Numerical Reasoning: The Complete Strategy Guide

Numerical reasoning divides candidates. For some of you, it's no big deal. You've been acing maths tests since you were four, and you don't really see what the fuss is all about. For others, it's the test you dread more than anything else. You thought you'd finally put maths behind you when you finished your GCSEs and breathed a sigh of relief. But now it is one of the obstacles between you and that Main Board pass.

The good news is that the maths in the numerical reasoning test isn't that complicated. It just needs to be done at speed, and that rewards practice above all else. The better news is that preparation here pays twice. The mental maths skills you develop for this test is exactly what you will rely on in the planning exercise at Main Board.

In this guide I will break the test down in full. The format, the strategy that works, and all fifteen question types you will meet, each with an interactive example you can try as you read.

What Is the Numerical Reasoning Test?

Numerical reasoning is one of the psychometric tests you sit at AOSB. It measures how accurately you can work with numbers, read data from tables and charts, and solve problems under time pressure.

No calculator is allowed, and you will sit it at both Briefing and Main Board. You are expected to answer 50 multiple-choice questions in 30 minutes, which gives you a limit of 36 seconds per question.

The Format

You are shown an exhibit containing numerical data. Its exact nature varies, but it often takes the form of a pie chart, bar chart, line graph, or data table. For each exhibit you are shown four questions, one at a time, and you must choose the correct answer out of four options.

The example below shows what this looks like in practice. Try it for yourself.

That exhibit is a simple one, chosen so the format is clear on a first read. What you sit at Briefing and Main Board is harder than this on every front. The exhibits are busier, more columns being one obvious example, and the questions asked are tougher. The tests on the Officer Ready platform are built to match.

The exhibit remains unchanged for several questions at a time. This means the first question on each exhibit will usually take slightly longer, as you find your bearings in the data. By the time you reach the remaining questions you will already know where everything sits, and you will answer more quickly.

The Skills It Draws On

Performing well draws on a handful of core skills:

• Accurate mental arithmetic across addition, subtraction, multiplication and division
• Confidence with percentages, ratios and proportions
• The ability to find the one figure you need in a cluttered table or chart
• A habit of estimating an answer before committing to the exact calculation
• Composure under the clock, so that pace never turns into carelessness

Notice that none of those need maths beyond GCSE level. What they need is speed, and speed is built through practice.

Why It Matters

Officers work with numerical information constantly. Budgets, logistics, timings, distances, and resource allocation all land on your desk, and the ability to process numbers quickly and accurately is essential for sound decision-making.

The assessors know this, which is why the test carries real weight in your overall psychometric picture. But there is a second reason to take it seriously.

The planning exercise at Main Board requires speed, distance, and time calculations under pressure, without a calculator. Every hour you spend building mental maths speed for this test is an hour spent preparing for the Plan Ex as well. Preparation here genuinely pays twice.

The Strategy: Eight Rules for Test Day

The way you approach the test will differ according to personal preference. Some candidates prefer to study the exhibit before turning to the first question. Others read the question first, and only then go looking for the figures they need.

You will need some trial and error on practice questions before you strike upon a method that feels natural. But whichever you choose, it is vital to know exactly what your method is before arriving at Westbury. Trying to work it out in the real test is a recipe for disaster.

I suggest you follow these eight rules as you work through your practice tests. They apply to every question, regardless of what the data describes.

1. Read the Question Before the Exhibit

Read the question before you read the exhibit. This lets you focus immediately on the data that matters for the question in front of you. The exhibit will often contain far more data than you need, so knowing exactly what you are looking for saves time on almost every question.

2. Watch for the Small Print

Some exhibits carry a condition that sits away from the main data, often in a footnote or a label. It might be a fee that applies below a certain threshold, a rate that only holds for certain customers, or figures quoted in thousands.

These details are easy to skim past, and the wrong options are usually built from the answers of those who missed them. So before you calculate, ask whether any of the exhibit's small print applies. Look at the example below.

The danger with details like this is that they are not needed for every question. A question about a 12-pallet shipment clears the threshold, and the footnote never comes into play. Answer two or three questions where it does not matter and it is easy to stop looking for it.

Treat every new question on an exhibit as a fresh check of the small print.

3. Watch the Clock

You have exactly 36 seconds per question. In practice you should aim to work a little faster, averaging 30 seconds or under where possible. Some questions will naturally take longer than others, so don't obsess over any single question.

It does help to have a few yardsticks memorised before the test, so you can keep track of your speed. The table below sets them out.

If you reach question 21 in under 12:00 and question 31 in under 18:00, you can relax in the knowledge that you are working at the right speed.

Candidates often report that the test ramps up in difficulty in the later stages. If you are comfortably ahead of time during the first half, you are buying yourself additional time for the harder questions to come.

4. Prioritise Correctness Over Speed

Work at a speed that is appropriate for you, even if that means guessing the last few questions. It should feel slightly rushed, but never so quick that you are making arithmetic slips or misreading the data.

Candidates report that the earlier questions feel easier, so you are more likely to get them right than the ones that come later. The later questions in psychometric tests are typically there to separate the higher-scoring candidates. Sacrificing marks on the easier questions in the hope of reaching the harder ones is a losing strategy.

The arithmetic of guessing also matters. A blind guess in verbal reasoning has a 1 in 3 chance of being correct. Here it is 1 in 4, so every question you surrender to a blind guess is worth even less.

Put another way, a question you work out properly is worth three blind guesses, since a properly worked answer will be correct around three times in four. Rushing to reach every question, and dropping rushed answers along the way, is a trade that almost never pays.

There is one caveat, and it comes next.

5. Get Comfortable with Estimations

In verbal reasoning, a guess has essentially a 1 in 3 chance of being correct however you arrive at it, and first impressions on difficult questions often mislead. The statement that feels right is frequently the trap. The same applies in abstract reasoning, where a shape cannot be roughly worked out.

In numerical reasoning the opposite holds. A quick estimation significantly improves the odds that a guess is correct. To see how, try the example below.

Estimation also has a second job. It acts as a check on the answers you do work out in full. If your estimate said the answer should be a little over 25% and your exact working produces 55%, you have slipped somewhere, and the estimate has caught the error before the test did.

In the same spirit, if the answer you work out is not among the four options, you have made a mistake. Go back and recheck rather than forcing the nearest option.

As you reach the later, more difficult questions, you should consciously choose whether to work out the real answer or estimate it. Consider a scenario. You have roughly two minutes left and six questions remaining, which gives you two realistic options:

• Estimate all six, at roughly 20 seconds each
• Fully work out one or two, and blind-guess the rest

The table below shows how the two options compare, with pure blind guessing as a baseline. The percentages are rules of thumb rather than exact figures, but they are broadly what candidates achieve in practice.

6. Answer Every Question

This follows from the last rule, but it is worth making explicit. There is no negative marking, so you will not lose marks for an incorrect guess. You are literally leaving marks on the table if you don't answer every question.

Because an estimate is worth so much more than a blind guess here, the switch point deserves more thought than a last-second click-through. As a rule of thumb, the final two minutes is when you should stop working answers out in full and start making educated guesses, meaning quick estimations at roughly 20 seconds each.

Glance at how many questions remain when you get there. Six or fewer and you can estimate them all. Any more, and you should estimate what you can, then reserve the final 15 seconds to click an answer on whatever is left.

A blind click is the last resort, not the plan, but an unanswered question is worse still. It is easy to lose track of time as you rush towards the end, so having a pre-defined switch point is key.

7. Move On If You Get Stuck

At some point you will reach a question that stumps you. When it happens, make a quick estimate, select the closest option, and move on. At worst you have a 1 in 4 chance, and an estimate pushes those odds considerably higher.

More time is unlikely to help much, and it will harm the rest of your test. If an extra minute spent here makes you rushed for the remaining questions, it will almost certainly cost you more marks than it wins.

8. Look for Shortcuts

Because the test is multiple choice, you do not always need to work out the answer at all. You only need to find something that discounts every option except one. Look at the example below.

Finally, a word on the arithmetic itself. Nothing in this test goes beyond GCSE level. There are no operations to learn from scratch and no advanced mathematics of any kind.

What the test actually demands is speed, and mental maths speed can only be built through practice. There is no trick or framework that substitutes for it. Your calculation speed will improve with every test you sit, so that when you arrive at Westbury you know exactly how you will approach the test.

The 15 Question Types

Once you have a strategy in place, you should familiarise yourself with the types of question you will face. The test draws on a set range of operations and processes, including arithmetic, percentages, ratios, fractions, averages, and currency conversions.

After each practice test, work through every question you got wrong and read the explanation of how you could have reached the correct answer. Engaging with this feedback is where most of the improvement happens. It shows you whether your errors come from a particular operation, from misreading the exhibits, or simply from time pressure.

The fifteen types are set out below, each followed by an interactive example. These examples are on the easy side by design, because their job is to show you the type and the trap it sets rather than the difficulty of the real thing. What you sit at Westbury, and what you will find on the Officer Ready platform, is a level harder than this.

Reading the Data

Not every question asks you to calculate. Some test whether you can find your way around the exhibit, asking which month meets a condition, where a gap is widest, or how many rows pass a threshold.

The danger is the half-scan. Because the work is looking rather than arithmetic, it is tempting to check only part of the exhibit, and the wrong options are built from exactly that. Scan every row or month before you commit, including the ones that look unpromising.

Totals & Differences

The backbone of the test. The answer is a number built by adding, subtracting or multiplying figures read straight off the exhibit. No single step is difficult, which is why the traps live in the housekeeping.

Wrong options come from missing a row in a long addition, subtracting the wrong row, or forgetting the final step altogether. When the exhibit prints a total, use it. One subtraction from a printed total is faster and safer than adding every other row by hand.

Parts of a Whole

Part-of-whole questions arrive in every dress. A percentage of a total, a fraction in simplest form, a pie slice turned into a count. The exhibit hands you a whole and asks about a part, or hands you shares and asks for amounts.

The classic wrong answers take the wrong slice, use the wrong whole, or give the complement of the share you were asked for. Before calculating, name the share you need and the whole it belongs to, then check you have both.

Percentage Change

These questions ask how much something rose or fell in percent, and the signature trap is compounding. Two rises of 10% are not a rise of 20%, because the second rise acts on a figure the first has already enlarged.

Whenever a change arrives in steps, multiply the steps together rather than adding them. Be equally careful with the base. A change is always measured against the earlier figure, not the later one.

Reverse Percentage

Here you are given the after figure and asked for the before figure. A price that already includes a surcharge, or a total that has already grown.

The signature slip is subtracting the percentage instead of dividing by the multiplier. Taking 20% off the final figure does not undo a 20% rise, because the rise was 20% of the smaller original. To go backwards, divide by 1.2.

Ratios & Proportions

The answer is a ratio, a split in given parts, or a per-unit rate. The wording fixes a direction, and the signature wrong answer is the correct ratio written the wrong way round.

Simplest form is the other regular. If the raw figures appear among the options, they are almost certainly there because the question asked you to simplify and someone did not.

Averages

The word average looks harmless, and a simple mean often is. The trap arrives when the groups being averaged are different sizes.

An average per doctor, per vehicle or per head must be built as one total divided by another. It is never the mean of the per-group figures, because larger groups carry more weight. If the per-group figures are laid out invitingly in a row, treat that row with suspicion.

Currency Conversion

A rate board and two currencies. Multiplying converts in one direction and dividing converts in the other, and the whole question is knowing which way you are travelling.

If £1 buys Fr 1.10, turning pounds into francs multiplies and turning francs back into pounds divides. The near miss multiplies when it should divide. Watch the other rows of the board too, because grabbing a neighbouring currency's rate is a slip the options will be waiting for.

Units, Scale & Geometry

Watch for questions where the units in the answer differ from the units in the exhibit, or where a shape's measure is being computed. Factor-of-ten slips and perimeter-for-area swaps do steady business here.

The signature trap belongs to scale drawings. Area scales with the square of the scale factor. If 1 cm on a plan is 3 m on the ground, each square centimetre is 9 square metres, not 3.

Costs & Charges

The tariff family. A fixed fee plus a rate per unit, banded prices, a surcharge with a threshold, or two plans to compare at a stated usage.

The signature slip is forgetting the fixed part. A plan with a low rate and a high fee can beat one with the reverse, but only above a certain usage, so both halves of each plan must go into the sum every time.

Speed, Distance & Time

Clock times, speeds and distances, including everything a timetable can throw at you. Two traps do most of the damage.

The first is time arithmetic. 1 hour 50 minutes is 110 minutes rather than 150, and every calculation has to respect the sixties. The second is using the wrong time altogether, most often an elapsed time that includes a wait the question told you to leave out. Decide exactly which minutes count before you touch the distance.

This skill matters well beyond the test, because the same calculations run through the planning exercise. I have written a dedicated speed, distance and time guide covering the formula triangle, the conversions worth memorising, and the drilling that makes them automatic.

Signed Values

Some exhibits carry values pointing in both directions. Over and under budget, profit and loss, money in and money out.

The questions ask for a net figure, and the trap is treating every number as if it pointed the same way. Adding the sizes of all the bars ignores the signs entirely. Set one direction against the other instead, and once you have your net figure, check its direction as carefully as its size.

The types above all turn on finding the right figures and working them accurately. The final three are different. They test judgement rather than arithmetic. Each one plants a claim or comparison that sounds reasonable but does not hold, and the skill being tested is spotting it.

Statement Judgement

A sweeping claim, judged against the whole exhibit. Words like every, all and more than half are the cue, because a claim about every row can only be settled by checking every row.

The planted answer is the one a skim produces. When four of five rows fit the claim, a candidate who stops early ticks true and moves on, and that is exactly what the question is counting on. Check every case before you judge.

Rate vs Count

A rate is not a count. Returns per 1,000 items, completions per cohort, complaints per customer. None of these becomes a number of events until you know the size of the base it acts on, and sometimes the exhibit simply never gives it.

When a question asks which entity had the most of something and the exhibit only supplies rates, resist the pull of the biggest number. If the base is missing, the honest answer is cannot say.

Share vs Count

The two-totals trap. A share and a count can move in opposite directions, because a smaller slice of a bigger pie can still be more pie.

When an exhibit shows shares from two different years or groups, the stem will invite you to read the movement in the share as a movement in the count. Decline the invitation. Work out each count from its own total, then compare the counts.

One last word on the examples above. Each one is lighter than what you will actually sit, so that the type and its trap stand out clearly. In the real test the same trap turns up in a harder question, on a busier exhibit, with the clock running. That is what practice is for.

Target Your Weak Spots

A single dropped mark tells you nothing, because everybody miscalculates under time pressure now and then. But the same question type going wrong test after test is a different matter. That is a genuine area for improvement, and it is worth paying attention to.

This is why every question in the Officer Ready practice bank carries the tag of the question type it belongs to. Here is how that reads at the end of a 25-question short test.

The interesting part sits at the bottom of the breakdown. Reverse Percentage, Rate vs Count and Share vs Count all went wrong. One test on its own proves nothing though, which is what the cross-test view is for.

With every test you sit the the picture becomes clearer. Every skill carries your accuracy across all the questions you have attempted, with a marker showing how the average candidate did on those same questions. Below is how it looks inside the Officer Ready platform.

Now the pattern is hard to miss. This candidate is above average almost everywhere, yet Reverse Percentage has settled at 42% across seven questions. That is not bad luck. That is a weakness that needs to be targeted, and spotting it is the first step.

It is a fixable one too. Working back from a percentage to the figure it came from is a method in its own right, and candidates who drop marks here are usually running the forward calculation in reverse. Walking into the next test already knowing that will do more for this candidate's score than another full test sat in the hope that volume alone sorts it out.

How to Prepare for Numerical Reasoning

Preparation here is a short loop, repeated. Sit a test, find the question type that cost you marks, then work to close that gap before continuing.

• Fix your method first. Decide whether you read the question or the exhibit first, and lock it in before you start practising.
• Sit a full test, timed. Fifty questions in 30 minutes, or a shorter test, with no calculator anywhere near you.
• Review by type. Go through every wrong answer and note if there were any patterns.
• Target the Weak Areas. Go into your next test knowing which question types to look out for.
• Keep practising. Sit enough tests that the method becomes automatic and the your speed picks up.

The Officer Ready tests are built for this. The Full-Length Tests match the real thing at 50 questions in 30 minutes, and the Short Tests offer 25 questions in 15 minutes at the same difficulty. Both sit a level above the examples in this guide, and every question is tagged with its type, so the review step takes care of itself.

Common Mistakes

Almost every mark dropped in this test comes from a handful of repeat offenders. Avoid these pitfalls:

Frequently Asked Questions

Final Thoughts

Whichever camp you started this article in, the path forward is the same. The maths never rises above GCSE level, the question types are knowable in advance, and the strategy is learnable. What remains is speed, and speed is simply banked practice.

And remember the double pay-off. Every hour here sharpens the mental maths you will rely on in the planning exercise, when the pressure is at its highest.