🧩 DILR

Grouping, Selection & Distribution

Allocating people or objects to groups under constraints — the form CAT actually tests (2021 distribution set, 2024 coach-allocation set).

of DILR

Why This Topic Matters

Total PYQs📊

of 1002 · 2021–2025

Years featured📅

2/5

of recent CAT years

% of DILR📈

~7%

of section questions

Est. hours⏱️

~8h

to master

2/20

2021

2022

2023

5/22

2024

2025

Grouping, Selection & Distribution

Allocate people or objects to groups under constraints — who can be together, how many each group holds, which attributes must be covered. Classic "pick a committee of 4" sets haven't appeared in recent CAT papers; what CAT actually runs is this skill in allocation form: distributing objects among people, assigning players to coaches, placing items into slots.

The tested form	Year	What it looked like
Distribution of objects	2021	Ten objects split among five people under count rules
Coach–player allocation	2024	Eight players assigned to three coaches with parity, count and rating rules
Constrained grid placement	2024	Numbers 1–10 placed into a grid under row/column orderings

🎯PYQ Evidence

How CAT 2024 framed it. : eight players, three coaches — "Yuki trained only even-numbered players, Zara only odd", "each coach trained at least two players", "Xena trained more players than Yuki." Before touching the ratings at all, those three rules force the group sizes: Yuki can only draw from four even players, Zara from four odd, everyone needs ≥ 2, and Xena > Yuki. Counting comes before placing. worked the same way: pin down how many each person got first; only then ask which ones.

The toolkit

Anchor the total. Objects, players, or slots — write the total and force the group-size split before anything else. "How many" precedes "which."
Partition by attribute. Parity, gender, department, city — when a rule says a group draws only from one pool ("only even-numbered"), compute each pool's size; small pools are your tightest constraints.
Translate pair rules.
- "A and B can't be together" → they sit in different groups; in counting questions, split into cases by where A goes.
- "If X is selected, Y must be" → a conditional: it fires only when X is in; its contrapositive (no Y → no X) is free information.
Min–max squeeze. "Each group at least 2, at most 4" plus a known total usually leaves only one or two size-splits — enumerate them as cases.
Distinctness as a constraint. "All got different counts/ratings" combined with a fixed sum is powerful: $n$ distinct non-negative integers summing to $S$ has very few solutions. Use it to force values.

A worked mini-set

✏️Worked Example

Fifteen prizes are split among A, B, C, D, E. Each gets at least 1; all five counts are different; B gets more than only D (i.e. B is second-lowest); A gets exactly 4.

Five different positive integers summing to 15: since $1+2+3+4+5 = 15$ , the counts must be exactly {1, 2, 3, 4, 5} — no freedom at all. Distinctness + total has already decided how many; only who gets which remains.
B is second-lowest ⇒ B = 2, and D = 1 (the only count below 2).
A = 4 is given. So C and E hold {3, 5} between them — one further clue would finish the set.

The lesson: arithmetic on the totals eliminates most of the universe before any "who" reasoning starts.

🎯PYQ Evidence

Team-formation sets are won by a who-goes-where grid plus one anchor that forces the rest. : build a player-by-coach table and let parity drive it — Yuki takes only evens, Zara only odds, so "coaches of Player-2, 3, 5 all differ" hands Player-2 to Yuki, and "Player-1 and Player-4 share a coach" (one odd, one even) can only be Xena, cascading the whole assignment. : anchor on the absolute clues first — a value of 10 means you hold that object (Barat-o9, Elise-o10), then the three bundles worth 16 and Disha's odd total uniquely fill the remaining pairs. In both, you don't guess: pin the forced placement, then the grid completes itself.

Common traps

⚠️CAT Trap

Jumping to "which" before "how many." In every recent CAT allocation set, the group sizes are forced (or nearly forced) by counts, parity pools, and min/max rules. Students who start placing individuals immediately branch into dozens of cases; students who count first branch into two or three.

Forgetting a conditional's contrapositive — "if X then Y" also bans "X without Y."
Treating "can't be together" as "must be apart in every question" — a new sub-question may add a hypothesis; re-read what each question fixes.

Checklist

Write the total; force group sizes with min/max + distinctness
Build attribute pools (parity, city, gender) and size them
Convert pair rules; harvest contrapositives
Case-split on the smallest pool, not the first clue
Verify every rule in the final allocation

Sample Questions

15 practice questions

Context

A four-member organizing committee is to be chosen from seven volunteers: P, Q, R, S, T, U and V. The selection must satisfy all of the following rules: (1) If P is selected, then Q must be selected. (2) R and S cannot both be selected. (3) At most one of T and U can be selected. (4) At least one of S and V must be selected. (5) If Q is selected, then R is not selected.

Easy

Which one of the following volunteers can NEVER be a member of the committee?

Context

Easy

Which one of the following volunteers must be a member of every valid committee?

Create a free account to access all 15 practice questions on this topic.

CAT PYQ Spotlight

Actual CAT questions on this topic

Context

Eight gymnastics players numbered 1 through 8 underwent a training camp coached by three coaches—Xena, Yuki, and Zara. Each coach trained at least two players. Yuki trained only even-numbered players, while Zara trained only odd-numbered players.

Coaches gave integer ratings on a scale of 1 to 7. Additional information:

1. Xena trained more players than Yuki.

2. Player-1 and Player-4 were trained by the same coach; coaches who trained Player-2, Player-3 and Player-5 were all different.

3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got unique ratings.

4. Average of all players' ratings = 4.

5. Player-2 got the highest rating (7).

6. Average rating of Yuki's players = 2 × (average of Xena's) = 2 + (average of Zara's).

7. Player-4's rating = 2 × Player-8's rating and is less than Player-5's rating.

CAT 2024 · Slot 2

Medium

What best can be concluded about the number of players coached by Zara?

Context

Coaches gave integer ratings on a scale of 1 to 7. Additional information:

1. Xena trained more players than Yuki.

2. Player-1 and Player-4 were trained by the same coach; coaches who trained Player-2, Player-3 and Player-5 were all different.

3. Player-5 and Player-7 were trained by the same coach and got the same rating. All other players got unique ratings.

4. Average of all players' ratings = 4.

5. Player-2 got the highest rating (7).

6. Average rating of Yuki's players = 2 × (average of Xena's) = 2 + (average of Zara's).

7. Player-4's rating = 2 × Player-8's rating and is less than Player-5's rating.

CAT 2024 · Slot 2

TITAHard

What was the rating of Player-7?

Your answer

Create a free account to access all 8 CAT PYQs on this topic.

Continue Your Prep

Flashcards →

Bite-size concept cards

PYQ Practice →

Filter from 1,002 PYQs

Mock Test →

Full CAT simulation

Practice Grouping, Selection & Distribution