DILR guide, sections 3–4
One method for any set
The five steps
- 1
Read the whole setup once without solving. List the entities (people, days, teams) and their attributes.
- 2
Draw one structure. Seats for arrangements, a grid for matching, a time axis for schedules, a results matrix for tournaments, a completed table for DI.
- 3
Place the direct facts first (fixed positions, given numbers, “X is on Tuesday”), then the strongest relative clues (“opposite”, “immediately after”, totals).
- 4
Branch into cases only when a clue allows two placements. Write each case as its own row and strike out any case that breaks a rule.
- 5
Answer: questions on the main grid first, conditional questions last.
Notation that saves time
- ✓ and ✗ in grids; ≠ for “not”; arrows for before and after.
- Circular seating: number the seats 1 to n clockwise and fix one person at seat 1. Facing the centre, a person’s left neighbour is the next seat clockwise and the right neighbour is anticlockwise. Facing outward, reverse it.
- Keep a checklist of the rules and tick each one as you use it. An unused rule is usually where the answer hides.
DI calculation shortcuts
- Percentage change = difference ÷ base. Use the fraction–percent table from the QA toolkit (1/8 = 12.5%, 1/7 ≈ 14.3%).
- Compare two ratios by cross-multiplying instead of dividing: 37/52 against 45/61 means comparing 37 × 61 with 45 × 52.
- Round to two significant figures first; calculate exactly only when the options are close.
- Two successive growth rates a and b combine to (1 + a)(1 + b) − 1, not a + b.
Counting tools you will need
- Round robin with n teams: n(n − 1)/2 matches. Knockout with n teams: n − 1 matches.
- Points: total points = (points for a win) × decisive matches + 2 × (points for a draw) × drawn matches.
- Calls, handshakes or messages, one per pair of n people: n(n − 1)/2.
- Three-set Venn diagram, when each pair count includes the people in all three:
A painted n × n × n cube cut into unit cubes: 8 cubes with three painted faces, 12(n − 2) with two, 6(n − 2)² with one and (n − 2)³ with none.
Set types CAT uses, and how to handle each
CAT DILR sets fall into about a dozen families. Learn to name the family within a minute, because the family tells you what to draw and which shortcut applies.
| Set type | Looks like | Draw this | Key move | Skip on first pass if | Worked in |
|---|---|---|---|---|---|
| Arrangements (linear, circular, ranking) | Seats, queues, floors, finishing orders | Numbered slots; fix one person in a circle | Place fixed and “opposite” or “immediately next” clues before “not next to” clues | 8+ people and mostly negative clues | Arrangement & distribution |
| Matching (who–what–where) | People × city × job | A ✓/✗ grid | Eliminate; a row or column with one blank left is solved | 5+ attributes per person | Matching & truth-tellers |
| Numeric distribution | Items shared out, with totals | A table with row and column totals | Start with the most constrained row; use “at least one” limits | Several unknowns per row and no totals | Arrangement & distribution |
| Scheduling and movement | Days, slots, durations, trains between stations | A time axis or a day × slot grid | Turn durations into one equation; anchor fixed times | Overlapping durations with many conditions | Scheduling & tournament |
| Tournaments and games | Round robin, knockout, points tables | A results matrix plus a points table | Use the total-points equation; find who must have won or lost | Many teams, partial results, only max/min questions | Scheduling & tournament |
| Scores, ratings and indices | Judges’ marks, ratings, weighted indices | A table of sorted scores | Apply the rule (drop high/low, weights), then push unknowns to extremes | The rule changes from round to round | Routes & scores |
| Sets and Venn | Surveys, overlapping groups | A 2- or 3-circle Venn with every region labelled | Fill from the centre outward; use extra memberships for max/min | Four or more overlapping sets | DI table & Venn |
| Routes and networks | Roads, flows, calls, messages | Nodes and edges | List paths by their first step; inflow = outflow at each node | Large one-way networks | Routes & scores |
| Data interpretation | Tables, bar, line, pie or scatter charts | The completed table | Fill cells with one unknown first; approximate | Heavy calculation with close options | DI charts |
| Binary logic | Truth-tellers and liars, yes/no answers | A case table (T or L per person) | Assume one case and look for a contradiction | 5+ people with nested statements | Matching & truth-tellers |
| Process and rule-based | Machines, games with moves, elimination rounds | A step-by-step table | Simulate step by step; look for a repeating cycle | Rules you cannot summarise in one line | Process & cubes |
| Cubes and spatial | Painted cubes, dice, nets | The counting formulas | Count by face type | Anything needing real 3-D visualisation | Process & cubes |
Max/min questions run across every type. “What is the maximum possible…” means: build the extreme case by pushing everything else to its limit, then check that the case breaks no rule.