Multi-Step Conditional Reasoning

Camp-activity survey questions look wordy, but they are really set puzzles: chain the “everyone who…” rules, then count who can land in each circle.

Nested preference / overlap items appear in the easy band of Selective TS — strong marks when you sketch overlapping groups instead of guessing from the options.

The examiner checks whether you can translate “all A are B”, “no A and C together”, and “more only-X than only-Y” into a consistent Venn picture and infer which activity has the largest audience.

A survey lists several activities and rules about who likes what together or apart. You choose which activity was most popular (or which scenario is forced).

Age-chain puzzles give you one concrete number and a series of "older/younger by" clues — follow the chain and fill in every age before touching the answer choices.

Deductive age-assignment questions appear in the easy-to-medium band of official NSW papers — they are reliable marks when you build a summary table and verify every option against it.

The examiner checks whether you can follow a chain of relative-age clues from a single anchor value, complete the full table, and identify the one true statement among four carefully crafted distractors.

Five or six children are related by age clues (twins, older by N years, younger by N years, between two ages). One concrete age is given. You find all ages, then test which of four statements is the only true one.

Four students, four positions in a race — and Stephen gets no clue of his own. But pin down Bruce (last), then Ethan (2nd), then James (3rd) one by one, and Stephen's 1st place is the only spot remaining.

Simple elimination ordering questions appear at the easier end of NSW Selective TS — they are reliable early-paper marks for students who work through clues methodically instead of guessing.

The examiner checks whether students can identify which clues give definite positions ('no one after X' = last; 'only one before X' = 2nd), chain them in the right order, and find the unmentioned person's position by elimination.

Four (or five) people in a race or ranking. Each clue pins down one person's position. One person is never directly mentioned in any clue — their position is found last by elimination. The options are the four possible finishing positions.

Four shops sell the same TV at different prices. Nathan wants the fastest delivery but can't afford the priciest. Two ordered lists — one for price, one for speed — are all you need to find his answer.

Multi-attribute ordering questions (two attributes: speed + price, or height + weight, etc.) appear regularly in NSW Selective TS. They often use a constraint to eliminate one or more options before the final ranking comparison.

The examiner checks whether students can build two separate ordered lists from scattered clues, apply a hard constraint (eliminate the most expensive) correctly, and then rank the remaining options on the second attribute.

Four or five items are compared on two attributes (e.g. delivery speed and price). A character has a preference for one attribute and a constraint on another. Students build each list from comparative clues and apply the constraint to find the answer.

A train travels from Jaspur to Salumbar with four stops in between. Three clues tell you the relative order of the stops. Jennifer gets off at the second-last station — but two different orderings are valid. Does it matter which one is correct?

Linear ordering questions with a 'between' clue appear regularly in NSW Selective TS. The key skill is chaining 'before/after' clues first, then slotting 'between' items. When two orderings are possible, check whether the target position (second-last, first, etc.) is the same in both — often it is, giving a unique answer.

The examiner tests whether students can (a) chain Clues 2 and 3 to get Wadi → Anjar → Gadarpur, (b) recognise that Kavali can slot in at two positions without changing Gadarpur's last-place status, and (c) conclude that the second-last station is always Gadarpur regardless of Kavali's position.

A journey has N stops between start and end. Three or four clues give pairwise 'before' and 'between' relationships. One or two positions can't be pinned down uniquely. A question asks for the position of one specific station — which turns out to be anchored by the clues even when the full order isn't unique.

When a rule has two different tracks depending on a person's situation, the first step is always to identify which track applies — then the only failure reason is whatever that track requires.

Eligibility rule questions with branching conditions appear regularly in the harder half of NSW Selective TS papers — they reward students who slow down, map the tracks clearly, and apply only the relevant rule.

The examiner tests whether you can parse a multi-branch conditional rule, identify which branch applies to a named person, and deduce the one necessary reason for their failure — not confuse requirements from the wrong branch.

An institution has two sets of entry requirements depending on whether an applicant has a certain qualification. A named person with that qualification fails. The question asks what must have been the reason — the answer is always the specific failure in their (simpler) branch.

The trick is in the words: "likely" and "might" leave gaps where exceptions can slip through — but "will not" and "doesn't stand a chance" are absolute. The impossible scenario is always the one that breaks a certain rule.

Multi-rule conditional chain questions with mixed certainty words appear in the harder band of NSW Selective TS — the examiner is specifically testing whether you notice the difference between probable and certain.

The examiner tests whether students can distinguish probabilistic language ('likely', 'might') from certain language ('will not', 'no chance') in a chain of conditionals, and use that distinction to identify which scenario is logically impossible.

Three or four if-then statements are given. Some use certain language ('will not'), some use uncertain language ('likely', 'might'). The question asks which scenario is NOT possible. The impossible option breaks a CERTAIN rule; the possible options rely on the uncertain gaps.

A substitution cipher maps 26 letters to only 10 digits — so several letters must share each digit. Gabi encodes four words. Luke decodes three with confidence. One word he can't be sure about. Why? Because its digit sequence also spells a different real word.

Code/cipher ambiguity questions appear occasionally in NSW Selective TS. They combine cipher-reading skills with the ability to systematically test alternative decodings — a neat crossover of logical and linguistic reasoning.

The examiner checks whether students can (a) correctly apply a repeating letter-to-digit mapping, (b) identify which digits have multiple letter options, and (c) check systematically whether any alternative letter combination from those options forms another real English word.

A cipher maps letters to digits (with repeats). Four encoded words are decoded. Students must identify which decoded word could also be decoded as a different real word — creating genuine ambiguity for the decoder.

Four people entered last year's pie-eating contest. One finished last. One finished worse than she did the year before. And the winner two years ago can't win again. Strip away the positions one by one — who's left for 2nd?

Contest/ranking elimination questions are a regular feature of NSW Selective TS deductive reasoning. They combine a 'no-repeat' rule with comparative clues ('didn't do as well') to pin down one specific position through elimination.

The examiner checks whether students can (a) apply the 'different winner each year' rule to eliminate Mr Green from 1st, (b) interpret 'didn't do as well' as a strict worsening of position, and (c) use process of elimination to fill the final remaining spot.

Several people competed in a ranked contest. A few clues fix specific positions (who finished last, who did worse than before). A background rule eliminates another candidate from a specific position. The remaining position is determined by elimination.

Three suspects, one guilty. Each makes a statement. But only one is telling the truth. Whose statement is true? Whose is a lie? You need to test each scenario — only one arrangement produces exactly one truth-teller.

Truth-teller and liar puzzles appear consistently on NSW Selective TS Deductive Reasoning. They seem complex but are completely mechanical: test each scenario, count truth-tellers, and eliminate those that violate the constraint.

The examiner tests whether students can (a) set up all possible scenarios for who is guilty, (b) evaluate each statement as true or false under each scenario, (c) count truth-tellers and discard scenarios that don't produce exactly the required number, and (d) read off what must be true from the surviving scenario.

Three or more people each make a statement. A constraint specifies exactly how many are telling the truth. Only one person can be guilty/correct/first, etc. Students must find the unique valid scenario and identify which answer option is consistent with it.

Tim has read Noon. Three rules tell us things about Morning and Night readers — but all three rules point TOWARD Noon, not FROM it. Can we use those rules to say anything about what Tim has read?

The affirming-the-consequent trap is one of the most frequently tested logical errors in NSW Selective TS. Students see that 'if P then Q' is true and Q is true, and incorrectly conclude P must be true. These questions appear across books, languages, group membership, and survey results.

The examiner checks whether students recognise that if-then rules only run in one direction. Knowing the 'then' part is true (Tim read Noon) gives us ZERO information about the 'if' part (whether he read Morning or Night). The correct answer is 'we cannot determine' — not because information is missing, but because the rules simply don't work backwards.

A set of if-then rules all point toward a common outcome (reading Noon, being in a club, passing a test). A student is told someone has that outcome and asked what we can conclude. The trick: the rules go toward the outcome; we can't infer anything from knowing the outcome alone. Multiple scenarios remain valid.

Four students competed to read the most books. Three clues narrow down the ranking — but not completely. Two valid orderings remain. Which statement is true in BOTH of them?

'What must be true?' ranking questions appear regularly on NSW Selective TS. They are harder than full-order deductions because the ranking is only partially determined, and students must test each answer option against every valid arrangement — not just one.

The examiner checks whether students can (a) fix Carlos at 2nd using the 'exactly two below' clue, (b) prove Bryan is always 4th by eliminating his other possible positions, (c) enumerate the two valid arrangements for Olivia and Sharon, and (d) recognise that only option A holds in both, while options C and D only hold in one arrangement.

Four people are ranked using clues about relative order ('fewer than', 'more than', 'did not finish last'). One clue fixes one person's position exactly. Another clue eliminates one person from the top. The full order can't be determined, but one pairwise relationship is guaranteed in every valid arrangement.

Four parrots, three rules about what they eat. Which conclusion must follow? Three of the options commit the inverse or converse fallacy. Only one chains two contrapositives correctly.

Multi-rule 'what must be true?' questions appear in every NSW Selective TS paper. The key skill is finding the contrapositive of each rule and then chaining rules together. The three wrong options always test the inverse and converse errors — recognising these patterns makes elimination fast.

The examiner tests whether students can (a) write the contrapositive of Rule 3 (eats peas → no carrots) and Rule 1 (no carrots → no apples), (b) chain them to get 'eats peas → no apples', and (c) recognise that Options A, B, D each commit a classic fallacy (converse or inverse) while Option C is the valid two-step chain.

Three if-then rules create a chain (apples → carrots → melons) plus a blocking rule (carrots → no peas). Four options test: forward use (often wrong direction), inverse (wrong), converse (wrong), and the valid contrapositive chain (correct). The correct answer always involves chaining two contrapositives.

Semester pass/fail chains are the Selective version of “must be true” logic: each rule is an arrow, and one option breaks a rule no matter how you try.

Multi-subject conditional grids sit in the difficult band of Selective mocks — the same trap as conditional syllogisms: you cannot assume two groups overlap just because they share a parent set.

You must test each Sara scenario against every rule (English → Geography, IT → History, no Geography+IT together) and eliminate the outcome that is impossible, not merely unlikely.

Several if-then rules about exam results are given, plus global facts (no one failed all four, no one passed all four). Four complete result patterns for one student are offered; one cannot happen.

Three friends take turns rolling a dice and swapping marbles. By the end you know everyone's total — but you have to work backwards to figure out the last roll.

Three-player marble (or counter) token-swap questions appear in the harder band of Selective TS papers — they test whether you can track state changes across multiple turns rather than just reading off a final answer.

The examiner wants you to simulate each turn in order, update all three players' totals correctly, and then reverse-engineer the unknown roll from the difference between the second-last state and the final totals.

Three players each start with the same number of tokens. A dice roll is even → that player gives the rolled amount to each other player. Odd → they receive it from each. Two rolls are given; you must find the third.

Five houses, five people, five sports, five transports — and eight clues to untangle them. The secret is to start with the clues that give you exact positions, then use contradictions to eliminate wrong arrangements.

Five-in-a-row grid puzzles appear in the harder half of NSW Selective TS papers and are worth nailing — once you have a system, they are very reliable marks.

The examiner tests whether you can manage multiple attributes across ordered positions simultaneously, using distance clues and attribute clues in combination without getting confused.

Five people sit or live in a row. Each person has two or three unique attributes (sport, transport, colour, etc.). Clues mix position clues (left end, middle, next to, two spaces from) with attribute clues (likes X, drives Y). One question asks who is in a specific position.

Three survey rules, four options — three of them use the rules backwards or in reverse. The only answer that works traces a clean two-step chain: Volleyball → Skiing → NOT Gymnastics.

Multi-rule 'must be true' questions with sport/activity survey setups appear in the harder half of NSW Selective TS and are excellent marks for students who know to test both direct and chained deductions.

The examiner tests whether students can follow a chain of two rules to derive a valid conclusion, while rejecting options that use rules in the wrong direction (converse and inverse errors) — common and well-disguised traps.

A survey or group describes three or four 'everyone who X does Y' rules. Options present conditional statements about one of the named individuals. Only one option follows directly from the rules (or from chaining two of them); the rest reverse or misapply the rules.

Five children, two rankings to track — speed and accuracy. Most options could go either way, but one directly contradicts a fact you can prove. The moment you fix Hailey as 1st, the impossible option jumps out.

'Cannot be true' questions with two parallel rankings (speed + correctness) appear in the harder half of NSW Selective TS and reward students who build both ordered lists before checking the options.

The examiner tests whether students can extract two separate rankings from interconnected clues, then correctly identify the one option that contradicts a provable fact — rather than guessing from instinct.

A set of 4–6 clues about a group gives partial ordering information across two or more attributes (e.g. speed and score). One option contradicts a ranking you can prove with certainty; the others are either true or could be true.

Four games, five clues about who likes what — and you have to figure out which game is most popular without a single number in sight. The key is realising that Koolchee quietly absorbs everyone else's fans.

Set-relationship questions with 'which group is largest?' conclusions appear in the harder section of NSW Selective TS — they reward students who can chain subset clues (A ⊆ B ⊆ C) to reach a size comparison without needing actual numbers.

The examiner tests whether students can build a mental Venn diagram from verbal clues — identifying subsets, exclusions, and overlaps — and then use those relationships to determine which group must be the biggest.

Four named groups are given. Clues describe subset relationships (everyone in A is also in B), exclusions (no one in A is in C), overlaps (some in A are also in D), and size comparisons (more in X-only than Y-only). The correct group is the one that all others feed into, plus has its own extras.

Runners, swimmers, gymnasts — three clues about who beats whom, and four tricky conclusions to evaluate. The surprise: most runners sit BELOW the gymnasts, yet the top runner beats everyone. That gap is what makes runners' range the widest.

'Which conclusion follows?' questions with partial ordering clues and range comparisons appear in the harder section of NSW Selective TS — they reward students who map out the full picture before evaluating any option.

The examiner tests whether students can (a) build a complete ordering from three partial clues, (b) reason about ranges (not just averages), and (c) resist options that sound plausible but contradict one of the clues (especially option C which flips clue 2).

Three groups have overlapping ordering clues: one group's TOP beats another group's TOP; one group beats MOST (not all) of another group; one group beats ALL of a third. Students must determine which conclusion is guaranteed — usually about ranges, not averages.

The sports coach is opening the hall on a school morning. That one observation, combined with four simple rules about who does what and when, leads to only one possible conclusion — but students who rush will pick a trap answer.

'Which must be correct?' questions with scheduling or role-based rules appear regularly in NSW Selective TS. They reward students who build a mental map of all the rules before evaluating each option.

The examiner checks whether students can chain multiple conditional rules together, use morning/afternoon timing to narrow possibilities, and resist options that are merely possible (not necessarily true).

A scenario describes people with different roles and schedules. One specific situation is observed. Students determine which of four conclusions must be true, using all rules together.

A school play has three conditional rules: ticket sales determine whether it goes ahead, working hard determines whether it succeeds, and success determines whether there will ever be a next play. Which outcome is logically impossible?

'Which is NOT possible?' questions are a premium variant of conditional-logic problems in NSW Selective TS. Instead of finding what must be true, you must find the one option that CANNOT happen under any circumstances — worth practising because students often confuse 'unlikely' with 'impossible'.

The examiner tests whether students can apply contrapositives: if the principal allows another play, the play must have been a success; if the play was a success, all must have worked hard and learned their lines. Chaining these together reveals that 'another play despite not learning lines' is a contradiction.

Three or more if-then rules create a chain of consequences. Four outcomes are offered; three are possible under some scenario, one directly contradicts the chain. The trap is confusing 'X doesn't guarantee Y' (so Y might not happen) with 'X prevents Y' (so Y is impossible).

Four rules govern who passed Maths, Physics and Computing. One of them says passing Maths forces you to pass Computing too. Another says no one passed all three. Together, those two rules make one particular combination impossible — but which one?

'Which is NOT possible?' questions using overlapping pass/fail rules are a top-tier Selective TS question type. They demand systematic rule-checking across all combinations — usually rewarding students who build a complete valid/invalid table rather than guessing from the options.

The examiner checks whether students can (a) write Rule 2 as 'pass Maths → pass Computing', (b) chain Rule 2 into Rule 3 to show that passing both Physics and Maths forces all three to be passed, creating a contradiction, and (c) confirm the other three options by finding at least one valid combination that matches each.

Four rules constrain who can pass/fail three subjects. There are only 8 possible pass/fail combinations. Students build a table eliminating invalid rows, then match each answer option to the remaining valid combinations. The impossible option is the one no valid combination can match.

15 cards, 3 shapes, numbers 1–9, no two identical. One constraint: only the number 7 appears in both a square and a circle. Which statement must be true? The answer requires working out the maximum possible for squares and circles combined — then subtracting.

'What must be true?' questions involving counting constraints and set overlaps appear regularly on NSW Selective TS. The key skill is finding the ceiling on one group (squares + circles ≤ 10) to establish the floor for another (triangles ≥ 5). This max-then-subtract approach works whenever two groups share a limited overlap.

The examiner tests whether students can (a) translate the 'only 7 is shared' constraint into a cap on squares + circles, (b) use subtraction to get a minimum for triangles, and (c) see that options C and D don't have to be true because squares or circles individually could be very small.

A fixed total is split among three categories with a constraint limiting overlap between two of them. Finding the maximum for those two (using the overlap constraint) gives the minimum for the third. The correct answer states that minimum as 'at least N'.

Sam needs to impress the music teacher to get into the band. Sara needs Sam in the band to have any chance of persuading Rhiannon to attend. Sam doesn't practice hard enough. Which scenario is completely impossible?

'What cannot be true?' with a multi-step necessary condition chain is a high-difficulty pattern on NSW Selective TS. The key is identifying the chain: NOT impress teacher → NOT in band → NOT Rhiannon comes. The impossible option tries to insert a conclusion that directly contradicts the end of this chain.

The examiner tests whether students can (a) recognise that 'only chance' creates a necessary condition (NOT Sam in band → NOT Rhiannon comes), (b) chain it with the impressing-teacher requirement (NOT impress → NOT in band), and (c) see that Options A, B, D each break at a permitted weak link (chance ≠ certainty), while Option C breaks an airtight link.

A prose scenario contains two nested necessary conditions forming a three-step chain. One option tries to break the last airtight link of the chain (claiming the final effect doesn't follow from the cause). The other options each involve links that are merely possible but not guaranteed, making them genuinely possible.

Three switches, four lights. Each switch flip toggles its lights. All start off. Which of the four statements must always be true? The key insight: Red and Green share the same two switches — so they're permanently in sync.

Toggle-switch 'what must be true?' questions appear in NSW Selective TS Deductive Reasoning. The approach is always: (a) map each light's controlling switches, (b) notice any lights that share the exact same set of controllers — those always match, and (c) enumerate the 2^n states to verify the other options are possible.

The examiner tests whether students can (a) recognise that Red and Green share the same controllers (Switch 1 and Switch 2), making them always in sync, (b) verify Options A, B, C by finding a state where each claim is false, and (c) confirm Option D by checking all 8 states or using the shared-controllers insight.

Switches toggle sets of lights. Starting from all-off, enumerate all possible states. Options claim that certain light combinations are impossible. The correct answer identifies a combination that is truly impossible across all 8 states, while the other three have at least one state where they occur.

Four students rate English, History and Maths. Four clues constrain their rankings. Some students' rankings are completely fixed by the clues; others have flexibility. To find the maximum who could like maths best, lock in the fixed ones and then choose the best arrangement for the flexible ones.

'Maximum/minimum count from partial rankings' is a high-difficulty NSW Selective TS pattern. Students must (a) deduce which rankings are fully determined, (b) identify which students have flexibility, and (c) choose the arrangement for flexible students that maximises (or minimises) the target count.

The examiner tests whether students can (a) use 'Only Gemma liked English > History' to set H > E for all others, (b) combine this with Clue 1 to fix Emily's ranking as M > H > E, (c) combine H > E with Clue 4 to fix Gemma's ranking as E > H > M (maths last), and (d) recognise Wesley and Rohit can each choose M > H > E, giving a maximum of 3.

Multiple clues constrain a group's relative preferences. Some individuals end up with completely fixed rankings; others retain one or more possible orderings. A 'maximum' or 'minimum' question asks you to optimise over the flexible individuals.

Five friends have either blue or brown eyes and each enjoy two activities. Two conditional rules link eye colour to activities. Q doesn't read → Q can't have brown eyes → Q has blue eyes. S only likes drawing (plus one more) → in every scenario, S ends up with blue eyes too. The key move is the contrapositive.

'What must be true?' questions with attribute grids and conditional rules are a difficult band NSW Selective TS type. The contrapositive (doesn't read → not brown → blue) must be applied without being confused by the many unknowns (R, T's attributes). Students who try to enumerate all arrangements waste time; those who spot the contrapositive finish in under 2 minutes.

The examiner tests whether students can (a) identify Q as not a reader (piano + fishing), apply the Rule 1 contrapositive to get Q = blue eyes; (b) handle S in both scenarios (S fishes → doesn't read → blue; S doesn't fish → non-fisher has blue eyes) and get the same result; (c) reject A (could have ≥3 blue), C (Q is blue, not brown), and D (T might not read if T is the blue-eyed non-fisher who likes piano + drawing).

People have an attribute (eye colour) and exactly two activities from a fixed set. Two conditional rules link attribute to activity. Some people's activities are fully known; others only partially known. The question asks which statement MUST be true. Apply contrapositive to those whose activities are fully known.

Someone is hiding in one of three rooms. Each door has two statements — but at most one per door can be false. Room 2 breaks the rule immediately. Room 1 forces a name contradiction. Only Room 3 survives. This is pure case-elimination logic at its sharpest.

Truth/falsity constraint puzzles with hidden-entity setups appear in the very hardest section of NSW Selective TS — they are rare but high-reward questions that separate top scorers from the rest.

The examiner tests systematic case-elimination: can students apply a truth constraint to each possible scenario, identify which scenarios are impossible (via rule violations or contradictions), and then correctly interpret what the surviving scenario forces to be true?

Two or three locations each have two statements. A constraint limits how many can be false per location. Students test each location as the 'answer', check statements for truth/falsity, and eliminate any location that violates the constraint or creates a logical contradiction. The surviving location is the answer.

Six friends in a circle. Five spatial clues build the seating map. Then a two-move pattern (throw opposite, hand left) repeats three times until Willow holds the bag. The question asks who started. This is the hardest NSW Selective TS format: spatial setup + sequential tracing combined.

'Circular arrangement + pattern tracing' is a top-difficulty NSW Selective TS question type. It appears rarely but always trips students who try to solve it in their head. The key is always: (1) draw the circle first with numbered seats, (2) confirm every clue fits, (3) only then trace the pattern step by step.

The examiner tests whether students can (a) deduce the three opposite pairs from the clues, (b) use 'left = clockwise' in an inward-facing circle, (c) place Max-Catherine-Grace consecutively, (d) confirm Liam between Karri and Willow, and (e) trace two sub-moves per repetition without losing track of the current holder.

People stand in a circle facing inward. Several clues give opposite pairs and adjacency. Then a multi-step pattern is applied repeatedly and the final position is given. You must find the starting position by forward-testing each option (or working backwards).