EPSO numerical reasoning practice is about choosing the right calculation from the information provided. You need to recognise the relevant figures, keep track of their units and check whether the result answers the question. Speed becomes useful when those steps are reliable.
This lesson contains five original exercises with explained answers. They cover percentages, percentage change, weighted averages, currency conversion and work rates. They are independent ReasoningCampus practice material, not official EPSO questions.
Use the same four checks for every question
- Name the quantity you need. Are you finding an amount, a percentage, a change or a rate?
- Identify the correct base. A percentage of a budget and a percentage increase in that budget use different calculations.
- Keep units visible. Write down whether the table shows euros, thousands of euros, people, days or percentages.
- Estimate before choosing. A quick estimate can expose a reversed division or a misplaced decimal point.
EPSO publishes official reasoning samples to help candidates become familiar with the assessment. Use the official EPSO sample tests alongside your own competition notice. The notice and invitation determine the tests, language, timing and permitted resources that apply to you.
Five EPSO numerical reasoning practice questions
Attempt each question before opening the answer. The figures and organisations below are fictional.
1. What percentage of the budget goes to training?
An office allocates its annual development budget as follows. All amounts are in thousands of euros.
| Area | Budget (€000) |
|---|---|
| Communication | 320 |
| Staff training | 480 |
| Digital services | 800 |
What percentage of the total budget is allocated to staff training?
- 20%
- 30%
- 40%
- 60%
Show the answer and explanation
B — 30%. The total is 320 + 480 + 800 = 1,600. The training share is 480 ÷ 1,600 × 100 = 30%.
The common unit cancels in the fraction, so you do not need to multiply every figure by 1,000. Dividing training by digital services would give 60%, but that would compare two areas rather than training with the whole budget.
2. Calculate the increase from the original value
A service processed 480 applications in one month and 552 in the next. By what percentage did the number processed increase?
- 13.0%
- 15.0%
- 72.0%
- 115.0%
Show the answer and explanation
B — 15%. First find the increase: 552 − 480 = 72. Then divide by the original number: 72 ÷ 480 × 100 = 15%.
Using 552 as the denominator gives about 13%, which answers a different question: the increase as a share of the new total. The figure 115% describes the new value as a percentage of the old value, not the increase itself.
3. Combine two groups using their actual sizes
Two teams review files. The table shows how many files each team received and the percentage completed by Friday.
| Team | Files received | Completed |
|---|---|---|
| A | 80 | 85% |
| B | 120 | 70% |
What percentage of all files was completed?
- 75%
- 76%
- 77.5%
- 80%
Show the answer and explanation
B — 76%. Team A completed 80 × 0.85 = 68 files. Team B completed 120 × 0.70 = 84. Together they completed 152 out of 200 files: 152 ÷ 200 × 100 = 76%.
The simple average of 85% and 70% is 77.5%, but the groups have different sizes. The larger group has the lower completion rate, so the combined result must be closer to 70% than to 85%.
4. Read the direction of an exchange rate
A fictional exchange-rate table states €1 = US$1.08. An invoice is US$86,400. What is its value in euros at that rate, ignoring fees?
- €80,000
- €86,400
- €93,312
- €108,000
Show the answer and explanation
A — €80,000. Each euro buys 1.08 dollars. To convert dollars back to euros, divide: 86,400 ÷ 1.08 = 80,000.
Check by converting back: 80,000 × 1.08 = 86,400. Multiplying the dollar amount by 1.08 would use the rate in the wrong direction. Treat the stated rate as part of the exercise; it is not a current market quotation.
5. Work with a rate per person per day
Four staff members process 160 files in five working days. Assume that everyone works at the same constant rate, the files require equal effort and working days have the same length. How many files would six staff members process in three working days?
- 96
- 144
- 192
- 240
Show the answer and explanation
B — 144 files. The original work uses 4 × 5 = 20 person-days. The rate is 160 ÷ 20 = 8 files per person-day. The new team has 6 × 3 = 18 person-days, so it processes 18 × 8 = 144 files.
The team is larger but works for fewer days. Compare total person-days instead of changing only the team size. The constant-rate assumption is given explicitly; without it, this calculation would not necessarily describe a real workplace.
Turn a wrong answer into a useful check
For each mistake, record one short explanation: wrong denominator, wrong unit, unweighted average, reversed exchange rate or incomplete rate conversion. Then repeat the calculation without looking at the worked answer.
Keep percentages and percentage points separate. A rate rising from 40% to 50% increases by 10 percentage points. Relative to the original rate, that is a 25% increase. The wording tells you which measure the question requires.
Should I use a calculator?
Follow the rules for your actual assessment. During practice, learn to set up the calculation before using a calculator, and use estimation to check the output. Do not infer that a calculator is permitted just because an independent practice exercise can be solved with one.
What should I do after these five questions?
Repeat the topic that caused the most errors, then combine different question types. Five questions can identify a skill to practise; they cannot predict an official EPSO result.
Build a balanced EPSO study plan
Continue with EPSO verbal reasoning practice and EPSO abstract reasoning practice. For the wider preparation programme, visit ReasoningCampus EPSO preparation.
Explore the EPSO preparation programme
For an overview of the different assessments and study planning, read our EPSO preparation guide.
ReasoningCampus provides independent preparation and is not affiliated with or endorsed by EPSO or the EU institutions. Official instructions take priority over this practice lesson.
