Logical and Abstract Reasoning
Logical and abstract reasoning tests whether you can draw valid conclusions from given premises and detect patterns in shapes, numbers and codes without relying on outside knowledge.
Deductive logic
In syllogisms, use Venn diagrams rather than intuition. "All A are B" means A is inside B; "no A are B" means the sets are disjoint; "some A are B" means at least one overlap. A conclusion is valid only if it must be true in every diagram consistent with the premises. Watch the middle term: "All auditors are staff; some staff are trained in procurement" does not imply "some auditors are trained in procurement", because the trained staff may sit outside the auditor group. The contrapositive of "if P then Q" is "if not Q then not P", which is valid.
Sequences and codes
For number series, check first differences, then ratios, then alternating or second-difference patterns. For letter series, convert letters to positions (A=1 … Z=26). In coding-decoding, test shifts, reversals and position swaps before assuming a complex rule.
Abstract figures
Track one feature at a time: number of sides, rotation (clockwise/counter-clockwise, 45°/90°), shading, line type and position. Colour and size often change independently of shape. The rule that explains all panels is the answer; a rule that fits three panels but not the fourth is a distractor.
Worked example
Series: 3, 6, 11, 18, 27, ? Differences: 3, 5, 7, 9 - consecutive odd numbers. The next difference is 11, so the term is 27+11=38. Checking with a second rule: each term equals n²+2 for n=1,2,3,4,5 (1+2=3, 4+2=6, 9+2=11, 16+2=18, 25+2=27), giving 36+2=38. Both methods agree, so 38 is robust.
Traps that cost marks
- Affirming the consequent: "If P then Q; Q, therefore P" is invalid.
- Assuming "some" is reversible or that it means "some but not all".
- Overfitting a sequence with a rule that uses only the last two terms.
- Ignoring rotation direction or mirror images in figure series.
- Treating a plausible pattern as the only pattern; check at least two rules.