Unit 12
Multi-Step Conditional Reasoning
About this unit
Follow chains of logical rules across multiple steps to determine what must, could, or cannot be true. This unit covers if-then implication chains, set membership overlaps, role assignment under constraints, deductive value assignment, and preference intersection puzzles.
What types of questions will you face?
- 1Implication chains: if A doesn't happen → B → C → D — trace what must follow from a starting condition
- 2Set membership: everyone who likes X likes Y; no one who likes Y likes Z — deduce who likes what
- 3Role/team assignment: 4-5 people need roles filled under a set of conditional constraints — find the valid assignment
- 4Preference intersection: four friends each have food/activity preferences — find the one option all can agree on
- 5Two-statement proofs: choose the two statements that together logically prove a given conclusion
- 6Deductive value assignment: match 5 people to 5 values (scores, prizes, ages) using a set of ordering clues
Skills you will build
- Chaining conditional statements across multiple steps without losing track
- Mapping set membership using inclusion/exclusion diagrams
- Using conditional rules to assign roles under constraints systematically
- Finding the intersection of preference sets by elimination
- Identifying which combinations of statements are logically sufficient
- Handling "if A then B" rules that cascade three or more levels deep
By the end of this unit, you will be able to
- Trace any multi-step if-then chain to its logical conclusion
- Determine what must, could, and cannot be true from a set of premises
- Assign roles and values under complex constraints by systematic elimination
- Find the unique solution satisfying all preference and constraint conditions
Difficulty profile
Medium difficulty (avg 3.26). Simple 2-step chains are Easy; set membership deductions are Medium; multi-person role/value assignment under multiple conditional rules is Difficult. This is one of the most intellectually demanding unit types.
Exam tip: Multi-Step Conditional Reasoning
Build a table or diagram as you read. For chain problems, trace forward from the given starting condition one step at a time. For role assignments, start with the person who has the fewest valid options and place them first.
Give Your Child the Best Chance at OC Entry
Join NSW families preparing their children for the Opportunity Class Placement Test with the most realistic online OC practice tests available. First tests free—no credit card required.
Claim Your Free OC Practice Tests