Numerical reasoning tests: example questions and explanations

Got a numerical reasoning test coming up? We’ve got you.

We’ll run through some numerical reasoning test practice questions, share the answers and explain how we worked things out. Once you’ve read through the example questions and our walkthrough solutions, you’ll know what to look for when tackling this type of test.

The table below sets out the revenue, costs and profit for GoToSpace, a company offering commercial flights to space.

The company hired new marketing executives in 2025 and projected a 10% increase in revenue as a result. The salaries agreed for the new hires has led to a £5m increase in variable costs. Assuming fixed costs are the same, what was the projected profit for 2025?

• £488.4m
• £484.3m
• £393.0m
• £483.4m
• None of the above

The first thing to do is work out what the table is showing and how the columns relate to each other. The data in the table tells us that the Profit column is equal to Revenue - (Fixed costs + Variable costs).

After this, we need to work out what a 10% increase in revenue would be. 2024’s revenue figure was £904m. To calculate a 10% increase, we need to multiply £904m by the decimal equivalent of 110% (that’s the current amount, ie. 100%, and the 10% increase put together). The decimal equivalent of 110% is 1.1.

£904m x 1.1 = £994.4m (the revenue)

Alternatively, you could calculate 10% of £904m by multiplying £904m x 0.1 (the decimal equivalent of 10%). That gives you £90.4m. You would then add the £90.4m onto £904m to get the same result, £994.4m.

That’s the revenue sorted. To calculate the profit, we now need to work out what the fixed costs and variable costs are so that we can subtract them from the revenue.

The question tells us that we should assume the fixed costs stayed the same, which means we can take this figure straight from the table in the 2024 row (£361m).

As for variable costs, the question says that the new hires have increased variable costs by £5m. To calculate the new variable costs, we need to add £5m to the 2024 figure (£145m) – making the new variable cost total £150m.

£361m + (£145m + £5m) = £511m (the total costs)

For the last step, we need to subtract the total costs (£511m) from our revenue (£994.4m) to calculate the profit.

£994.4m - £511m = £483.4m (the profit, AKA the answer)

The table below summarises the working hours and performance of four employees at PaperSells Limited last year.

Employees work five days a week and 48 weeks per year.

Bonuses are allocated annually and are dependent on performance. ‘Average’ performers earn 50% of their maximum bonus percentage, ‘Good’ performers receive 75% of it and ‘Excellent’ performers get their maximum bonus percentage.

How much did Anisha make last year, including her bonus?

• £5,040
• £39,900
• £30,240
• £25,155
• £30,000

For this question, we only need to look at Anisha's stats. So, ignore all the information about her colleagues in the table.

First let's work out Anisha’s baseline salary, excluding her bonus. Here, we need to take her hourly rate (£17.50) and multiply it by the number of hours she works (30) and the number of work weeks per year (48).

£17.50 x 30 x 48 = £25,200 (Anisha’s baseline salary)

Now, we need to work out her bonus. Because she received an 'Excellent' rating on her performance review, she's entitled to her maximum bonus. The table tells us that Anisha’s max bonus is 20%.

To calculate Anisha’s bonus, we need to work out 20% of £25,200. To do this, we first need to convert 20% to a decimal by dividing it by 100 (20 ÷ 100 = 0.2). Now that we know that 20% is 0.2, we need to multiply 0.2 against Anisha’s full earnings (£25,200).

0.2 x £25,200 = £5040 (Anisha’s bonus)

We now need to add Anisha’s baseline salary and bonus together.

£25,200 + £5040 = £30,240 (how much Anisha made last year AKA the answer)

The table below summarises the working hours and performances of four employees at PaperSells Limited last year.

Employees work five days a week and 48 weeks per year.

Bonuses are allocated annually and are dependent on performance. ‘Average’ performers earn 50% of their maximum bonus percentage, ‘Good’ performers receive 75% of it and ‘Excellent’ performers get their maximum bonus percentage.

"Hang on, haven't we had this question already?" Keep reading and you'll notice the difference. It's common to receive multiple questions based on a similar scenario. Make sure you always read everything thoroughly each time and don't assume it's the same!

Including bonuses, which employee earned the least last year?

• Jacob
• Anisha
• Sandy
• Graham
• Anisha & Graham

Here you're repeating the steps you used for Anisha, but with all employees.

Unlike Anisha, not all employees received 100% of their bonus which makes things a little trickier. For example, Sandy received an ‘Average’ rating in her performance review meaning she’ll earn 50% of her maximum bonus percentage (15%). You need to add in an extra step to calculate her bonus. Multiplying 0.5 (50%) by 0.15 (15%) tells us that Sandy’s new bonus percentage is 0.075 (7.5%).

Check below to see how we calculate the variable rate for the differing performance review scores.

Earnings including bonus:

Jacob = 48 x 35 x 20 x (1 + 75% x 25%) = £39,900
Anisha = 48 x 30 x 17.5 x (1 + 100% x 20%) = £30,240
Sandy = 48 x 32.5 x 15 x (1 + 50% x 15%) = £25,155
Graham = 48 x 15 x 45 x (1 + 50% x 30%) = £37,260

Once you’ve worked out how much each person earns, you need to compare salaries. Sandy’s final number is the lowest, therefore Sandy earns the least.

Numerical reasoning tests help employers assess your mathematical abilities and how well you interpret the information given to you. Running through numerical reasoning test practice questions will help you prepare for any similar questions that could come up at an assessment centre or in a different test environment.