Logical Reasoning and Problem Solving
This domain tests deductive and inductive reasoning: syllogisms, conditional statements, ordering, grouping and identifying assumptions. You must decide what necessarily follows from the information given, not what is plausible in the real world.
Core rules
- 'If P then Q' does not mean 'if Q then P'.
- 'Only if' introduces a necessary condition, not a sufficient one.
- From 'all A are B' you cannot conclude 'all B are A'.
- From 'some A are B' you cannot conclude 'some A are not B'.
- Draw only conclusions that must be true; test each option against the premises.
Worked example
Premises: 'If the alarm is activated, the keyholder is called. The keyholder was not called.' Question: What necessarily follows? A The alarm was activated. B The alarm was not activated. C The keyholder was unavailable. D Someone forgot to call. Reasoning: B follows by valid contrapositive reasoning. If activation always leads to a call, and no call occurred, activation cannot have occurred. A contradicts the premises. C and D introduce explanations not given. This is not a guess about what probably happened; it is the only conclusion forced by the logic.
Traps
Affirming the consequent ('Q, therefore P'); denying the antecedent ('not P, therefore not Q'); reversing 'all' and 'some'; adding real-world assumptions; choosing an answer that explains the situation rather than one that follows from it.