This is the section that catches strong maths students out. It is an ability test, not a content test — the arithmetic is deliberately simple, and the difficulty lives in spotting the rule, reading the table and knowing when an estimate is enough. Here is every question type, with original samples you can try.
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EduTest Numerical Reasoning is a timed, multiple-choice, non-calculator section of roughly 30 minutes. It tests how well your child reasons with numbers — finding the rule behind a sequence, pulling a figure out of a table or chart, translating a worded scenario into a calculation, and judging when an estimate will do.
It is deliberately light on taught content. You will not be asked to factorise or to recall a circle formula. What you will be asked is to notice that 5, 10, 9, 18, 17 alternates between doubling and subtracting one — and to notice it in about twenty seconds.
That is why it trips up children who are strong at school maths. The arithmetic is easy; the seeing is the test. Familiarity with the recurring rule families is what turns it around, and that is what most of this page is about. For the taught-content section, see our EduTest Mathematics guide.
Families routinely prepare for these two sections as if they were the same thing. They are not, and preparing for one does very little for the other.
Tests reasoning with numbers: sequences, patterns, relationships, data interpretation and estimation. Content is kept minimal on purpose so that a student who has covered more of the syllabus is not advantaged.
Improves through: exposure to rule families and question shapes. Slower to move than content, but very responsive to volume of practice.
Tests taught curriculum content: fractions, percentages, area, volume, equations, statistics. If your child has not met a topic at school, they cannot reason their way to it.
Improves through: closing content gaps and building arithmetic speed. The fastest-moving section on the paper.
What this means in practice: a child who scores well in Mathematics and poorly in Numerical Reasoning is not bad at maths. They are unfamiliar with the pattern types. That is a fixable, specific problem — and it is fixed by working through many short sequences, not by revising topics.
EduTest does not publish a breakdown, so the shares below are indicative — our estimate from working through practice material at each entry level. The ordering is the reliable part: sequences and data interpretation dominate.
A run of numbers with one missing, usually at the end. Find the rule, apply it. Arithmetic steps, multiplying steps, alternating steps and second-difference patterns all appear.
The missing term sits in the middle, or the pattern runs across a grid or shape rather than a line. Same rule families, harder to see because the layout hides them.
Pairs that follow a hidden rule — 4 gives 13, 6 gives 19, so 9 gives what? Or analogies such as 8 : 24 :: 11 : ?. Name the operation, then apply it.
A small table of figures with several questions attached. Read the row and column labels before the numbers — most losses here are reading errors, not calculation errors.
Column graphs, line graphs and pie charts. Typical asks: largest change, total, average, or how much more one category is than another.
Drawing a conclusion rather than reading a value — converting a percentage of a stated total, comparing two categories, or spotting which statement the data supports.
Rates, unit pricing, time intervals, sharing and scaling, expressed in a sentence or two. The work is in the translation, not the arithmetic.
Explicitly asking for the closest approximation. Rounding to friendly numbers is the intended method — exact calculation is the trap, because it burns the time the question was designed to save.
On the percentages: EduTest has never released a question-type breakdown, and the mix varies between forms and entry levels. These are our estimates from practice material and we label them as such rather than presenting them as official. Treat them as a guide to where revision time goes.
Sequences look infinite in variety. In practice a small number of rule families cover the overwhelming majority of what appears. A child who checks them in a fixed order stops guessing and starts recognising.
| Check this | What it looks like | Example | Next term |
|---|---|---|---|
| 1. Constant difference | Same amount added or subtracted each time | 3, 7, 11, 15, … | 19 (+4) |
| 2. Constant ratio | Same amount multiplied or divided each time | 2, 6, 18, 54, … | 162 (×3) |
| 3. Growing difference | The gaps themselves form a pattern | 2, 3, 5, 8, 12, … | 17 (gaps 1, 2, 3, 4, 5) |
| 4. Shrinking difference | Gaps get smaller by a fixed amount | 100, 91, 83, 76, … | 70 (gaps 9, 8, 7, 6) |
| 5. Alternating rule | Two rules taking turns | 5, 10, 9, 18, 17, … | 34 (×2, then −1) |
| 6. Squares & cubes | Recognisable number families | 1, 4, 9, 16, … | 25 (squares) |
| 7. Add the previous two | Each term is the sum of the two before it | 1, 1, 2, 3, 5, 8, … | 13 |
| 8. Two interleaved series | Odd positions form one series, even positions another | 2, 100, 4, 90, 6, 80, … | 8 (then 70) |
Before anything else, work out the difference between each pair of terms. This single habit solves families 1, 3 and 4 outright and tells you instantly whether the sequence is growing steadily or accelerating.
Gaps first, alwaysDifferences of 4, 12, 36 mean the terms are tripling, not adding. Divide each term by the one before it and see whether you get the same number twice.
Ratio checkA sequence that rises sharply then falls slightly is almost always two rules taking turns. Look at every second term instead of every term.
Every second termSquares to 15, cubes to 5, and the doubling chain 2, 4, 8, 16, 32, 64 should be recognised on sight. A surprising share of sequences are one of these lightly disguised.
Recognise, don't calculateIt is multiple choice. Put each option in the blank and ask whether it makes the run consistent. This is often faster than finding the rule from scratch, and it always beats staring.
Work backwardsRehearse this order until it is automatic. The children who do well here are not more numerate — they have a checklist and they run it. Ten short sequences a day for a month will do more for this section than any amount of general maths work.
Data questions are the most avoidable losses in the section. The arithmetic is usually trivial; the errors come from taking the wrong row, the wrong column, or the wrong units.
Row headings, column headings, axis titles and units, before a single number. Ten seconds here prevents the most common error in the whole section: answering with the right calculation on the wrong data.
Total, difference, average, increase, how many more. These four or five command words decide the whole question and they are easy to skim past.
Charts often count in fives, tens or hundreds, and a bar reaching the third gridline may be 30, not 3. Read one labelled point before trusting any unlabelled one.
If the question wants the difference, do not give the larger value. Distractors are built from the intermediate steps, so a half-finished question usually has an option waiting for it.
Where a total is given, your parts should sum to it. Where percentages are given, they should reach 100. Both are free error-detectors that cost two seconds.
Several questions usually attach to one table. Read it properly once, then answer them as a block rather than starting fresh each time.
The habit that matters most: read the question, then go to the data — not the other way round. Children who study the table first absorb information they will not need and arrive at the question with less time and no advantage.
Some questions ask outright for the closest approximation. Many more do not ask, but reward it anyway — because a rough figure eliminates two or three options in seconds.
397 × 21 becomes 400 × 20 = 8000. The true answer is 8337, and if the options are 800, 4000, 8000 and 80 000 then the estimate has already finished the question.
6120 ÷ 29 becomes 6000 ÷ 30 = 200. The true answer is about 211 — close enough to pick from options spaced a hundred apart.
48% of 812 becomes half of 800 = 400. Nothing more precise is needed unless two options sit close together.
Estimation fails when two options are near each other — 407 and 413, say. That closeness is itself the signal: the question wants exact work, and it is telling you so through its options.
So the decision is made by looking at the options, not the question. Widely spaced options mean estimate; tightly spaced options mean calculate.
Reading the options before working is the single highest-value habit in this section.
| Situation | Round to | Why it is safe |
|---|---|---|
| Multiplying two large numbers | Nearest ten or hundred | Errors stay proportionally small, and the order of magnitude is what the options usually test |
| Dividing | Make the divisor friendly first | 29 becomes 30, 19 becomes 20; adjust the dividend to match so the division stays clean |
| Percentages | Nearest 5% or 10% | 48% is a half, 33% is a third, 26% is a quarter — all instant |
| Adding a column of figures | Nearest ten, then correct | Add the rounded values, then adjust by the leftovers; far fewer carrying errors |
| Reading a chart | Nearest gridline | Bars are rarely meant to be read to the unit; the question is about comparison |
Twenty-six questions across all the recurring types, in EduTest's four-option multiple-choice style. Click an option to see whether it is right and read the worked solution. Aim for about thirty seconds each.
These are original questions written by Selectivetrial. EduTest has never released its real papers, so nobody has genuine past questions — anything advertised as one is a reconstruction. Everything below was written by our team to match the level, style and timing of the real section. They are for practice, not a prediction of what will appear.
Find the rule, then apply it. Write the gaps underneath before you do anything else.
What number comes next?
What number comes next?
What number comes next?
What number comes next?
What number comes next?
Same rule families, but the missing term is buried in the middle or the pattern alternates. Harder to see, not harder to solve.
What number is missing?
What number comes next?
What number comes next?
What number comes next?
A hidden rule links each pair. Name the operation, test it on a second pair, then apply it.
If 4 gives 13 and 6 gives 19, what does 9 give?
If 3 ★ 4 = 25 and 5 ★ 2 = 29, what is 6 ★ 3?
8 is to 24 as 11 is to which number?
Read the labels before the numbers. Several questions usually hang off one display, so read it properly once.
| House | Track | Field | Swimming |
|---|---|---|---|
| Ashby | 45 | 30 | 25 |
| Byron | 38 | 42 | 30 |
| Corio | 50 | 28 | 22 |
| Darley | 32 | 40 | 43 |
Points awarded in each of the three event groups.
Which house scored the most points overall?
How many more points did Byron score in Field than Ashby did?
What was the total number of Field points awarded across all four houses?
Number of books read, January to May.
Which month showed the largest increase on the month before it?
How many books were read in total across the five months?
What was the mean number of books read per month?
| Method | Share of students |
|---|---|
| Walk | 35% |
| Car | 30% |
| Bus | 25% |
| Cycle | 10% |
Survey of all 400 students at one school.
How many students travel to school by bus?
How many more students walk than cycle?
Ordinary arithmetic wrapped in a sentence. Find the "one" first — the unit rate — and most of these collapse.
A shop sells pens at 3 for $5. How much would 12 pens cost?
A train leaves at 9:45 am and arrives at 12:20 pm. How long is the journey?
Cinema tickets cost $14 for adults and $9 for children. What is the total for 3 adults and 4 children?
The options tell you how precise to be. Widely spaced options mean round and move.
Which is the best estimate of 397 × 21?
Roughly what is 6120 ÷ 29?
Which is closest to 48% of 812?
The real section runs about thirty minutes with a clock going and four other sections around it. That pressure is the thing worth practising, and it only exists in a full timed paper.
Numerical Reasoning punishes persistence more than any other section. A sequence either resolves quickly or it does not, and the skill is knowing which within about twenty seconds.
They tell you how precise to be, whether the answer is a value or a difference, and often let you work backwards. In estimation questions the spacing of the options is the instruction.
Options before workingGaps, then ratio, then alternation, then number families, then work backwards from the options. A fixed order stops the random guessing that eats time when a pattern does not jump out.
Checklist, not intuitionMany rules fit one pair of numbers; few fit two. Before applying a rule to the blank, confirm it works somewhere else in the sequence. This one check removes most wrong answers in relationship questions.
Test twice, apply onceSequences are unusually all-or-nothing. If the rule has not appeared in twenty seconds it is unlikely to appear in sixty. Eliminate what you can, commit, flag it and move.
Flag and moveEduTest awards marks for correct answers and deducts nothing for wrong ones. Sweep the final minute and fill every empty box. On a four-option question even a blind guess is worth 25%.
Always → blank sweepTwo passes, always. Bank everything that resolves quickly, flag the rest, then come back. Question order is not guaranteed to run easy to hard, so a student working strictly in order can lose easy marks at the end of the section to one stubborn sequence in the middle. The full method across all five sections is in our EduTest exam strategies guide.
Almost every one of these is a reading or decision error rather than a reasoning failure — which means a habit fixes it, not more practice.
Checking the first difference, finding 4, and stopping. Always check at least three gaps before committing to a rule.
A sequence that rises then dips is two rules taking turns. Read every second term before deciding it is irregular.
Giving the larger value when the question asked for the difference. Distractors are built from exactly these half-finished answers.
Right calculation, wrong data. Put a finger on the row and the column heading before reading the cell.
Assuming gridlines count in ones. Read one labelled value before trusting any unlabelled bar.
Answering 25 when the question wanted 25% of 400. Check whether the answer should be a share or a number of people.
Doing exact long multiplication when the options are an order of magnitude apart. The options were telling you not to.
Ninety seconds on one sequence costs three easy questions elsewhere. Every question is worth the same.
The diagnostic that tells you what to do next: if most errors are "never saw the rule", your child needs breadth — many short sequences across all eight families. If they are "saw it too late", they need speed under a timer. If they are data-reading errors, they need the labels-first habit, not more sequences at all. Treating all three the same is why some students plateau here.
This section rewards little and often far more than long sessions. Ten sequences a day beats a two-hour block at the weekend. It sits inside the wider schedule in our EduTest preparation guide.
| Phase | Weeks | Focus | Weekly shape |
|---|---|---|---|
| Diagnose | 1–2 | One timed section, then sort every error into the four buckets to find out which problem you actually have. | 1 timed section · 1 review · 10 sequences daily |
| Build breadth | 3–6 | Work through all eight rule families deliberately, one or two per session, including the ones your child finds awkward. | 2 rule sessions · 1 data set · 10 sequences daily |
| Build speed | 7–9 | Same material against a timer. Twenty sequences in ten minutes, then full sections. Enforce the twenty-second ceiling out loud. | 2 timed sets · 1 full section · error log review |
| Rehearse | 10–11 | Full mock papers with all five sections, so switching between reasoning and content sections is practised rather than met on the day. | 1 full mock · 1 review · targeted re-drills |
| Taper | 12 | Error log only, no new material. Short daily sequences to keep the checklist warm, early nights, logistics confirmed. | 10 min daily · no new topics |
The one non-negotiable: ten short sequences every day, from week one to the day before. Recognition is built by volume and frequency, not by session length — and recognition is the entire section.
The questions families ask us most often about this section.
It is one of the five EduTest sections: a timed, multiple-choice, non-calculator paper of about 30 minutes that tests reasoning with numbers rather than taught mathematics. Questions cover number series and patterns, numerical relationships, tables, charts, data interpretation, word problems and estimation. The arithmetic is deliberately simple; the difficulty is in spotting the rule or reading the data correctly.
Mathematics is an achievement test — it assesses curriculum content your child has been taught, such as fractions, area and equations. Numerical Reasoning is an ability test — it assesses pattern recognition and logic, using very little taught content so that students who have covered more of the syllabus are not advantaged. They are separate, separately timed sections, and preparing for one does little for the other.
Because it is not testing maths. It is testing whether they notice that a sequence alternates between doubling and subtracting one. That is a recognition skill built by exposure to many short sequences, not by revising topics. It is one of the most fixable problems on the paper once you know that is what it is.
Around 30 minutes. The number of questions varies by entry level and test form, but it works out to roughly thirty seconds each — which is why the twenty-second decision to abandon a stubborn sequence matters so much.
No. EduTest is a non-calculator test throughout. Students work mentally or on whatever scrap space is provided. This is why estimation and friendly-number rounding are genuine exam skills here rather than shortcuts.
No. Marks are awarded for correct answers and nothing is deducted for incorrect ones, so an unanswered question can only score zero while a guess always has a chance. Every box should be filled before time is called.
Eight families cover most of what appears: constant difference, constant ratio, growing difference, shrinking difference, alternating rules, square and cube numbers, add-the-previous-two, and two interleaved series. Working through them in a fixed order — gaps first, then ratio, then alternation, then number families — converts guessing into recognition.
No. EduTest has never released its real papers, so genuine past papers do not exist publicly and anything sold as one is a reconstruction. What works is well-matched practice written to the same level, style and timing. We explain the distinction in our EduTest past papers guide.
Use real displays — a sports ladder, a weather table, a train timetable, a supermarket receipt — and ask the four question types that actually appear: what is the total, what is the difference, what is the average, and which changed most. The reading habit transfers directly; the source of the table does not matter.
Little and often. Ten short sequences a day for three months will move a Numerical Reasoning score more than a weekly two-hour block, because recognition is built by frequency. Add one timed section a week from about week seven to build the speed.
Six to twelve months before the test is the usual window, with a twelve-week intensive phase at the end. This section in particular benefits from an early start, since recognition accumulates slowly and cannot be crammed in the final fortnight.
No. The five sections are timed and standardised separately, then considered together, so one weak section lowers the overall picture without ending the attempt. Telling your child this before the day matters, because students who believe otherwise often turn one bad section into two.
Reading about the rule families changes nothing on its own. Ten short sequences a day, a timed section each week and an honest error log are what move this number — and you can start the first paper today at no cost.
