Logical and Abstract Reasoning
What this domain tests
Logical and abstract reasoning test valid deduction, conditional reasoning, ordering and pattern recognition. You may see syllogisms, 'if-then' statements, queue or seating ordering, number series or shape matrices. The exam rewards the answer that must be true, not the one that could be true.
Core rules
- For 'If P, then Q', the valid inference is 'not Q, therefore not P' (the contrapositive). 'Q, therefore P' and 'not P, therefore not Q' are invalid.
- 'Only if' reverses the condition: 'P only if Q' means P implies Q.
- 'All A are B' does not imply 'all B are A'. 'Some A are B' does not imply 'some A are not B'.
- In ordering puzzles, draw a line and place fixed items first. Treat 'immediately before or after' as a single block.
- In sequences, test differences, ratios, alternating operations and position-based rules. A pattern must explain every term, not just the last two.
Worked example
Statement: 'If an application is incomplete, it is returned to the applicant. This application was not returned.' Question: What follows? A. The application was complete. B. The application was incomplete. C. The application was refused. D. Nothing follows.
Let P = incomplete; Q = returned. The premise is P implies Q. The second premise is not Q. By contrapositive, not Q implies not P. Therefore the application was not incomplete, i.e. it was complete. Answer A. B reverses the implication. C introduces a decision not in the premises. D ignores the valid contrapositive.
Traps
- Affirming the consequent ('returned, therefore incomplete') or denying the antecedent ('not incomplete, therefore not returned').
- Reading 'some' as 'all' or assuming 'some' excludes 'all'.
- Overfitting a number series with a rule that fails on an earlier term.
- In abstract matrices, tracking only rotation and ignoring count, shading or position.
- Adding real-world assumptions that are not in the premises.