Free Numerical Ability Reasoning Tests: Practice Questions, Examples & Expert Tips to Boost Your Score

If you are going to sit an aptitude test as part of the job selection process then it will almost certainly include some numerical aptitude questions. 

Both the proportion of numerical questions and the type of questions will depend on the job you are applying for.

Obviously, if the job involves dealing with figures on a day-to-day basis then you can expect the proportion of these questions to be quite high.

 

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This will include a wide range of jobs such as those dealing with money, buying, selling, processing invoices, processing orders, administration, engineering, science, statistics and numerical analysis of any sort.

However, even if figure work does not form a substantial part of the job, you will probably still have to answer questions of this type as most employers want some indication of your level of numeracy.

Numerical ability questions are invariably multiple-choice and strictly timed. You will not usually be allowed to use a calculator unless this is expressly stated in the question.

These questions can be classified into four types:

 

Numerical Computation

These questions test your ability to use the basic principles of arithmetic like addition, subtraction, multiplication and division.

They may also use mathematical terms and methods such as decimals, percentages, ratios, roots, fractions, powers and exponents.

These questions make no attempt to test your reasoning abilities.

The method you need to get the correct answer will be obvious and to score well on these questions you will simply need to make quick and accurate calculations.

 

Numerical Estimation

These questions test your ability to make quick estimates of the answers to fairly straightforward numerical questions.

To score well on these questions you will need to make quick approximations of the answer.

You must avoid the trap of working out the answer exactly, which will take up too much time and prevent you from answering enough questions to get a good score.

Numerical estimation is key in many craft and technical jobs where the ability to quickly and accurately estimate material quantities is essential.

 

Numerical Reasoning

Information is provided that requires you to interpret it and then apply the appropriate logic to answer the questions.

In other words, you need to work out how to get the answer rather than what calculations to apply.

Sometimes the questions are designed to approximate the type of reasoning required in the workplace.

The questions will often use very specific illustrations, for example the question may present financial data or use information technology jargon.

However, an understanding of these areas is not required to answer the question.

Number series questions can also be classified as numerical reasoning questions.

These types of question are very commonly used in graduate and managerial selection.

 

Data Interpretation

The ability to interpret data presented in tables, graphs and charts is a common requirement in many management and professional jobs.

If you are applying for a job which involves analysis of or decision-making based on numerical data then you can expect to answer this type of question.

 

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Numerical Ability Reasoning Test Example Questions

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Numerical Computation

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Evaluate:

$\dfrac{3}{4} \times \dfrac{16}{9}$

a) $\tfrac{3}{16}$
b) $\tfrac{4}{9}$
c) $\tfrac{4}{3}$
d) $\tfrac{16}{27}$

The correct answer is: c) $\tfrac{4}{3}$

Multiply numerator × numerator and denominator × denominator:

$\tfrac{3×16}{4×9} = \tfrac{48}{36} = \tfrac{4}{3}$

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A jacket costs £120. It is discounted by 25% and then a further 10%.

What is the final price?

a) £78
b) £81
c) £90
d) £96

The correct answer is: b) £81.

First discount: £120 × 0.75 = £90. Second discount: £90 × 0.9 = £81.

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Simplify: $(2^3 \times 2^4) \div 2^2$

a) $2^3$
b) $2^5$
c) $2^7$
d) $2^9$

The correct answer is: b) $2^5$

Laws of exponents: $2^3 × 2^4 = 2^7$

Then divide by $2^2$

$2^7 ÷ 2^2 = 2^5$

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Numerical Estimation

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Estimate: $198 \times 51$

a) ~8,000
b) ~9,000
c) ~10,000
d) ~12,000

The correct answer is: b) ~9,000.

Round: $200 × 50 = 10,000$. Adjust down slightly since both are rounded up → closer to 9,000.

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A car travels 248 km in 3.9 hours.

Estimate the average speed.

a) ~50 km/h
b) ~60 km/h
c) ~70 km/h
d) ~80 km/h

The correct answer is: c) ~70 km/h.

Approximate: $250 ÷ 4 = 62.5$

Since the actual time (3.9 h) is slightly less than 4, the real speed will be slightly higher than 62.5 km/h. That makes ~70 km/h the closest estimate.

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Estimate the square root of 950.

a) 29
b) 30
c) 31
d) 32

The correct answer is: c) 31.

$30^2 = 900$, $31^2 = 961$.

950 is closer to 961, so ~31.

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Numerical Reasoning

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A firm’s sales grew from £4.8m to £6m in one year.

What is the percentage increase?

a) 20%
b) 22%
c) 24%
d) 25%

The correct answer is: a) 25%.

Increase = £1.2m. Percentage = $1.2 ÷ 4.8 × 100 = 25$.

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A box contains red, blue, and green balls in the ratio 3:5:7.

If there are 75 balls total, how many are green?

a) 25
b) 30
c) 35
d) 40

The correct answer is: c) 35.

Ratio parts = 3 + 5 + 7 = 15

Each part = 75 ÷ 15 = 5

Green = 7 × 5 = 35

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A train covers 180 km at 60 km/h, then another 180 km at 90 km/h.

What is the average speed for the whole journey?

a) 70 km/h
b) 72 km/h
c) 75 km/h
d) 80 km/h

The correct answer is: b) 72 km/h.

Time = $180÷60 + 180÷90 = 3 + 2 = 5$ hours.

Distance = 360 km. Average = $360 ÷ 5 = 72$ km/h.

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Data Interpretation

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A company’s quarterly profits (in £m) were: Q1 = 12, Q2 = 15, Q3 = 18, Q4 = 15.

What was the average quarterly profit?

a) £14m
b) £15m
c) £15.5m
d) £16m

The correct answer is: b) £15m.

Total = 12 + 15 + 18 + 15 = 60.

Average = 60 ÷ 4 = 15.

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A bar chart shows staff by department:

HR = 20
Finance = 30
IT = 50

What % of staff are in IT?

a) 40%
b) 45%
c) 50%
d) 55%

Correct answer is: c) 50%.

Total = 20 + 30 + 50 = 100.

IT = 50/100 × 100 = 50%. 

Half of the 100 staff are in IT.

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A line graph shows sales rising from 200 units in January to 320 in June.

What is the average monthly increase?

a) 20 units
b) 22 units
c) 24 units
d) 25 units

The correct answer is: b) 24 units.

Increase = 320 – 200 = 120. Over 5 months = 120 ÷ 5 = 24 units per month.

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Final Thoughts

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Numerical ability and reasoning tests are a common feature of graduate recruitment and professional selection processes. They are designed not just to check whether you can perform calculations, but to see how quickly and accurately you can apply logic, interpret data, and make sound decisions under pressure.

The best way to prepare is through practice. By working on a variety of question types — from computation and estimation to reasoning and data interpretation — you’ll build both speed and confidence. Even if the role you’re applying for doesn’t focus heavily on numbers, employers want to see evidence of strong analytical and problem-solving skills.

Remember: accuracy matters, but so does efficiency. Practise timed tests, review worked solutions carefully, and focus on developing strategies for eliminating wrong answers quickly. With consistent preparation, you’ll be in a strong position to perform well on the day and maximise your overall test score.