Cognitive Tests
Free Numerical Reasoning Test: Practice Questions & Answers
Percentages, ratios, and business numbers under a clock. Not advanced mathematics, but applied arithmetic tested at a pace designed to catch anyone doing it from scratch.
Written by the founder · Ten years in HR and recruitment · Published August 6, 2026 · Updated October 28, 2026 · 11 min read
Key takeaways
- Numerical reasoning tests applied arithmetic in a business context (percentages, ratios, unit costs), not advanced mathematics.
- Most questions fall into a handful of recurring calculation types; recognizing the type is faster than solving from first principles each time.
- The most common preventable error is skipping the instruction screen. Without knowing the question count and time limit, you cannot pace yourself at all.
- Estimation and elimination often beat exact calculation under time pressure.
- A small set of mental shortcuts for percentages and ratios saves real time across an entire test.
How employers use a test score
Hiring processes differ. A score may determine whether you advance, contribute to a wider assessment, or provide topics for an interview. Ask the recruiter how this particular assessment is used; do not assume a low score will be overlooked.
The examples below are original practice questions for learning the format. They are not copied from an employer test, and your practice result is not a validated hiring score.
Practice 1: percentage of an amount
A department has a $2,400 training budget. It spends 15% on materials. How much is that? A: $160 · B: $240 · C: $360 · D: $400.
Answer and explanation
C: $360. Ten percent is $240 and five percent is $120. Add them: $240 + $120 = $360. Option B stops after calculating 10%; always check the requested percentage.
Practice 2: percentage increase
Revenue rises from $60,000 to $78,000. What is the percentage increase? A: 18% · B: 23.1% · C: 30% · D: 130%.
Answer and explanation
C: 30%. The increase is $18,000. Divide by the ORIGINAL $60,000, then multiply by 100: 18,000 / 60,000 × 100 = 30%. Dividing by the new revenue gives 23.1%, which answers a different question.
Practice 3: scaling a ratio
Four identical gift packs require 200 g of filling. How much filling do ten packs require? A: 80 g · B: 400 g · C: 500 g · D: 800 g.
Answer and explanation
C: 500 g. One pack requires 200 / 4 = 50 g. Ten packs require 10 × 50 = 500 g. The number of packs increases by a factor of 2.5, so the filling must do the same.
Practice 4: unit cost
A supplier charges $180 for twelve notebooks. At the same unit price, what do seven notebooks cost? A: $15 · B: $84 · C: $105 · D: $126.
Answer and explanation
C: $105. Each notebook costs $180 / 12 = $15. Multiply by seven: $105. Option A is only the intermediate unit price, not the requested total.
Practice 5: margin versus markup
A product costs $80 to buy and sells for $100. What is its gross profit margin as a percentage of the selling price? A: 20% · B: 25% · C: 80% · D: 125%.
Answer and explanation
A: 20%. Gross profit is $100 − $80 = $20. Margin uses the selling price: $20 / $100 × 100 = 20%. The 25% answer uses cost as the denominator; that is markup, not margin.
What is actually being measured
Numerical reasoning tests do not measure how advanced your mathematics is. They measure whether you can extract the right numbers from a business scenario (a budget, a growth rate, a cost breakdown) and apply basic arithmetic to them correctly, quickly, and under pressure. The math involved rarely goes beyond percentages, ratios, and simple multiplication or division.
The difficulty is almost never the calculation itself. It is doing that calculation for the twentieth time in fifteen minutes, with the numbers embedded in a paragraph you also have to read correctly.
The recurring question types
- Percentage of a value: "what is 15% of $2,400." The most basic form, and the fastest to answer once the shortcut below is automatic.
- Percentage change: "revenue grew from $60k to $78k; what was the increase." Requires finding the difference, then expressing it as a percentage of the starting value.
- Ratios and proportional scaling: "a recipe for 4 servings uses 200g; how much for 10 servings." Find the per-unit rate, then scale it.
- Unit cost: "$180 for 12 units; what is the cost per unit." A single division, disguised inside a sentence.
- Discounts and margins: final price after a percentage discount, or profit margin as a percentage of selling price.
Once you can name which of these a question is, you already know the operation required. That recognition is most of the speed advantage practice actually builds.
Shortcuts worth automating
- To find 10% of a number, move the decimal point one place left. 5% is half of that. 15% is 10% plus 5%. Nearly every percentage question can be built from these three moves faster than long multiplication.
- To find a percentage change, do not calculate the new value from scratch. Subtract, then divide the difference by the original value.
- For ratios, find the value of "one part" first, then multiply. Scaling from one unit is almost always faster than trying to jump straight to the target quantity.
- Round aggressively when scanning the answer options first. If the choices are $180, $220, $340, and $410, you often do not need an exact answer. You need to know which bracket it lands in.
Look at the options before you calculate
If the four answer choices are far apart, a rough estimate is often enough to identify the correct one, and it is considerably faster than computing an exact figure you did not need.
The most preventable mistake
The error I see most often is not mathematical at all. Candidates arrive focused, sometimes too focused, and move straight past the instruction screen. They start answering without having registered how many questions the test contains, how long they have, or what the format is going to be.
That single omission removes any possibility of pacing. If you do not know whether you are facing twelve questions or thirty, you cannot judge whether ninety seconds on the one in front of you is sensible or ruinous. The candidates who handle timing well are not calmer or quicker than everyone else. They simply know what race they are running before they start it.
Read the brief twice
Check four things before the first question: how many questions there are, how long you have in total, whether you can return to a question you have skipped, and whether a calculator is permitted. It costs thirty seconds and it determines how you should approach everything after it.
Where time actually gets lost
More time is lost to misreading the question than to the arithmetic itself. "Percentage increase" and "percentage of the new total" are different calculations that use the same numbers. Mixing them up produces a confident, wrong answer.
- Identify exactly what is being asked before doing any calculation. The final price, the change, and the difference itself are three different targets.
- Note which value is the "before" and which is the "after" in a change question. Reversing them flips the sign of the answer.
- When a table is involved, confirm the units in the header before reading numbers out of it. Thousands, percentages, and raw counts get mixed in the same table more often than expected.
The one thing worth doing beforehand
When someone I know tells me they have a numerical reasoning test on Thursday, my answer is the same every time, and it has nothing to do with mathematics. Practice. Then practice again.
Practice can help you recognize recurring calculations and manage your time. Start with the worked examples, then try a fresh set without looking at the answers. Compare your mistakes, not just your scores.
Improvement on these exercises is not a guarantee of a particular employer-test score or a job offer. Use the practice to identify what you need to review.
Frequently asked questions
Can I use a calculator?
Follow whatever the platform explicitly allows. Some permit an on-screen or physical calculator; others rely on mental math and simple numbers by design. If it is not stated, ask the recruiter before the test begins.
Do I need to know advanced formulas?
No. Nearly everything in a standard numerical reasoning test is built from percentages, ratios, and basic arithmetic. Advanced formulas rarely appear outside specialist quantitative roles.
How is this different from a data interpretation test?
Numerical reasoning questions are typically self-contained word problems. Data interpretation questions require reading a chart or table first, then combining several values from it, which is a related but distinct skill covered in its own guide.
Practice more numerical questions. Formats and scoring vary between employers.
Practice numerical reasoning free