Numerical Reasoning Test: 10 Basic Arithmetic Questions With Answers (2026 Guide)
Justyna Wachulka-Chan
- August 6, 2026
- 18 minutes read
Table of Contents
The basic arithmetic section of a numerical reasoning test is not hard maths. It is percentages, ratios and rates under a clock that gives you roughly 45 to 90 seconds a question — and that clock, not the arithmetic, is what costs candidates their marks. Below are ten questions in the format you’ll actually face, each with a full worked answer and an explanation of the specific trap built into every wrong option.
I’ve sat one of these myself. An SHL-style numerical paper was the gate I had to get through for the KPMG graduate scheme, and in the twenty years since — nearly a decade in finance, then ten years coaching CIMA and ACCA candidates — I’ve watched the same thing happen over and over. Bright people, entirely capable of the maths, walking out of a 25-minute test convinced they’d failed at arithmetic. They hadn’t. They’d failed at pacing, and they’d been caught by wrong answers that were designed to look right.
- Basic arithmetic is the opening section of most SHL-style numerical reasoning tests — and the section where the most marks quietly disappear.
- Almost nobody fails on the maths. They fail on the clock, at roughly 45–90 seconds a question.
- Every wrong option is engineered around one specific, predictable error — wrong base, wrong group, wrong conversion.
- Ten worked questions below, the trap in each explained, plus the three costliest mistakes and a 48-hour plan.
What does “basic arithmetic” actually mean in a numerical reasoning test?
Employers aren’t testing whether you can do long division. In my experience, what they’re really measuring is four things:
- Whether you spot which operation a question actually requires — not the one that looks obvious
- Whether you can work accurately at speed; most questions allow 45–90 seconds each
- Whether you can hold a multi-step calculation together without losing the thread
- Whether you avoid the specific calculation traps built into the wrong-answer options
That last one matters far more than candidates realise, and it’s the point I’d most want you to take from this post. In a well-built psychometric test, every wrong answer corresponds to a specific, common mistake — using the wrong operation, dividing by the wrong base, forgetting to convert a percentage to a decimal, applying a ratio the wrong way round. If you make that mistake, there’s an answer sitting there waiting for you, and it feels reassuring precisely because it’s there. That single design feature is what makes these tests feel so much harder than the underlying arithmetic. It’s also why marking your own practice “7 out of 10” tells you almost nothing, while working out which trap caught you tells you everything.
Which employers use SHL numerical reasoning tests?
SHL is the largest test publisher in the graduate market and powers a substantial share of the numerical reasoning tests candidates actually encounter — across the Big Four, investment banks, energy and FMCG companies, large parts of the public sector and major retailers. Its assessments appear under names such as Verify G+ and Verify Interactive.
Public-sector recruitment is worth a specific mention, because it varies. The Civil Service uses a numerical test among its suite of online assessments for many roles, but the graduate Fast Stream has moved to a different two-test format. Read the advert, not the folklore.
The practical consequence is the useful bit, and it’s the advice I give every candidate who asks me which employer to prepare for: don’t. Someone preparing for a Deloitte numerical test, a Goldman Sachs assessment and a Shell online test is largely preparing for the same format. Practise the format rather than the employer, and one block of preparation serves every application in your pipeline. Other publishers you may meet — TalentQ, cut-e and Cappfinity — use different timing and adaptive rules, but the underlying arithmetic is the same.
One thing I’d insist on: read your invitation email properly. It almost always names the publisher, the time limit and whether a calculator is permitted, and those three facts should shape everything about how you prepare. SHL also publishes its own free practice tests — worth twenty minutes purely to see the interface before test day, though the difficulty sits below the real thing.
Ten basic arithmetic practice questions with worked answers
Work through each one before you read the solution — and time yourself at 60 seconds a question, because that pressure is the entire point of the exercise. A calculator is permitted on most SHL numerical tests, but I’d do the first pass without one. It exposes exactly where your mental arithmetic is slow.
Part 1 — Operations, fractions and percentages
Question 1: Multi-rate calculation (Easy)
A delivery firm charges £12 per parcel for the first 20 parcels in a consignment, and £9 per parcel for every parcel after that. What is the total cost of sending 34 parcels?
A. £306
B. £348
C. £366
D. £408
Answer: C — £366
Split the consignment before you calculate anything. The first 20 parcels cost 20 × £12 = £240 The remaining 14 parcels cost 14 × £9 = £126 Total: £240 + £126 = £366
The traps: £408 is 34 × £12 — the higher rate applied to everything. £306 is 34 × £9 the lower rate applied to everything. £348 is the two rates swapped round: 20 parcels at £9 plus 14 at £12 Read which rate attaches to which block before you multiply anything.
Question 2: Comparing fractions, decimals and percentages (Easy)
Which of the following is the largest value?
A. 3/5
B. 62%
C. 5/8
D. 0.63
Answer: D — 0.63
Convert everything into a single format before comparing. As decimals: 5/8 = 0.625, 0.63 = 0.63, 62% = 0.62, 3/5 = 0.6. The largest is 0.63.
The traps: 5/8 sits just 0.005 below the answer, which is close enough that anyone eyeballing rather than converting will pick it. Test writers choose these gaps deliberately. Convert first — it takes ten seconds and removes the guesswork entirely.
Question 3: Estimation under time pressure (Medium)
Which value is closest to 19.6% of 2,480?
A. 375
B. 486
C. 520
D. 620
Answer: B — 486
Don’t calculate it precisely. Round to friendly numbers: 20% of 2,500 is 500. Your answer must sit slightly below 500, because both the percentage and the base were rounded up. Only 486 fits. The exact value is 486.08.
Why this matters: Options spaced this widely are a deliberate signal that estimation is intended. Calculating precisely here burns 40 seconds you’ll want later. This is the habit I’d drill first if you only had an hour: scan the gaps between the options before you start. Wide gaps mean estimate; narrow gaps mean calculate.
Part 2 — Ratios, rates and averages
Question 4: Ratio and proportion (Easy)
A project team of 45 people is made up of analysts, associates and managers in the ratio 5:3:1. How many associates are on the team?
A. 5
B. 9
C. 15
D. 25
Answer: C — 15
Add the ratio parts first: 5 + 3 + 1 = 9 parts in total. Divide the team by the number of parts: 45 ÷ 9 = 5 people per part. Associates hold 3 parts, so 3 × 5 = 15.
The traps: 25 is the analyst figure — the right method applied to the wrong group, and the single most common ratio error I see under time pressure. 5 is the manager figure. 9 is the number of parts, mistaken for a headcount.
Question 5: Rates and time conversion (Medium)
A machine produces 450 units per hour. How many units does it produce in 3 hours and 20 minutes?
A. 1,350
B. 1,440
C. 1,500
D. 1,800
Answer: C — 1500
Convert the time into hours properly: 20 minutes is one third of an hour, so the period is 3⅓ hours, not 3.2. Then 450 × 10/3 = 1,500 units.
The traps: 1,440 is 450 × 3.2 — reading “20 minutes” as “0.2 hours”. This is the one that catches my students out most, and it turns up constantly in real tests. 1,350 ignores the extra 20 minutes altogether, and 1,800 rounds the period up to a full 4 hours. Minutes divide by 60, never by 100.
Question 6: Weighted averages (Medium)
A team of 8 analysts scored an average of 72 on an assessment. A team of 12 associates scored an average of 82. What is the average score across all 20 people?
A. 76
B. 77
C. 78
D. 79
Answer: C — 78
You cannot average the averages when the group sizes differ. Work back to totals: (8 × 72) + (12 × 82) = 576 + 984 = 1,560. Divide by the combined headcount: 1,560 ÷ 20 = 78.
The traps: 77 is (72 + 82) ÷ 2 — averaging the averages, which quietly assumes both groups are the same size. Because the larger group scored higher, the true answer has to sit above the midpoint. I’d sense-check the direction before touching the arithmetic; here it eliminates three of the four options on its own.
Part 3 — Percentages in business contexts
Question 7: Percentage change (Medium)
A company’s annual revenue fell from £5m to £4m. What was the percentage decrease?
A. 7.2%
B. 15%
C. 17.6%
D. 85%
Answer: B — 15%
Work out the change in absolute terms: £5m − £4m = £1m. Then divide by the original figure, not the new one: 0.72 ÷ 4.8 = 0.15, which is 15%.
The traps: 17.6% comes from dividing by the new figure (0.72 ÷ 4.08) — the classic wrong-base error, and it looks plausible enough that most candidates never re-check it. 85% is the new revenue as a proportion of the old, which answers a different question entirely.
Question 8: Reverse percentages (Medium)
After a 12% increase, a graduate salary is £33,600 What was the salary before the increase?
A. £29,400
B. £29,568
C. £30,000
D. £37,632
Answer: C — £30,000
The new salary represents 112% of the old one. To reverse it, divide rather than subtract: £33,600 ÷ 1.12 = £30,000 Check it forwards: £30,000 × 1.12 = £33,600
The traps: £29,568 is £33,600 minus 12% — taking the percentage off the wrong base, which is the defining reverse-percentage error. £37,632 adds 12% instead of removing it. My rule: whenever a question hands you the figure after a change, you divide.
Question 9: Margin versus mark-up (Medium)
A retailer buys an item for £40 and sells it for £50 What is the profit margin, expressed as a percentage of the selling price?
A. 10%
B. 20%
C. 25%
D. 80%
Answer: B — 20%
Profit is £50 − £40 = £10 Margin is measured against the selling price: £10 ÷ £50 = 0.20, or 20%.
The traps: 25% is the mark-up — £10 ÷ £40 measured against cost. Both are legitimate business measures, which is exactly why the question specifies which one it wants. I spent years in finance watching people use these two interchangeably in real reporting, so I have some sympathy — but in a test, margin uses selling price and mark-up uses cost. Read the final clause before you divide.
Question 10: Successive percentage changes (Medium)
A company’s revenue rises by 20% in year one, then falls by 20% in year two. What is the overall change across the two years?
A. 4% decrease
B. 4% increase
C. No change
D. 20% decrease
Answer: A— 4% decrease
Percentage changes multiply; they don’t add. Take a starting value of 100: after a 20% rise it becomes 120, and a 20% fall from 120 is a fall of 24, leaving 96. That’s a 4% decrease overall. As a single calculation: 1.20 × 0.80 = 0.96.
The traps: “No change” is the intuitive answer and it’s wrong, because the 20% fall is applied to a larger base than the 20% rise was. “4% increase” catches anyone who gets the magnitude right but the direction wrong, and “20% decrease” catches anyone who lets the fall cancel the rise outright. A rise followed by an equal-percentage fall always leaves you below where you started — and the reverse order gives you exactly the same result.
What are the three mistakes that cost the most marks?
Across every candidate I’ve coached, the same three errors account for the overwhelming majority of lost marks — and none of them is a maths problem.
1. Dividing by the wrong base
Percentage change is always measured against the starting figure; margin is measured against selling price; mark-up against cost. Under time pressure, candidates reach for whichever number is closest to hand, and the answer they produce is sitting right there in the options waiting to reassure them. My advice is almost embarrassingly simple: before you divide, name the base in your head. It takes one second and it removes an entire category of error.
2. Answering the question you expected rather than the one asked
Ratio, rate and profit questions almost always hand you more than one plausible group or measure. In the scripts I mark, the arithmetic is frequently correct — it’s simply been applied to analysts rather than associates, or to cost price rather than selling price. Re-read the final clause of the question before you select an option. I’d argue it’s the highest-value ten seconds in the whole test.
3. Refusing to abandon a question
There’s no negative marking on the overwhelming majority of these tests, and every question carries the same weight. Spending three minutes rescuing one hard question costs you three or four easy ones later in the paper. If you’re 60 seconds in with no clear route, estimate, flag it and move on. The candidates I’ve seen score best are almost never the ones who got everything right — they’re the ones who finished.
How should you prepare in 48 hours?
Most test invitations arrive within a few days of application and give candidates only 48 to 72 hours to complete the assessment. If that’s where you are, this is the sequence I’d follow — and I’d resist the urge to start with practice questions:
- Hour 1 — Read your invitation email properly. Note the publisher, the time limit, the number of questions and whether a calculator is allowed. Divide the time by the questions so you know your per-question budget before you start.
- Hours 2–4 — Drill the four mechanics that appear in almost every paper: percentage change, reverse percentages, ratios and weighted averages. These four cover a disproportionate share of basic arithmetic marks.
- Hour 5 — Sit one full timed set without pausing. Untimed practice builds false confidence, and the entire difficulty of these tests is the clock.
- Hour 6 — Review only the questions you got wrong, and write down which of the three mistakes above caused each one. Patterns emerge fast, and they're usually the same one or two errors repeating.
- Before the test — Set up a quiet room, a stable connection, paper, a pen and a calculator if permitted. I've lost count of the number of candidates who lost marks to logistics rather than arithmetic.
If you take one thing from this guide, make it the review step. Scoring your practice tells you where you are; naming the trap that caught you is what actually moves your numerical reasoning test score between the first attempt and the third.
Numerical reasoning tests: your questions answered
What is a numerical reasoning test?
A numerical reasoning test is a timed assessment used by employers to measure how accurately and quickly you can work with numerical information — arithmetic, percentages, ratios, and data presented in tables and charts. It measures applied reasoning under time pressure rather than mathematical knowledge, which is why strong maths graduates sometimes score poorly on their first attempt.
Are you allowed a calculator in an SHL numerical reasoning test?
In most SHL numerical reasoning tests a calculator is permitted, and the questions are designed on that assumption. Rules vary by employer and test version, so your invitation email is the authoritative source. Practise both ways: with a calculator to match test conditions, and without one to expose weak mental arithmetic.
What is a good score on a numerical reasoning test?
Scores are usually reported as percentiles against a comparison group rather than as a raw mark. Many graduate employers set their sift somewhere around the 50th to 70th percentile, and the most competitive schemes sit higher again. The comparison group matters as much as the score — being benchmarked against graduate applicants is a tougher standard than against the general population.
How long is a numerical reasoning test?
Most sit between 15 and 30 minutes, typically working out at 45 to 90 seconds per question. Some formats are adaptive, adjusting difficulty as you answer, which means the number of questions isn't fixed. Work out your per-question budget from your invitation email before you begin.
Is there negative marking on aptitude tests?
The overwhelming majority of graduate aptitude tests do not use negative marking, which means an unanswered question and a wrong one score identically. Always answer everything, even if the final few are educated guesses. If your invitation email states otherwise, follow it — but this is rare.
Can you actually improve at numerical reasoning tests?
Yes, and more than most candidates expect. Raw reasoning ability moves slowly, but the things that lose marks — recognising question types, choosing the right base, knowing when to estimate rather than calculate, and pacing across the paper — all improve quickly with deliberate practice. Most candidates see their largest gain between their first and third timed set.
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About the Author
Justyna Wachulka-Chan
Justyna Wachulka-Chan is a CIMA-qualified finance professional with over 20 years of experience in accounting and finance, including roles at KPMG. She founded Practice Tests Academy in 2016, helping 35,000+ CIMA and ACCA students pass their exams through structured practice questions and mock exam resources.
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