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🧩 DILR

Logical Reasoning

CAT-style reasoning sets: arrangements, distribution, matching, scheduling, games, routes and binary logic — 4–6 questions per set. Selection and representation decide your score.

21%
of DILR

Why This Topic Matters

Total PYQs📊
66
of 1002 · 2021–2025
Years featured📅
4/5
of recent CAT years
% of DILR📈
~21%
of section questions
Est. hours⏱️
~25h
to master
~11/20
2021
2022
~4/20
2023
~7/22
2024
~2/22
2025

What CAT actually tests

In CAT, "Logical Reasoning" does not mean syllogisms or blood relations — those have not appeared since the IIMs took over the paper. It means multi-question reasoning sets: a block of conditions, then 4–6 questions you can only answer once you've cracked the underlying arrangement. On average about 4 LR questions per slot (plus another ~3 per slot in arrangement-heavy sets), typically 2–4 sets per paper. One well-chosen set is worth 8–12 marks; one badly-chosen set can swallow 15 minutes for nothing. Selection and representation matter as much as raw logic.

What the last five years of LR sets looked like

Set flavour20212022202320242025Avg/slot
Puzzles (allocation, grids, mixed)5.01.0
Scheduling2.01.70.7
Games & tournaments1.31.30.5
Relations / family-tree style2.00.4
Distribution of objects2.00.4
Voting1.70.3
Routes1.70.3
Other classic LR3.30.7
🎯PYQ Evidence

Read the rotation, not the rows. No LR flavour repeats reliably — 2023 brought a voting set and a routes set, 2024 a 15-question puzzles wave (coach–player allocation, a constrained number grid, an election scenario), 2025 a tournament set (counting "taps" across rounds). What is stable: every set rewards the same five moves — pick a representation, anchor on the most restrictive clue, branch narrow, prune on contradiction, re-read the question stem. Train the moves, not last year's costume. And note what's absent: truth-teller/liar sets have not appeared even once in 2021–2025.

The recurring set archetypes

Recognising the type in the first read tells you which diagram to draw and where the marks hide.

ArchetypeWhat it looks likeCrack it with
ArrangementsOrder people/objects in a line, circle, or gridSlot diagram; lock fixed positions first
Distribution / AllocationHand out items or people under min–max rulesAnchor the total; squeeze with min/max and "all distinct"
MatchingMap entities to attributes (one-to-one)Tick/cross matrix
SchedulingTasks vs. time/days with precedence & capacityTime-resource grid
Games & TournamentsMatches, scores, rankingsMatch counts + the scoring rule; tie-breakers carry marks
Routes & NetworksPaths, flows, connectionsEnumerate every complete route; never trust a greedy guess

Step 1 — pick the right representation

Most sets are won or lost at the diagram. Match structure to template before you start deducing:

  • Matrix — entities × attributes, one-to-one (who ordered what)
  • Slot diagram — a linear order (positions 1…n)
  • Circular template — seating, cycles (mind clockwise vs. anticlockwise)
  • Table — entities × several attributes at once
  • Case tree — when a rule forces an either/or split

Step 2 — deduce, branch, and prune

  • Start from the most restrictive clue, not the first one. The clue that fixes a value or kills the most options is your anchor.
  • When forced to split, split on the constraint that creates the fewest branches. Carry all the conditions down each branch.
  • One contradiction kills a branch — prune it immediately and don't look back.
  • Conditionals fire only when their trigger is met. "If A then B" says nothing until A is known. Its contrapositive is free information: if A then Bif not B then not A.
🎯PYQ Evidence
The 2024 gymnastics set is the modern template. : eight players, three coaches, parity rules ("Yuki trained only even-numbered players"), count rules ("Xena trained more players than Yuki", "each coach at least two") and rating constraints (average = 4, one shared rating, the rest distinct). The crack: the counting constraint comes first — with 8 players, "Zara only odd, Yuki only even, Xena > Yuki, everyone ≥ 2" collapses the group sizes to almost nothing before you touch a single rating. When a set mixes structure rules with number rules, exhaust the structure first; the numbers then fall into a frame.

A worked matching set

✏️Worked Example

Four friends — Asha, Bittu, Chen, Dia — each ordered a different drink: coffee, tea, juice, soda. (1) Asha ordered neither coffee nor tea. (2) Bittu ordered neither juice nor soda. (3) Chen ordered tea. (4) Dia did not order juice.

Deduce in matrix form:

  • (3) Chen = tea. Tea is now gone for everyone else.
  • (2) Bittu ≠ juice, ≠ soda, and ≠ tea (taken) ⇒ Bittu = coffee.
  • (4) Dia ≠ juice; coffee & tea are taken ⇒ Dia = soda.
  • Asha takes what's left ⇒ Asha = juice (consistent with clue 1).
Coffee Tea Juice Soda Asha Bittu Chen Dia

Result: Asha–juice, Bittu–coffee, Chen–tea, Dia–soda. Every "who/which" question on this set now answers itself from the grid.

Timing and traps

⚠️CAT Trap

A short set is not a safe set. Under-constrained ("vague conditional") sets force heavy enumeration; numeric, additive constraints usually mean a determinate, faster set. The 2024 number-grid set looked tiny — ten numbers, six conditions — but each condition interacted with all the others. Judge sets by constraint type, not by paragraph length.

  • Greedy guessing on routes/distribution is the classic killer — enumerate completely.
  • Carry every constraint into every branch. Most wrong answers come from a rule dropped during a case split.

Watch this

2IIM lays out the full CAT DILR landscape — what the sets look like and how to read them:

🎯PYQ Evidence
Turn the puzzle into a grid or a fixed rule, then let the totals do the work. : five people answer each other with 1, 2, or 3 taps (Yes/No/Maybe), so the trick is a 5x5 grid where every clue is a sum of entries — all taps total 40, and the three given person-totals plus the "Clive more than Badal" rule pin the rest one cell at a time. : here the engine is a single formula — base turnout = 20 x (sum of campaign levels)%, split by level — and an "attack" only ever shifts or abstains a fixed fraction of a candidate's would-be votes, so each question is just choosing the level combination that maximises or minimises that expression. Recognise whether the set wants a grid you fill by totals or a rule you optimise, and the cases fall out mechanically.

Checklist

  • Name the archetype, then draw the matching template
  • Anchor on the most restrictive clue
  • In mixed sets, exhaust structure rules before number rules
  • Split on the fewest-branch constraint; prune on contradiction
  • Use contrapositives as free clues
  • Don't marry a set — if there's no traction in ~3–4 minutes, bank the easy sub-questions and move on

Sample Questions

22 practice questions

Medium

In a 3x3 grid with corners (top): 4,7,9; (middle): 10,?,5; (bottom): 6,8,6 — which number will replace the question mark?

Medium

Island has truth-tellers (always true) and liars (always false). Exactly 1 liar among aa, bb, cc. aa: 'I am a truth-teller.' bb: 'aa is not a truth-teller.' cc: 'bb is not a liar.' Who is lying?

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CAT PYQ Spotlight

Actual CAT questions on this topic

Context

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means 'Yes', two taps mean 'No', and three taps mean 'Maybe'. A total of 40 taps were heard across the five questions. Each question received at least one 'Yes', one 'No', and one 'Maybe'.

The following information is known.

1. Alia tapped a total of 6 times and received 9 taps to her question. She responded 'Yes' to the questions asked by both Clive and Dilshan.

2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded 'No' to Badal.

3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions.

4. No one responded 'Yes' more than twice.

5. No one's answer to Alia's question matched the answer that Alia gave to that person's question. This was also true for Ehsaan.

6. Clive tapped more times in total than Badal.

CAT 2025 · Slot 1
TITAHard

How many taps did Clive receive for his question?

Your answer
Context

Alia, Badal, Clive, Dilshan, and Ehsaan played a game in which each asks a unique question to all the others and they respond by tapping their feet, either once or twice or thrice. One tap means 'Yes', two taps mean 'No', and three taps mean 'Maybe'. A total of 40 taps were heard across the five questions. Each question received at least one 'Yes', one 'No', and one 'Maybe'.

The following information is known.

1. Alia tapped a total of 6 times and received 9 taps to her question. She responded 'Yes' to the questions asked by both Clive and Dilshan.

2. Dilshan and Ehsaan tapped a total of 11 and 9 times respectively. Dilshan responded 'No' to Badal.

3. Badal, Dilshan, and Ehsaan received equal number of taps to their respective questions.

4. No one responded 'Yes' more than twice.

5. No one's answer to Alia's question matched the answer that Alia gave to that person's question. This was also true for Ehsaan.

6. Clive tapped more times in total than Badal.

CAT 2025 · Slot 1
Hard

Which two people tapped an equal number of times in total?

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