The PwC numerical reasoning test is the numerical reasoning part of the timed cognitive assessment PwC runs on the SHL platform at its first stage. The arithmetic is GCSE level, so speed comes from having a fixed method for each question shape rather than from being faster at sums. Read the question before the data, take percentage changes over the original figure rather than the new one, check the units line before you calculate, and know your method within the first quarter of your time budget or move on. The maths itself is rarely where the difficulty sits. Marks go on the wrong row, the wrong base, a missed footnote, and one question that ate 90 seconds and was never worth it.
What the PwC numerical reasoning test covers
It is the numerical part of the cognitive assessment at PwC's first stage, sat alongside inductive and deductive reasoning. PwC states that its online assessment is hosted on the SHL platform and that the cognitive part is an ability test including numerical, inductive and deductive reasoning. It does not publish the question format, the question count or the time limit, so this guide teaches the reasoning rather than inventing a spec. For what PwC does and does not say about the assessment as a whole, see the online assessment guide.
Where the marks actually go
When you mark your own practice, sort the errors rather than counting them. They fall into five shapes, and only one of them is arithmetic.
- Wrong row or wrong column. The table has four regions and three years; you answered for the right year in the wrong region.
- Wrong base. You calculated the change over the new figure instead of the original one.
- Missed units. The table was in thousands and the answer was wanted in millions, or the footnote said one column excluded VAT.
- Answered a different question. It asked for the percentage point difference and you gave the percentage change, or it asked for the largest increase and you gave the largest value.
- Time. You got it right, eventually, and lost two easier questions doing so.
Read the question before you read the data
This single habit removes most of the first two failure modes. A chart is designed to be interesting; the question needs one or two numbers out of it. If you study the chart first, you absorb everything and then have to search it again anyway.
- Read the question stem and note what is being asked for: a value, a change, a share, a rank.
- Note the unit the answer must be in, and the unit the data is in. If they differ, write the conversion down before you start.
- Go to the chart or table and find only the figures named in the stem. Two numbers, usually. Point at them.
- Then calculate. Not before.
The methods, with the numbers shown
Percentage change: divide by the original
A company's revenue rises from £480m to £552m. The change is £72m. The percentage change is 72 ÷ 480 = 0.15, so a 15% increase. The wrong turn is 72 ÷ 552 = 13.04%, and 13% will usually be sitting there as an available answer because it is the error the question is built to catch.
Note what that means going the other way. If revenue falls from £552m back to £480m, the fall is 72 ÷ 552 = about 13.0%, not 15%. A rise and the fall that undoes it are different percentages, because the base changed.
Reverse percentages: when the figure already includes the change
A reverse percentage question gives you the figure after the change and asks for the figure before it. You divide, you do not multiply back.
Revenue after a 15% rise is £552m. Before the rise it was 552 ÷ 1.15 = £480m. The wrong turn is 552 × 0.85 = £469.2m, which is close enough to look plausible and is wrong. Check it the fast way: 480 × 1.15 = 552, so the answer stands.
Falls work the same way. Headcount fell 12% to 1,320. Before the fall it was 1,320 ÷ 0.88 = 1,500. The wrong turn, 1,320 × 1.12 = 1,478, fails the check because 1,478 × 0.88 = 1,301, not 1,320.
Percentage points are not percentages
A margin moves from 27% to 32%. That is a rise of 5 percentage points. It is also a rise of 5 ÷ 27 = about 18.5% in relative terms. Both are correct answers to different questions, and the question stem tells you which one it wants. If it says "percentage points", subtract. If it says "percentage increase", divide by the original.
A percentage of a percentage: multiply the decimals
Total revenue is £480m. One region accounts for 40% of it, and one service line is 35% of that region's revenue. That service line in that region is 0.40 × 0.35 = 14% of the total, which is £67.2m. The wrong turns are adding the two percentages to get 75%, or taking 35% of the whole £480m and answering £168m.
Ratios: find one part first
A ratio question is only ever asking you to find the value of one part. A team of 96 splits 5:3:4 between three offices. There are 12 parts, so one part is 8, and the offices get 40, 24 and 32. Add them back to 96 as a check.
The harder version gives you one side rather than the total. The ratio of associates to managers is 3:5, and there are 240 managers. One part is 240 ÷ 5 = 48, so there are 144 associates and 384 people in total. The wrong turn is applying the part-to-whole fraction to a part: 240 × 3/8 = 90, which answers a question nobody asked.
Averages, and the question that asks which grew fastest
A weighted average is not the average of the averages. Three offices bill £4m, £6m and £20m at margins of 30%, 25% and 10%. Averaging those three margins gives 21.7%, and it is the wrong answer. The profits are £1.2m, £1.5m and £2m, so the combined margin is 4.7 ÷ 30 = 15.7%. The large office drags the figure down because it carries two thirds of the revenue, and any average that ignores the weights ignores that.
The same trap runs the other way when a question asks which row grew fastest. Fastest means the largest percentage change, not the largest jump: +40 on a base of 200 is a 20% rise, while +60 on a base of 600 is only 10%. Work down the column dividing each change by its own starting figure, because the biggest number in the change column is often not the answer.
Thousands, millions, and the footnote under the table
This is the cheapest mark on the page and the easiest to drop. A table headed "£000s" showing 4,820 means £4.82m, not £4,820m. A table where one column is headed "m" and the rest are in thousands is a deliberate trap, and so is a footnote reading "figures in thousands except where stated". Before you calculate anything, say the unit out loud in your head: four point eight two million.
| What the question asks | What you do | The wrong turn it is built to catch |
|---|---|---|
| Percentage increase or decrease | (new − old) ÷ old | Dividing by the new figure |
| The value before a rise of 15% | figure ÷ 1.15 | Multiplying by 0.85 |
| The value before a fall of 12% | figure ÷ 0.88 | Multiplying by 1.12 |
| A share of a share | 0.40 × 0.35 = 14% of the whole | Adding the two percentages, or applying the second to the total |
| A share from a ratio | One part = a known quantity ÷ its own number of parts | Applying the part-to-whole fraction to a single part |
| Movement from 27% to 32% | 5 percentage points, or about 18.5% relative | Calling a 5 point move a 5% change |
| A combined margin across several units | Total profit ÷ total revenue | Averaging the individual margins |
| Which row grew fastest | Each change ÷ that row's own starting figure | Picking the largest absolute increase |
Reading charts and tables under time pressure
Chart questions fail at the reading stage far more often than the calculating stage. Three specific habits fix most of it.
On a stacked bar, read the gap, not the top
A bar reaches 90 with a segment boundary at 62. The upper segment is 28, not 90. Every stacked chart question that asks about a middle or top segment is testing whether you subtracted the boundary below it.
Check what the axis points actually are
If the question asks about the change from 2023 to 2024 but the x-axis runs in half-years, the point next to 2023 is the first half of 2024, not the year. Count the tick marks once rather than assuming the spacing.
Read the legend before the bars
Legends are commonly ordered top-down while a stack is built bottom-up, so the series printed first in the legend can be the segment at the bottom of the bar. Read a 100% stacked bar as 45/35/20 off the legend order when the stack actually runs 20/35/45 and every figure after that is wrong, with no arithmetic error anywhere to warn you. Check the legend against one labelled segment before you read a single value off the chart.
The five-second sanity check
Before you commit an answer, round everything and see whether the result is in the right neighbourhood. Ten per cent is the tool, because you can take it off any number instantly.
- 18.5% of 6,400. Ten per cent is 640, twenty per cent is 1,280, so the answer sits just under 1,280. If the calculator says 1,184, good. If it says 11,840 or 118, you have slipped a decimal.
- A bar that has clearly not doubled cannot be a 400% increase. It cannot even be a 100% one.
- A part cannot exceed its whole. If a segment you calculated is larger than the total above it, you read the wrong boundary.
- A reverse percentage answer must reproduce the figure you were given. 480 × 1.15 = 552. One multiplication, and the question is closed.
The abandon rule, which is a timing decision and not a maths one
Work out your budget before you start: total time divided by number of questions. PwC does not publish a question count or a time limit, only that the cognitive test is timed, so work your budget out on the day from what the screen tells you. On our own 36-minute, 24-question test it comes to 90 seconds each. Then apply two cutoffs.
- At about 20 seconds, you should know the method. Not the answer, the method: which two figures you need and what you will do with them. If you do not know that yet, the question is not going to get easier, and you should move on.
- At about 1.5 times your budget, you stop regardless. A question you have half solved feels like a sunk cost. It is not. The next question is worth exactly the same and you have not read it yet.
Running out of time is usually not a question of difficulty. It is a question of two items quietly taking four minutes between them. The abandon rule gives up a question you might eventually have got, deliberately, in exchange for the ones further down the paper you would otherwise never reach.
How to practise for the PwC numerical reasoning test
Do untimed sets until percentage change, reverse percentages and ratios come out without thinking, then do three timed sets in a row and compare your error log across them. If the untimed error rate was 1 in 12 and the timed rate is 1 in 5, the gap is pacing rather than method, and more untimed practice will not close it. If both rates are the same, the clock is not your problem and you should go back to the methods.
When you review, do not just look at what you got wrong. Write down which of the five failure modes caused it. A page of "wrong base, wrong base, missed units, wrong base" tells you what to drill in a way that a bare score never will. Our practice tests run the full 36 minutes and are timed, with a worked explanation on every question that names the wrong turn as well as the right method, and the first full test is free.
Calculator or no calculator
PwC's own description says nothing about whether a calculator is provided, so practise both ways: one set with it and one set without. The rounding check above is what saves you if there is not one, and it is also the fastest way to catch a mistyped figure when there is.
Multiple choice or interactive
Nobody outside PwC can tell you whether its questions are multiple choice or interactive. Our own questions are our design, and they are interactive by choice, so you drag a line, resize a pie segment or set a bar rather than picking from four options. That removes the option of eliminating answers by eye, which is the point, because the underlying reading skill is identical either way.
If numerical is your weakest of the three, it is worth remembering that PwC's own description names all three: numerical, inductive and deductive reasoning. Nothing published says how they are weighted or scored, so give deductive and inductive the same share of your practice. They reward it at least as quickly as this one does, and the online assessment guide sets out what each of them involves.
Frequently asked questions
What level of maths do you need for a numerical reasoning test?
GCSE level arithmetic is enough: percentages, percentage change, reverse percentages, ratios, fractions, weighted averages and reading values off charts and tables. Tests of this kind lean on arithmetic rather than algebra, geometry or advanced statistics, though PwC does not publish what its own questions contain. The difficulty is not the maths itself but doing it accurately and quickly while reading data correctly, so practice should focus on method and pace rather than on learning new mathematics.
How do you calculate percentage change?
Subtract the old value from the new one, then divide by the old value. If revenue rises from 480 to 552, the change is 72 and 72 divided by 480 is 0.15, a 15% increase. The most common error is dividing by the new value instead, which gives 13.04% and is usually offered as a tempting wrong answer. Percentage change is always measured against where you started.
What is a reverse percentage question?
A reverse percentage question gives you a figure after a change has already been applied and asks what it was before. You divide rather than multiply back. A figure of 552 after a 15% rise was 552 divided by 1.15, which is 480. A headcount of 1,320 after a 12% fall was 1,320 divided by 0.88, which is 1,500. Check by applying the change forward again: the result must reproduce the figure you were given.
What is the difference between percentage points and percentage change?
If a margin moves from 27% to 32%, that is a rise of 5 percentage points, found by subtracting. It is also a relative rise of about 18.5%, found by dividing 5 by 27. Both are correct answers to different questions. Read the stem: if it says percentage points, subtract; if it says percentage increase, divide by the original figure.
How long should you spend on one numerical reasoning question?
Divide the total time by the number of questions to get your budget, then hold yourself to it. PwC does not publish a question count or a time limit, so work yours out on the day from what the screen tells you. Our own tests are 24 questions in 36 minutes, which is 90 seconds each. A useful discipline is to know your method within about 20 seconds and to abandon any question at roughly 1.5 times your budget, because two overrunning questions cost more marks than they can ever win.
Does the PwC online assessment include numerical reasoning?
Yes. PwC states that its online assessment is hosted on the SHL platform and that the cognitive assessment is an ability test including numerical, inductive and deductive reasoning. PwC publishes neither a question count nor a time limit for it, so treat exact figures quoted elsewhere as unsourced.
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