Reasoning and Problem Solving
Reasoning and Problem Solving tests logical deduction, ordering, pattern recognition, and conditional statements rather than memorized facts. You will see short scenarios that require you to decide what must be true, what could be true, and what cannot be concluded.
Core rules
- Separate premises from the conclusion. The conclusion must follow from the premises alone.
- For 'If P, then Q': P is sufficient for Q; Q is necessary for P. Valid moves are affirming P, which yields Q, and denying Q, which yields not P.
- Invalid moves are affirming Q and denying P.
- For ordering items, draw a line or table and place fixed positions first.
- Treat 'some' as 'at least one' and never convert it to 'all.'
Worked example
Premises: 'If the radio is not charged, the patrol car cannot be dispatched. The patrol car was dispatched.' Let P = radio not charged; Q = car cannot be dispatched. The second sentence denies Q. By modus tollens, not Q implies not P: the radio was charged. You cannot conclude anything about who dispatched the car or how long the charge will last.
Traps
- Affirming the consequent: 'The car cannot be dispatched, so the radio is not charged' does not follow.
- Reversing 'all A are B' into 'all B are A.'
- Adding information not in the premises.
- Missing 'except' or 'not' in the question stem.
- Treating a possible conclusion as a necessary one.