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NSW SelectiveYear 7 entry

Number reasoning in Selective Thinking Skills

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Number reasoning questions are number puzzles solved by thinking, not long sums. In Selective Thinking Skills, your child can treat the options as suspects: estimate to rule some out, then test each one against every clue.

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The full lesson is in the SelectiveReady app. A free account opens How and Why Authors Write; this lesson needs a paid plan.

Updated 16 October 2026 · Facts checked 12 October 2026

Number Reasoning Without Formulas (lesson preview)

A short preview from the SelectiveReady lesson “Number Reasoning Without Formulas”, on number reasoning for the NSW Selective test.

Published:

Read the video transcript

So here's how we crack this case, using our working backwards technique. Let's just grab one of the suspects, say the number 14. First, we test it against clue one. If you divide 14 by three, do you get a remainder of two? Let's see, three goes into 14 four times, which is 12. And yup, there's a remainder of two. Okay, so far so good, now for clue two. If you divide 14 by five, is the remainder four? Well, five goes into 14 two times, which is 10, and you've got four left over. Yes, it works. Since 14 fits both clues, we've found our culprit. Any other number that failed even one of those tests, it would have been eliminated immediately. And boom, there it is, the answer is 14. See, no crazy formulas, no complicated algebra, just a simple logical process of elimination. Case closed.

Number Reasoning Without Formulas is a full lesson in the SelectiveReady app. A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published. The clip on this page has English and Chinese captions.

2

What will your child learn in this lesson?

Your child learns to be a number detective, not a calculator. They'll be able to test answer options against the clues, estimate to throw out silly ones, and look for a short path before any long working.

In the clip, the number 14 is tested against two clues about remainders. The full lesson adds the detective's toolkit and the three rookie errors.

3

How does number reasoning show up in Selective Thinking Skills?

Number puzzles are part of the Thinking Skills test, which needs no previous knowledge. 2NSW Education · 12 October 2026 · Published They use simple numbers in unusual situations, so thinking matters more than fast sums.

The ruleWhat it means for number puzzles
No calculator2NSW Education · 12 October 2026 · PublishedClever shortcuts beat long multiplication
23NSW Education · 12 October 2026 · Published sheets of working-out paperRoom to jot clues and test options
42NSW Education · 12 October 2026 · Published options per questionA short list of suspects to test
402NSW Education · 12 October 2026 · Published questions in 402NSW Education · 12 October 2026 · Published minutesNo time for a page of algebra
The practice papers say there are no marks lost for incorrect answers4NSW Education · 13 October 2026 · PublishedRuling out two options and choosing beats a blank
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What is number reasoning?

Number reasoning is solving a problem about numbers by logic rather than a memorised formula. A Year 6 child meets it in sharing puzzles, ages, leftovers, weights in pairs and "how many must you take" questions.

The lesson's big idea feels backwards at first. The options are a lineup of suspects, and the fastest way to the answer is often to test them.

If the question...Try this tool
Has numbers as optionsTest each option against every clue
Tells a story that ends on a known numberWork backwards from the end
Says at least, at most or certainPicture the unluckiest case
Has options that are far apartEstimate first and cross out the impossible
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What is the method for number reasoning?

Read every clue, estimate a sensible range, then test the options that are left. An answer counts only when it fits every clue, not just the first.

Test the suspects: list the clues, estimate first, test each answer option, then check it against every clue.

  1. List the clues

    Write each clue as a short note. Words like at least and at most are hard rules, not filler.

  2. Estimate first

    Work out roughly how big the answer must be. Cross out options that can't be right.

  3. Test the suspects

    Put an option into the story and check it against every clue, one by one.

  4. Check the whole story

    A partial match is not a match. Confirm the winner fits all the clues.

6

What does a worked number reasoning question look like?

We wrote this puzzle to show the method.

Question: Sam is three times as old as his sister Lily, and in two years' time their ages will add up to 24. How old is Sam now?

  • A. 9
  • B. 12
  • C. 15
  • D. 21
StepWhat your child does
EstimateEach of them is two years younger now, so take away 4: 24 − 4 = 20. Sam alone must be under 20, so D (21) is out.
Test C (15)Lily is 5. In two years: 17 + 7 = 24. Every clue fits.
Test B (12)Lily is 4. In two years: 14 + 6 = 20, not 24. Out.
Test A (9)Lily is 3. In two years: 11 + 5 = 16, not 24. Out.

The answer is C. No equation was needed, and the estimate removed one suspect before any testing.

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Which mistakes catch children on number reasoning?

The most common mistake is stopping at an option that fits the first clue. The lesson's rule: a partial match is not a match.

Rookie errorWhat happensThe fix
Reaching for a formulaLong working eats the timeTest the options first
Skimming small wordsAt least or at most changes the answerUnderline them on working paper
A partial matchAn option fits one clue and fails anotherCheck every clue before choosing
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Can my child try one on their own?

Here is a number question from our free Thinking Skills set. Your child answers it, then reads the explanation.

Practice question · SEL-TS-TST-13

Lachlan collected some shells at the beach. He gave half of them to his sister. Then he found 5 more. Now he has 17 shells.

How many shells did Lachlan collect at first?

  1. A

    44

  2. B

    6

  3. C

    34

  4. D

    24

Show answer and explanation

Answer: D

Answer: D (24)

Work backwards from the end.

  1. He has 17 after finding 5, so before that he had 17 − 5 = 12.
  2. 12 is the half he kept, so at first he had 12 × 2 = 24.
  3. Check: half of 24 is 12, and 12 + 5 = 17.

Why the other options are wrong

  • A (44): This adds the 5 shells instead of taking them away when working backwards.
  • B (6): This halves 12 instead of doubling it; 12 is the half he kept, not the whole.
  • C (34): This doubles 17 and forgets that 5 of those shells were found later.

  1. Know where the story ends

    Lachlan ends with 17 shells. Every option has to land there.

  2. Test a suspect

    Try D, 24. He gives away half and keeps 12. Then he finds more: 12 + 5 = 17, so it fits.

  3. Rule out the rest

    A gives 22 + 5 = 27, B gives 3 + 5 = 8 and C gives 17 + 5 = 22. None of them lands on 17.

  4. Check by working backwards

    Before finding more he had 17 − 5 = 12. That was half, so he started with 24.

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How can my child practise number reasoning at home?

Everyday numbers make good puzzles. Keep them short and ask your child to explain the check, not just the answer.

Guess my number

Give two clues, such as "shared among three, one is left". Your child tests numbers until both clues fit.

Sharing snacks

Split a packet between the family and talk about the leftovers before counting.

The unluckiest case

Ask how many socks from a drawer make certain of a matching pair, then test it.

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Questions parents ask about number reasoning for Selective

Is number reasoning the same as the Maths test?

No. Mathematical Reasoning tests applying the maths your child knows to new problems2NSW Education · 13 October 2026 · Published. Thinking Skills number puzzles need no previous knowledge, just careful reasoning. 2NSW Education · 12 October 2026 · Published

My child is quick at sums. Is that enough?

Speed helps, but the traps are in the reading. Most errors come from a missed clue, not a wrong sum.

Is the full lesson free?

A free account opens one lesson, How and Why Authors Write; the other lessons need a paid plan1SelectiveReady · 13 October 2026 · Published.

Next questions

Selective Thinking Skills →Lesson: Solving Logic Puzzles →Lesson: Number Operations Mastery →Free Selective practice test →The NSW Selective test explained →

Sources and checks

  1. SelectiveReady

    SelectiveReady · Checked 13 October 2026

  2. Selective high school practice tests

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Page text: CC BY 4.0.

  3. Placement test

    NSW Department of Education · Checked 12 October 2026 · CC BY 4.0 (NSW Department of Education copyright notice); quotes credited

  4. Selective High School Placement Test, Thinking Skills Question Paper, Practice Test 1 (2026 entry practice tests, PDF)

    NSW Department of Education · Checked 13 October 2026 · Practice materials: personal or non-commercial use only; CC BY 4.0 does not apply (page notice). Quoted briefly with credit. Saved text: the cover-page instructions only; the question pages are not stored (W§3.22).

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