to the east of C?
• Q2. How many people face north?
• Q3. Who stands immediately to the right of E?
• Q4. Who stands at the east end, and which direction does that person face?

Answers

• Arrangement (west to east): A (north), C (south), B (north), E (south), D (north), F (south)
• Q1: B
• Q2: 3 (A, B and D)
• Q3: B (E faces south, so E’s right is west)

• Q4: F, facing south

  Key steps: Clue 2 fixes A in position 1. A faces north, so A’s right is east: clue 7 puts C in position 2, facing south. C faces south, so C’s left is east: clue 1 puts B in position 3, not position 1. Clue 6 makes B face north. Clue 8 puts E in position 4, and clue 3 makes E face south. Positions 5 and 6 remain. F faces south, so F’s right is west, which means D is directly west of F: D = 5, F = 6. Clue 4 makes D face north.

Set 4: Row with Scores (Moderate to Hard, about 10 minutes)

Six candidates, A, B, C, D, E and F, sit in a row of six seats facing north, numbered 1 to 6 from the left. Each scored a different mark from 40, 50, 60, 70, 80 and 90.

1. A sits immediately to the left of F.
2. B sits immediately to the right of F.
3. C sits at the extreme right end.
4. B scored the highest and A scored the lowest.
5. C scored 20 marks more than E.
6. F scored more than C.
7. The candidate in seat 1 scored more than the candidate in seat 5.

• Q1. Who sits third from the left?
• Q2. What did the candidate in seat 1 score?
• Q3. How many candidates sit between the highest and the lowest scorer?
• Q4. What is the total score of the two candidates sitting next to E?

Answers

• Arrangement: D (60), A (40), F (80), B (90), E (50), C (70)
• Q1: F
• Q2: 60
• Q3: 1 (only F sits between A and B)

• Q4: 160 (B 90 + C 70)

  Key steps: Do the scores first. Clue 4 gives B = 90 and A = 40. Clue 5 allows C and E to be 70 and 50, or 80 and 60. Clue 6 needs F above C, and 90 is taken, so C = 70, E = 50, F = 80, D = 60. For positions, C is in seat 6 and A–F–B is a three-seat block somewhere in seats 1–5. That gives three cases. Block in 1–3 puts A (40) in seat 1, and block in 3–5 puts B (90) in seat 5, so clue 7 kills both. Block in 2–4 leaves D and E for seats 1 and 5, and clue 7 needs D (60) in seat 1.

Set 5: Two Rows Facing Each Other (Moderate, about 8 minutes)

Six friends, A, B, C, D, E and F, sit in two parallel rows of three seats each. Row 1 is the northern row and faces south. Row 2 is the southern row and faces north. In both rows the seats are numbered 1, 2, 3 from west to east, and each Row 1 seat is directly opposite the same-numbered seat in Row 2.

1. A sits in the middle of Row 1, and C sits directly opposite A.
2. B sits immediately to the left of A.
3. D sits immediately to the right of A.
4. E sits at the west end of Row 2.

• Q1. Who sits opposite B?
• Q2. Who sits immediately to the left of F?
• Q3. Who sits at the west end of Row 1?
• Q4. Who sits opposite D?

Answers

• Arrangement (west to east): Row 1: D, A, B. Row 2: E, C, F.
• Q1: F
• Q2: C (Row 2 faces north, so F’s left is west)
• Q3: D

• Q4: E

  Key steps: Row 1 faces south, so its left is east and its right is west. B, on A’s left, takes seat 3. D, on A’s right, takes seat 1. C sits opposite A in Row 2, seat 2. E takes the west end, seat 1, so F takes Row 2, seat 3.

Common Mistakes in Linear Arrangement Questions for CAT 2026

• Reading “left of” as “immediately left of”. The first allows gaps.
• Ignoring facing direction. In Set 3, B is not in seat 1 because C faces south.
• Opening cases too early. Fewer, smarter cases beat a wall of possibilities.
• Mixing cases. Keep each case’s deductions in its own row.
• Answering a different question. “People between”, “position from the right”, “pairs of neighbours” and “largest group together” are four different asks. Underline what is asked.
• Skipping the final check. One wrong seat ruins the whole set.
• Staying on a stuck set. Time already spent is gone. Move on.

Which Set Should You Attempt in the Exam?

• Skim all five sets for two to three minutes.
• Look for anchors: a fixed seat, an extreme-end clue, a distance clue with limited room.
• Start with the set that has the most anchors and the fewest layers.
• No seat fixed after about five minutes? Leave it and return if time allows.
• Benchmark: 10 to 12 minutes per set. Judge a set by its anchors, not its length.

Practice Plan for the Final Weeks

• Week 1: Revise the concepts. Redo the Quick-Fire Check and Sets 1 and 2 untimed, with neat diagrams.
• Week 2: Solve Sets 3 to 5 against the clock, then 10 to 12 more sets with attributes and mixed directions.
• Week 3: Move to arrangement sets from previous CAT papers and DILR sectionals. Keep an error log of misread clues and needless cases.
• Final days: Re-solve error-log sets without looking at solutions. Take one or two sectionals to rehearse set selection.

A good target is 20 to 30 well-reviewed sets before you start mixing topics.

Frequently Asked Questions

Are CAT linear arrangement questions still important for CAT 2026? 

Yes. CAT has no fixed topic-wise pattern, and arrangement sets of different kinds keep appearing. Linear arrangement is also the base for circular and two-row sets.

How many practice sets should I solve? 

Aim for 20 to 30 reviewed sets across formats, then mix them into full DILR practice.

Should I learn linear or circular arrangement first? 

Linear. Circular sets add a reference point and facing direction to the same logic.

How do I get faster? 

Waste fewer moves: scan all clues, use the strongest first, glue blocks, and open cases only when forced.

Final Thoughts

Linear arrangement is a method, not a talent: read all clues, anchor first, glue blocks, branch only when forced, and verify at the end.

At TCM Education, we help CAT, CLAT, IPMAT and CUET aspirants build this kind of step-by-step clarity. If you would like guided practice and feedback on your approach, explore our CAT preparation programmes.

For today: pick Set 3, draw six boxes, and solve it in ten minutes.