Logical Reasoning and Problem Solving
What the questions test
Conditional reasoning ('if...then'), syllogisms using all/some/none, ordering and scheduling puzzles, assumption identification, and strengthen/weaken items. The exam rewards validity - what must follow - not what seems plausible in real life.
Concepts to know
In 'If P, then Q,' P is sufficient and Q is necessary. Only two moves are valid: affirm the antecedent (P, therefore Q) and deny the consequent (not Q, therefore not P). The converse (Q, therefore P) and the inverse (not P, therefore not Q) are invalid. In syllogisms, 'all A are B' and 'all B are C' yields 'all A are C,' but 'some A are B' tells you nothing about 'some A are not B.' For ordering puzzles, draw a line or grid and place fixed items first.
Traps
- Affirming the consequent or denying the antecedent.
- Treating a plausible conclusion as a proven one.
- Assuming 'some' excludes 'all.'
- Bringing in outside knowledge the prompt never states.
- Reversing a relationship ('A is taller than B' read as 'B is taller than A').
- Missing the word EXCEPT, which flips the task.
Worked example
'All officers who work night shift receive differential pay. Rivera does not receive differential pay. Therefore Rivera does not work night shift.' This is valid: denying the consequent. Compare the invalid version: 'Rivera works night shift, therefore Rivera receives differential pay' would be valid only in the affirm-the-antecedent direction; 'Rivera receives differential pay, therefore Rivera works night shift' is the converse error. Rule of thumb: before answering, restate the conditional and check which of the two valid moves, if any, the argument makes.