EPSO’s numerical reasoning test gives you ten questions in twenty minutes, a data table and an on-screen calculator. The calculator is not the bottleneck: choosing the right operation is. Almost every question is one of eight calculations — percentages, changes, ratios, averages, growth, currency — and each has a fast route and a classic trap. This page sets out all eight, with a worked example on real EU data for each.
The two data tables
Table A. The six most populous EU Member States (rounded 2025 values)
| Country | Population (millions) | GDP 2025 (€ billion) |
|---|---|---|
| Germany | 83.1 | 4,470 |
| France | 67.4 | 2,979 |
| Italy | 59.0 | 2,258 |
| Spain | 48.9 | 1,687 |
| Poland | 37.8 | 918 |
| Netherlands | 17.6 | 1,180 |
Table B. EU budget 2021–2027 (Multiannual Financial Framework), current prices
| Heading | € billion |
|---|---|
| Single Market, Innovation and Digital | 149.5 |
| Cohesion, Resilience and Values | 426.7 |
| Natural Resources and Environment | 401.0 |
| Migration and Border Management | 25.7 |
| Security and Defence | 14.9 |
| Neighbourhood and the World | 110.6 |
| European Public Administration | 82.5 |
| Total | 1,210.9 |
Rounded values, as used in the EU Testing numerical
questions. GDP per head in shortcuts 2 and 8: Eurostat, nama_10_pc.
The eight shortcuts
1. A percentage of a number: build it from 10% and 1%
Ten per cent is the number with the decimal point moved one place; 5% is half of that; 1% is one more place. Any percentage is a sum of these, and you can check the calculator’s answer in your head.
Show the working
2. Percentage change: always divide by the old value
Change = (new − old) ÷ old. The most common wrong option divides by the new value instead, which gives a smaller number for an increase and a larger one for a fall.
Show the working
The trap: 1,990 ÷ 24,700 = 8.1%, the same rise measured against the new value.
3. Reverse percentage: divide, do not subtract
If a value is the result of a 10% increase, the original is the value ÷ 1.10. Taking 10% off the new value does not give the original, because the 10% was calculated on a smaller base.
Show the working
The trap: 82.5 × 0.90 = 74.25, which is 10% of the new value taken off.
4. Percentage points are not per cent
The difference between two shares is in percentage points. The relative difference between them is in per cent. Questions offer both, so read the unit in the question twice.
Show the working
In per cent, Cohesion’s share is 426.7 ÷ 401.0 − 1 = 6.4% larger. Both are right answers to different questions; the wording decides which one is asked.
5. Ratios: turn them into a decimal and compare
Divide once, then work out the decimal of each ratio offered (4:3 = 1.33, 9:7 = 1.29, 5:4 = 1.25, 6:5 = 1.20). The closest one wins, and you never have to simplify fractions by hand.
Show the working
The trap: 918 ÷ 1,180 = 0.778, the ratio the wrong way round, which matches 7:9.
6. Per head and averages: add the totals, never the averages
A figure per head is a total divided by a population. To combine two countries, add their totals and divide by their combined population. The simple average of two figures per head ignores that the countries differ in size.
Show the working
The trap: Spain alone is €34,499 per head and Poland €24,286; their simple average, €29,392, gives the smaller country the same weight as the larger.
7. Compound growth: multiply, do not add
Three years of 4% growth is 1.04 × 1.04 × 1.04, not 12%. For a quick check, 1 + n·r + (n(n−1)/2)·r² is close enough for the small rates EPSO uses.
Show the working
The trap: 918 × 1.12 = 1,028.2, three years of 4% added instead of multiplied.
8. Currency conversion: check the direction with common sense
A rate quoted as €1 = 4.25 zloty means euros × 4.25 = zloty, and zloty ÷ 4.25 = euros. Before you choose, ask which number must be bigger: there are always more zloty than euros.
Show the working
Common sense check: the zloty figure must be the bigger one.
The eight shortcuts on one page
| Calculation | Shortcut | The trap in the options |
|---|---|---|
| Percentage of | Build it from 10%, 5% and 1% | Decimal point one place off |
| Percentage change | (new − old) ÷ old | Dividing by the new value |
| Reverse percentage | Value ÷ (1 + rate) | Taking the rate off the new value |
| Shares | Points = difference; per cent = ratio − 1 | Points reported as per cent |
| Ratio | Compare decimals | The ratio the wrong way round |
| Per head, averages | Total ÷ total | Average of averages |
| Compound growth | (1 + r)n | n × r |
| Currency | Which number must be bigger? | Multiplying instead of dividing |
Four habits that save more time than any formula
- Estimate first. A rough answer usually rules out three options before you touch the calculator.
- Write the units down. Billions divided by millions give thousands. Many wrong options are the right digits with the wrong magnitude.
- Do not round in the middle. Keep the full figure until the last step; options are often close enough that early rounding picks the wrong one.
- Type a dot for decimals. The on-screen calculator in the AD5 tests accepts only a dot as the decimal separator (see the invitation to test week). If your language writes a comma, practise with a dot.
For the format of the test and its recurring traps, read the EPSO numerical reasoning test, explained; for full EPSO-style questions with five options, the eight worked practice questions.
Practise the shortcuts on real questions
The Numerical Reasoning Focus cards have 180 questions on tables of real EU data, from medium to very hard, each with a worked explanation that names the trap.
Open the Numerical Focus I card → With Premium · try 5 free questions firstFrequently asked questions
What maths do I need for the EPSO numerical reasoning test?
Arithmetic at secondary-school level: percentages and percentage change, percentage points, ratios, averages, figures per head, compound growth and currency conversion. The difficulty is choosing the right operation quickly from a data table, not advanced mathematics.
Can I use a calculator in the EPSO numerical test?
Yes. EPSO provides an on-screen calculator. In the AD5 tests it accepts only a dot as the decimal separator, so practise with a dot if your language uses a comma.
How much time do I have per numerical question?
In the AD5 competition (EPSO/AD/427/26), 20 minutes for 10 questions, so two minutes each. Estimating first and using the shortcuts on this page keeps you within that.
What is the difference between percentage points and per cent?
Percentage points measure the difference between two percentages: a share rising from 33.1% to 35.2% rises by 2.1 percentage points. Per cent measures the relative change: the same rise is 6.4% of the starting share.
How do I avoid the averaging trap?
When you combine groups of different sizes, add the totals and divide by the combined base. Averaging two figures per head or two percentages gives the wrong answer unless the groups are the same size.
Test format as in the AD5 notice EPSO/AD/427/26; data rounded as in the EU Testing numerical questions; as on 29 October 2026.