Selective thinking skills: if–then statements (10 questions)

Quick Answer

"If A, then B" tells you what follows when A happens. It does not say that B only happens with A, and it does not say that no A means no B. The one safe reversal is: if B did not happen, A did not happen. This page from Braintree Coaching Australia has ten original if–then questions for Year 5–6 children preparing for the NSW Selective test, and every unsafe conclusion is defeated by a counterexample. It is free, needs no sign-up and takes about 25 minutes including review.

Who is this practice for?

This set suits a Year 5 or Year 6 child who reads short rules confidently and is ready to ask "what must be true?" rather than "what feels true?". It is skill practice for thinking skills, not a copy of official test items, and we do not claim that any number of if–then questions appear on the real test.

The NSW Department of Education describes the Thinking Skills Test as 40 multiple-choice questions in 40 minutes. Its Selective practice tests are the place to see the real format. Our thinking skills test guide lists logical deduction as one of the question families; this page gives that family some worked examples.

No question needs outside knowledge. Everything you need is in the sentences. If a question says something is true, treat it as true, even if the real world is a bit different.

What does an if–then statement tell us?

Take the rule: if it rains, the oval is wet.

• On a rainy day, the oval is wet. That is what the rule promises.
• On a wet oval, we cannot say it rained. A sprinkler could have been on.
• On a dry day with no rain, we cannot say the oval is dry. The sprinkler could still be on.
• If the oval is dry, it did not rain. If it had rained, the oval would be wet. This is the safe backwards step.

So an if–then rule is a one-way street. It points from the first part to the second. The only safe way to go backwards is to flip both parts and add "not".

Which conclusions are safe? A worked rule with counterexamples

Use the rule: if Mia has swimming, she packs her goggles.

What we know	Safe conclusion?	Why
Mia has swimming	Yes: she packs her goggles	This is the rule used forwards
Mia packed her goggles	No	She may pack goggles for a beach trip, with no swimming lesson at all
Mia has no swimming today	No	She may still pack goggles, because she might be going to the beach
Mia did not pack her goggles	Yes: she has no swimming	If she had swimming, she would have packed them

A counterexample is one picture that fits the facts but breaks the conclusion. One is enough. When you suspect a conclusion is unsafe, try to picture a day where the facts are true and the conclusion is false. If you can, the conclusion is unsafe.

"Only if" works the other way round. "Mia may swim only if she has a swim cap" means: if she has no cap, she may not swim. It does not mean a cap is enough.

The questions

Work on paper. For each question, choose the one statement that must be true. Do not choose one that is merely likely.

Question 1

On the school bus, the rule is: if a seat has a bag on it, the seat is taken. Maya sees a seat with a bag on it.

Which statement must be true?

• A. The seat is taken.
• B. Someone is sitting in the seat.
• C. The bag belongs to Maya.
• D. The seat is next to the window.

Question 2

At the local pool, the rule is: if there is thunder, the pool is closed. On Saturday afternoon the pool is open.

Which statement must be true?

• A. It rained on Saturday afternoon.
• B. It is sunny on Saturday afternoon.
• C. There is no thunder on Saturday afternoon.
• D. The pool was closed in the morning.

Question 3

Tom has two rules. If it is a school day, Tom wakes up at 6:30. If Tom wakes up at 6:30, he eats breakfast before 7:00. Tuesday is a school day.

Which statement must be true?

• A. Tom eats toast on Tuesday.
• B. Tom eats breakfast before 7:00 on Tuesday.
• C. Tom walks to school on Tuesday.
• D. Tom wakes up at 7:00 on Tuesday.

Question 4

The rule is: if it rains, the oval is wet. On Thursday, Sam sees that the oval is wet.

Which statement must be true?

• A. It rained on Thursday.
• B. It did not rain on Thursday.
• C. The wet oval does not tell us whether it rained.
• D. The oval was wet on Wednesday too.

Question 5

The rule is: if a shape is a square, it has four sides. Jess draws a shape with four sides.

Which statement must be true?

• A. The shape is a square.
• B. The shape is not a square.
• C. The shape has four equal sides.
• D. The four sides do not tell us whether the shape is a square.

Question 6

The rule is: if the library is open, its lights are on. Kai walks past and sees the lights on.

Which conclusion is not safe?

• A. If the lights had been off, the library would be closed.
• B. The library is open.
• C. The rule says that an open library has its lights on.
• D. The lights are on.

Question 7

The rule is: if Omar has soccer training, he brings his boots. Today Omar has no soccer training.

Which statement must be true?

• A. Omar does not bring his boots.
• B. Omar brings his boots.
• C. Omar has no training, so the rule does not tell us whether he brings his boots.
• D. Omar brings his sneakers instead.

Question 8

The rule is: if Hana has a library card, she can borrow books. Hana does not have a library card.

Which statement must be true?

• A. Hana can borrow books.
• B. Hana cannot borrow books.
• C. Hana will get a library card tomorrow.
• D. The rule does not tell us whether Hana can borrow books some other way.

Question 9

The sign at the swimming carnival says: you may enter the grandstand only if you are wearing your house colour. Zac is in the grandstand.

Which statement must be true?

• A. Zac is wearing his house colour.
• B. Zac is a house captain.
• C. Zac is not wearing his house colour.
• D. Everyone wearing a house colour is in the grandstand.

Question 10

The class rule is: you may borrow a tablet only if you have signed the form. Leo has signed the form.

Which statement must be true?

• A. Leo may borrow a tablet.
• B. Leo has borrowed a tablet.
• C. Leo may not borrow a tablet.
• D. Signing the form does not guarantee that Leo may borrow a tablet.

Answers and worked explanations

Open each answer after your child has chosen. For every wrong option we give the counterexample: a picture where the facts are true and the conclusion is false.

Answer to question 1

Answer: A, the seat is taken.

The rule is used forwards: bag on seat, so the seat is taken. This is a safe deduction.

Why the other options are wrong:

• Option B (someone is sitting in it) goes further than the rule. The seat is taken, but a bag can hold a seat while its owner is at the front of the bus.
• Option C (the bag belongs to Maya) is a new fact. The rule says nothing about whose bag it is.
• Option D (next to the window) is a new fact too. The rule says nothing about where the seat is.

Answer to question 2

Answer: C, there is no thunder on Saturday afternoon.

This is the safe backwards step. If there were thunder, the pool would be closed. The pool is open, so there is no thunder.

Why the other options are wrong:

• Option A (it rained) is not needed. The pool can be open on a day with rain and no thunder, or on a dry day.
• Option B (it is sunny) is the same trap. The pool is open on a grey, drizzly afternoon with no thunder.
• Option D (closed in the morning) is a new fact. The rule says nothing about the morning, and the pool could have been open all day.

Answer to question 3

Answer: B, Tom eats breakfast before 7:00 on Tuesday.

Chain the rules: Tuesday is a school day, so Tom wakes up at 6:30. He wakes up at 6:30, so he eats breakfast before 7:00.

Why the other options are wrong:

• Option A (toast) is a new fact. The rule says before 7:00, not what he eats.
• Option C (walks to school) is a new fact. He could be driven.
• Option D (wakes up at 7:00) is the opposite of the first rule's result.

Answer to question 4

Answer: C, the wet oval does not tell us whether it rained.

This is a reversed statement. The rule goes from rain to wet. It does not go from wet to rain.

Why the other options are wrong:

• Option A (it rained) reverses the rule. Counterexample: on a sunny Thursday, the sprinklers ran all morning and the oval is wet.
• Option B (it did not rain) is also unsafe. Counterexample: it rained overnight, and that is why the oval is wet.
• Option D (wet on Wednesday) is a new fact the rule does not give.

Answer to question 5

Answer: D, the four sides do not tell us whether the shape is a square.

A square always has four sides, but four sides do not make a square.

Why the other options are wrong:

• Option A (a square) reverses the rule. Counterexample: a rectangle that is 5 cm long and 3 cm wide has four sides and is not a square.
• Option B (not a square) is also unsafe. The shape could be a square. We cannot tell from the number of sides.
• Option C (four equal sides) is the same trap. The 5 cm by 3 cm rectangle has four sides but only opposite sides are equal.

Answer to question 6

Answer: B, the library is open.

The question asks for the conclusion that is not safe. Lights on does not mean open.

Why option B is unsafe: counterexample, the cleaner arrives at 7 am and switches the lights on before the library opens. The lights are on and the library is closed.

The other options are safe:

• Option A is the safe backwards step: lights off means closed.
• Option C only repeats the rule.
• Option D is what Kai saw.

Answer to question 7

Answer: C, the rule does not tell us whether he brings his boots.

This is a "no A, so no B" trap. The rule says what happens on training days. It says nothing about other days.

Why the other options are wrong:

• Option A (does not bring his boots) is unsafe. Counterexample: Omar has a Saturday game and takes his boots.
• Option B (brings his boots) is also unsafe. Omar could leave his boots at home on a day with no training.
• Option D (sneakers) is a new fact the rule does not give.

Answer to question 8

Answer: D, the rule does not tell us whether Hana can borrow books some other way.

The rule says a card is enough to borrow. It does not say a card is the only way.

Why the other options are wrong:

• Option A (can borrow) is unsafe. Counterexample: Hana has no card and no other pass, so the desk will not lend her a book.
• Option B (cannot borrow) is unsafe too. Counterexample: the school library lets students borrow with their student pass, so Hana borrows a book with no library card.
• Option C (card tomorrow) is a new fact the rule does not give.

Answer to question 9

Answer: A, Zac is wearing his house colour.

"Only if" names something you must have. Entry only if house colour: if Zac is in, he is wearing it.

Why the other options are wrong:

• Option B (house captain) is a new fact. Any student in house colour can enter.
• Option C (not wearing it) is the opposite of what the sign requires.
• Option D (everyone wearing a house colour is in the grandstand) reverses the sign. Counterexample: a student wearing house colour is on the oval, running the 100 metres, and is not in the grandstand.

Answer to question 10

Answer: D, signing the form does not guarantee that Leo may borrow a tablet.

Signing is something Leo must do. It is not necessarily enough.

Why the other options are wrong:

• Option A (may borrow) turns a requirement into a promise. Counterexample: Leo has signed, but all of the tablets are already out on loan, or the teacher is also asking for a book to be returned first.
• Option B (has borrowed) goes further again. Being allowed is different from having done it.
• Option C (may not borrow) is unsafe. Leo has met the requirement the rule names and may well be allowed.

What mistake patterns should we look for?

Tally which kind of error came up. Each one needs a different fix.

Pattern	Seen in	What to practise next
Ran the rule backwards (wet, so it rained)	Questions 4, 5, 6	Ask "what else could make the second part true?" and name one other cause
Said "no A, so no B"	Questions 7, 8	Picture a day when A is missing and B happens anyway
Treated "only if" as a promise	Questions 9, 10	Say it as "I need this", never "this is enough"
Added a fact the rule never gave	Questions 1, 2, 3, 7, 8, 9	Underline the words in the rule that support the answer; if none, the option is a guess

For parents, the technical names are useful when you read about this elsewhere. The reversed statement in Questions 4 to 6 is the converse. The "no A, so no B" statement in Questions 7 and 8 is the inverse. Your child does not need either word.

Can my child write a rule and break a wrong conclusion?

Ask your child to invent a house rule in the form "if ___, then ___", for example "if it is a weekday, the shoes go on the rack". Then ask for:

1. One conclusion that is safe from the rule.
2. One conclusion that sounds right but is unsafe.
3. A counterexample that breaks the unsafe one, in a single sentence.

Self-check: the unsafe conclusion must be either the reversed statement or the "no A, so no B" statement, and the counterexample must be a day where the facts are true and the conclusion is false. If the counterexample changes a fact in the rule, it is not a counterexample.

What should we do after this set?

• If two or more answers showed the same pattern in the table, repeat only those questions tomorrow with new rules from your own house. Do not sit a full test yet.
• For argument questions that ask which assumption an argument needs, try necessary assumptions practice.
• For mixed Selective practice with worked solutions, open the Selective sample questions.
• To see how this question family fits the whole section, read the thinking skills test guide and the new format guide.
• The free mock tests need a free classroom account. Create one only when your child is ready for a timed sitting.
• If you want a structured course after that, see what the Selective course includes and check that it matches your child's entry year before buying.

Sources and review

Official source (checked 2026-10-15): NSW Department of Education, Selective high school practice tests: the Thinking Skills Test is 40 questions in 40 minutes, multiple choice.

Where the questions came from: all ten questions, the worked rule and every counterexample are original Braintree Coaching Australia material written for this page. None is taken from an official or third-party paper.

Author: James Rush, content writer, Braintree Coaching Australia.

Answer check: the answer key was checked by the author against the rules as written. A named teacher review has not yet been recorded for this set. If you find an error, please tell us.

Last updated: 2026-10-15.