Logical and abstract reasoning (pattern and sequence recognition)
Domain 3 - Logical and abstract reasoning (pattern and sequence recognition)
This section tests rule-finding rather than arithmetic: number and letter series, figural matrices, odd-one-out sets and short ordering puzzles with constraints. The answer is always determined by a rule that holds for every element, not by a pattern that happens to fit the last two.
Core rules and concepts
- Check differences first, then second differences, then ratios. Constant difference = arithmetic; constant ratio = geometric; constant second difference = quadratic (n², n²+2 …).
- Interleaved series: odd positions and even positions may follow separate rules. Test this when the difference pattern looks chaotic.
- Letter series use alphabet positions; wrap-around after Z, and alternating steps (+3, +1, +3, +1) are common.
- Matrices usually combine movement (rotate 90°, shift one cell) with quantity (dots, shaded cells). Check one attribute at a time across a row.
- Ordering puzzles: write constraints as short symbols (A < B, C ≠ last) and eliminate; do not hold them all in memory.
Worked example
Sequence: 3, 6, 11, 18, 27, ?
Differences: 3, 5, 7, 9 - increasing by 2 each time, so the next difference is 11 and the term is 27 + 11 = 38. Cross-check with a second rule: the terms are n² + 2 for n = 1, 2, 3, 4, 5 (1+2, 4+2, 9+2, 16+2, 25+2), so the sixth term is 36 + 2 = 38. Two independent rules agreeing is strong confirmation.
Traps that cost marks
- Extending a two-step pattern that breaks at the third step; always verify against every given term.
- Using a rule that fits but is not minimal - if a simpler rule explains everything, prefer it.
- Forgetting that a matrix may change two attributes in different directions (shape rotates while count decreases).
- In ordering puzzles, reading "A is not last" as "A is first".
- Spending too long on one figural item: mark a plausible answer, flag it, and return only if time allows.