CAT DILR Grouping Sets: Constraints + 3 Solved Sets
Grouping and team-formation sets are a distinct DILR family from seating and scheduling. This guide teaches the constraint-matrix method for building and verifying a valid grouping, then walks through three fully solved sets: a team-skills split, a compatibility grouping, and a role assignment.
A pool of eight analysts needs to be split into two teams. One of them refuses to work with a particular colleague. A third can only join the finance-heavy group. This is a grouping set, and in CAT DILR it looks nothing like the seating puzzles most aspirants drill. Grouping sets in DILR CAT ask you to divide people into teams or groups under skill, compatibility, and role constraints, then work out which groupings hold and which are ruled out. Get the rules tangled, and a single wrong placement collapses the whole set.
These sets feel slippery because everything is connected. Move one person and three other placements shift with them. This guide gives you the constraint-matrix method, a repeatable way to build a valid grouping and verify it before you commit to an answer. Then it walks through three self-contained solved sets: a team-skills split, a compatibility grouping, and a role assignment.
What makes grouping sets in CAT DILR different
A grouping set hands you a pool and asks you to sort it into buckets. The buckets might be two project teams, three tents on a trek, or four job roles. What matters is membership, which item lands in which bucket. Nothing else.
That single feature separates grouping from the two other arrangement types. Seating sets fix positions, so who sits next to whom carries information and order changes the answer. Scheduling sets pin people or tasks to time slots, so sequence matters. Grouping drops both. Two people are either in the same group or they are not.
The constraints follow from that. Grouping sets run on three rule types: together rules (these two share a group), apart rules (these two cannot), and count rules (each group needs so many of a type). You will rarely see a left-of or a before rule, which are the backbone of seating and scheduling. Reading a set correctly starts with spotting which family it belongs to. This is the same triage that decides your DILR set attempt order in the opening scan.
The most expensive early error is importing seating habits. Aspirants draw a row of positions and try to order the people, when order does not exist here. You waste minutes chasing an adjacency that the set never asked about. If the questions only ask who is with whom, or which grouping is possible, treat position as irrelevant and track membership alone.
The constraint-matrix method
The method has four moves, run in order. The point is to get every rule out of your head and onto the page, then let the forced placements reveal themselves.
Step four is the one aspirants skip under time pressure, and it is where the marks leak. A grouping that breaks a single buried rule can still look tidy on the page. The verification pass is your check against that. If you want the full discipline of checking a build before you commit, our companion piece on the DILR constraint check drills it further.
George Miller's 1956 paper in Psychological Review put working memory at roughly seven items, give or take two. A grouping set with six people and five rules already sits past that limit. Trying to hold every condition in your head is how good reasoning produces a wrong answer. The constraint-matrix method moves the rules onto the page so your working memory is free to reason, not to store. The grid remembers; you deduce.
Solved set 1: splitting a team by skills
Six management trainees, P, Q, R, S, T and U, must form two project teams, Alpha and Beta, with three members each. Each trainee has one specialization: P and Q are in Finance, R and S in Analytics, T and U in Design. The rules:
- Each team contains exactly one Finance specialist.
- P and R must be on the same team.
- S and T cannot be on the same team.
- U must be on Team Beta.
Start with the forced marks. Rule 1 keeps the two Finance people apart, so P and Q sit on different teams. Rule 2 ties P to R. Rule 4 fixes U on Beta. Now test where P can go. Suppose P joins Beta. Then R joins Beta too, and with U that fills Beta completely. That pushes Q, S and T onto Alpha, which puts S and T on the same team and breaks rule 3. So P cannot be on Beta.
P must be on Alpha. Q, the other Finance trainee, goes to Beta. R follows P onto Alpha. U is already on Beta. That leaves S and T for the last seat on each team, one apiece, which satisfies rule 3 automatically. Here is the matrix after the deduction runs.
| Trainee | Specialization | Team Alpha | Team Beta |
|---|---|---|---|
| P | Finance | Yes (fixed) | No |
| Q | Finance | No | Yes (fixed) |
| R | Analytics | Yes (fixed) | No |
| S | Analytics | Open | Open |
| T | Design | Open | Open |
| U | Design | No | Yes (fixed) |
Read the matrix and the answer falls out. Ask who is certain to be on Team Beta, and the reply is Q and U, fixed by the deduction. S and T are the only floating pair, and they split one to each team, so neither is pinned. That is the honest limit of what the rules force, and a good grouping set will only ask about the parts that are actually determined.
Solved set 2: a compatibility grouping
Six colleagues, A, B, C, D, E and F, are divided into two working groups of three, Group 1 and Group 2. The rules are about who works well together and who does not:
- A and B have a conflict and cannot share a group.
- C and D must be in the same group.
- E cannot be in the same group as C.
- A and D must be in the same group.
- B must be in Group 2.
Chain the together rules first. Rule 2 binds C and D. Rule 4 binds A and D. So A, C and D all sit together, and since a group holds exactly three, they form one complete group on their own. The other three, B, E and F, take the remaining group.
Now check the apart rules against that split. Rule 1 wants A and B apart: A is with C and D, B is in the other group, so that holds. Rule 3 wants E away from C: E is with B and F, C is in the A group, so that holds too. Rule 5 places B in Group 2, which fixes the labels. B, E and F are Group 2, and A, C and D are Group 1.
In compatibility sets, chase the must-be-together rules before the cannot rules. Together rules glue people into blocks, and a block that reaches the group size closes on its own, as A, C and D did here. Once the blocks are set, the apart rules usually just confirm the split rather than drive it. Lead with the rules that build structure, then use the rest to check it.
The grouping is fully determined this time. Ask which group E belongs to, and the answer is Group 2, alongside B and F. Ask whether A and E can share a group, and the answer is a clean no, since A is locked into Group 1 with C and D. When the together rules stack up like this, one set can resolve to a single valid grouping.
Solved set 3: a role assignment
Four new hires, Meera, Nikhil, Omar and Priya, are each assigned one distinct role on a media project: Anchor, Editor, Producer or Researcher. Every role goes to exactly one person. A role assignment is a grouping set where each group holds one seat. The rules:
- Meera is the Anchor or the Editor.
- Nikhil is not the Producer.
- Omar is the Producer or the Researcher.
- Priya is neither the Anchor nor the Editor.
- Meera is not the Editor.
Look at rules 3 and 4 together. Omar can only be Producer or Researcher. Priya can only be Producer or Researcher as well, since she is barred from Anchor and Editor. Two people confined to the same two roles must fill exactly those two roles between them. So Omar and Priya take Producer and Researcher, in some order, and neither can be Anchor or Editor.
That leaves Anchor and Editor for Meera and Nikhil. Rule 5 says Meera is not the Editor, and rule 1 says she is Anchor or Editor, so Meera is the Anchor. Nikhil takes the Editor role, which also satisfies rule 2, since Editor is not Producer. The question that follows is usually which role Nikhil must hold, and the forced answer is Editor.
One honest caveat keeps you from overreaching. Omar and Priya are locked to Producer and Researcher, but no rule separates them, so either order is valid. A careful grouping set will not ask you to pin Omar to one role, because the constraints do not. Knowing what stays open is as useful as knowing what is fixed. That instinct comes from working plenty of DILR practice sets until the pattern of forced versus open placements reads at a glance.
Mistakes that break a grouping set
Three errors show up again and again in mock reviews of team formation DILR CAT 2026 sets. Each feels reasonable in the moment, which is why they keep costing marks.
- Pinning an open placement too early. When a person could go in either group, aspirants fix them to force a neat answer, then stack deductions on a guess. Keep open cells open until a rule closes them. A wrong lock this early poisons everything after it.
- Skipping the verification pass. A grouping can obey four rules and quietly break the fifth. If you jump to the questions without walking every constraint against your build, that buried break rides straight into your answer.
- Missing a count rule. Grouping puzzles CAT often cap how many of a type each group can hold. Aspirants track the together and apart rules, then forget the group is already full. Mark the count limits on the grid before you place anyone.
All three share a root cause, which is trusting memory over the page. The grid exists so you do not have to hold the set in your head. These slips also eat time you cannot spare, so pairing the method with sound DILR time management keeps a hard grouping set from swallowing your whole section. Build the habit in practice, not on exam morning. Run full grouping sets in your mocks, verify every build, and review the ones you rushed. For the wider drill plan, browse the CAT preparation articles that sit alongside this one.
What to remember
- Grouping sets sort a pool into buckets, and only membership matters. Position and order, the heart of seating and scheduling, do not exist here.
- Grouping runs on three rule types: together, apart, and count. Spot the family first, and never read a grouping set as a seating row.
- Use the constraint-matrix method: list people and groups, translate every rule onto the grid, lock the forced cells, then build and verify.
- Chain the together rules first. A block that reaches the group size closes on its own, and the apart rules usually confirm the split.
- Know the limit of what the rules force. Some placements stay open, and a fair set only asks about the parts that are actually determined.
- The costly mistakes are pinning an open cell early, skipping verification, and missing a count rule. The grid and a final check fix all three.
Turn Grouping Sets Into Reliable Marks for CAT 2026
Bring two recent mocks to a free session. We will walk your DILR grouping sets together, find where a missed rule or an early guess cost you a solvable set, and fold the constraint-matrix habit into your routine. Most aspirants fix one recurring slip and steady their DILR score.
Get Your Free CAT 2026 Strategy CallCommon doubts, answered
Solve real CAT DILR sets timed
Hand-picked LR puzzles and DI caselets with timer + solution breakdown.