Question Templates
Master the patterns behind every EPSO reasoning question — numerical formulas, text comprehension, and visual sequences.
Why understanding templates gives you a real advantage
Every EPSO numerical reasoning question is built from a template — a specific mathematical pattern. There are only a handful of these patterns, and they repeat across every competition. Candidates who recognize the pattern can solve the question in 30 seconds. Candidates who don't are guessing.
When you train without understanding templates, you are memorizing answers instead of learning methods. The next competition will use different numbers, different countries, different years — but the same templates. If you mastered the template, you solve it instantly. If you didn't, you're back to guessing.
Candidates who master all 5 templates consistently score 85%+ on the numerical section. Those who don't average 45%.
The 5 Mathematical Templates
Percentage Change
Numerical ReasoningCalculates the variation between two values expressed as a percentage. Used when EPSO asks "by what percentage did X change between year A and year B?"
Formula
In plain words
Take the difference between the new value and the old value. Divide that difference by the old value. Multiply by 100 to get a percentage.
Worked Example
Spain's GDP was 1,208 billion in 2018 and 1,329 billion in 2022.
What was the percentage change in Spain's GDP?
Dividing by the final value (1,329) instead of the starting value (1,208) gives 9.1% -- wrong but close enough to seem right.
Common Traps
- Dividing by final value instead of initial
- Forgetting to multiply by 100
- Confusing absolute change with percentage
Related Concepts
Ratio
Numerical ReasoningCalculates how many times one value contains another. Used when EPSO asks "what is the ratio of X to Y?"
Formula
In plain words
Simply divide the first number by the second number. The result tells you how many times bigger (or smaller) the first is compared to the second.
Worked Example
Germany exported 1,576 billion in goods. France exported 586 billion.
What is the ratio of German exports to French exports?
"Ratio of A to B" means A / B, not B / A. Swapping them gives 0.37 -- the inverse.
Common Traps
- Inverting numerator and denominator
- Using sum instead of ratio
- Confusing ratio with percentage
Related Concepts
Weighted Average
Numerical ReasoningCalculates an average where some values count more than others. Used when EPSO gives per-capita data alongside population data and asks for a combined figure.
Formula
In plain words
Multiply each value by its "importance" (weight). Add up all those results. Then divide by the total of all the weights. Think of it as: bigger countries should count more when calculating an EU average.
Worked Example
CO2 per capita: France 4.5t (pop. 67M), Germany 7.3t (pop. 83M).
What is the weighted average CO2 per capita?
A simple average gives (4.5 + 7.3) / 2 = 5.9. But Germany is bigger -- its higher emissions should pull the average up more. The weighted answer (6.05) is higher.
Common Traps
- Using simple average instead of weighted
- Wrong weights applied
- Forgetting to divide by sum of weights
Related Concepts
CAGR (Compound Annual Growth Rate)
Numerical ReasoningCalculates the steady annual growth rate over a period. Used when EPSO asks "what was the annual growth rate?"
Formula
In plain words
Divide the final value by the starting value. Then take the "nth root" of that result (where n is the number of years). Subtract 1 and multiply by 100. Think: "if growth had been perfectly steady each year, what would that yearly rate be?"
Worked Example
Poland's GDP: 498 billion in 2018, 658 billion in 2022 (4 years).
What was the compound annual growth rate?
Total growth / years = 32.1% / 4 = 8.0% is WRONG. Compounding means each year builds on the last. The compound rate (7.2%) is always lower than this naive division.
Common Traps
- Dividing total growth by years (simple instead of compound)
- Using wrong number of years
- Confusing total growth with annual rate
Related Concepts
Percentage of Total
Numerical ReasoningCalculates what share of a total is represented by one part. Used when EPSO asks "what percentage of total X does Y represent?"
Formula
In plain words
Divide the part you care about by the whole total. Multiply by 100. That gives you the percentage. Think: "out of everything, how much does this one piece represent?"
Worked Example
EU budget: Agriculture 54.8B, Cohesion 53.9B, Research 18.7B, External 13.2B.
What percentage of the EU budget goes to Research?
Dividing the total by the part (140.6 / 18.7 = 7.52) gives "how many times bigger the total is" -- not a percentage.
Common Traps
- Dividing total by part instead of part by total
- Using part/(total-part) instead of part/total
- Forgetting to multiply by 100
Related Concepts
Verbal, Digital Skills & EU Knowledge
Comprehension, inference, digital literacy, and institutional knowledge — the text-based components of the EPSO CBT.
Visual Pattern Families
Geometric sequences following hidden rules. Learn to recognise the 8 core pattern families.
Ready to Practice?
Now that you understand the templates, apply your knowledge with real EPSO-style questions.
Start practicingQuestion Templates
Master the patterns behind every EPSO reasoning question — numerical formulas, text comprehension, and visual sequences.
Why understanding templates gives you a real advantage
Every EPSO numerical reasoning question is built from a template — a specific mathematical pattern. There are only a handful of these patterns, and they repeat across every competition. Candidates who recognize the pattern can solve the question in 30 seconds. Candidates who don't are guessing.
When you train without understanding templates, you are memorizing answers instead of learning methods. The next competition will use different numbers, different countries, different years — but the same templates. If you mastered the template, you solve it instantly. If you didn't, you're back to guessing.
Candidates who master all 5 templates consistently score 85%+ on the numerical section. Those who don't average 45%.
The 5 Mathematical Templates
Percentage Change
Numerical ReasoningCalculates the variation between two values expressed as a percentage. Used when EPSO asks "by what percentage did X change between year A and year B?"
Formula
In plain words
Take the difference between the new value and the old value. Divide that difference by the old value. Multiply by 100 to get a percentage.
Worked Example
Spain's GDP was 1,208 billion in 2018 and 1,329 billion in 2022.
What was the percentage change in Spain's GDP?
Dividing by the final value (1,329) instead of the starting value (1,208) gives 9.1% -- wrong but close enough to seem right.
Common Traps
- Dividing by final value instead of initial
- Forgetting to multiply by 100
- Confusing absolute change with percentage
Related Concepts
Ratio
Numerical ReasoningCalculates how many times one value contains another. Used when EPSO asks "what is the ratio of X to Y?"
Formula
In plain words
Simply divide the first number by the second number. The result tells you how many times bigger (or smaller) the first is compared to the second.
Worked Example
Germany exported 1,576 billion in goods. France exported 586 billion.
What is the ratio of German exports to French exports?
"Ratio of A to B" means A / B, not B / A. Swapping them gives 0.37 -- the inverse.
Common Traps
- Inverting numerator and denominator
- Using sum instead of ratio
- Confusing ratio with percentage
Related Concepts
Weighted Average
Numerical ReasoningCalculates an average where some values count more than others. Used when EPSO gives per-capita data alongside population data and asks for a combined figure.
Formula
In plain words
Multiply each value by its "importance" (weight). Add up all those results. Then divide by the total of all the weights. Think of it as: bigger countries should count more when calculating an EU average.
Worked Example
CO2 per capita: France 4.5t (pop. 67M), Germany 7.3t (pop. 83M).
What is the weighted average CO2 per capita?
A simple average gives (4.5 + 7.3) / 2 = 5.9. But Germany is bigger -- its higher emissions should pull the average up more. The weighted answer (6.05) is higher.
Common Traps
- Using simple average instead of weighted
- Wrong weights applied
- Forgetting to divide by sum of weights
Related Concepts
CAGR (Compound Annual Growth Rate)
Numerical ReasoningCalculates the steady annual growth rate over a period. Used when EPSO asks "what was the annual growth rate?"
Formula
In plain words
Divide the final value by the starting value. Then take the "nth root" of that result (where n is the number of years). Subtract 1 and multiply by 100. Think: "if growth had been perfectly steady each year, what would that yearly rate be?"
Worked Example
Poland's GDP: 498 billion in 2018, 658 billion in 2022 (4 years).
What was the compound annual growth rate?
Total growth / years = 32.1% / 4 = 8.0% is WRONG. Compounding means each year builds on the last. The compound rate (7.2%) is always lower than this naive division.
Common Traps
- Dividing total growth by years (simple instead of compound)
- Using wrong number of years
- Confusing total growth with annual rate
Related Concepts
Percentage of Total
Numerical ReasoningCalculates what share of a total is represented by one part. Used when EPSO asks "what percentage of total X does Y represent?"
Formula
In plain words
Divide the part you care about by the whole total. Multiply by 100. That gives you the percentage. Think: "out of everything, how much does this one piece represent?"
Worked Example
EU budget: Agriculture 54.8B, Cohesion 53.9B, Research 18.7B, External 13.2B.
What percentage of the EU budget goes to Research?
Dividing the total by the part (140.6 / 18.7 = 7.52) gives "how many times bigger the total is" -- not a percentage.
Common Traps
- Dividing total by part instead of part by total
- Using part/(total-part) instead of part/total
- Forgetting to multiply by 100
Related Concepts
Verbal, Digital Skills & EU Knowledge
Comprehension, inference, digital literacy, and institutional knowledge — the text-based components of the EPSO CBT.
Visual Pattern Families
Geometric sequences following hidden rules. Learn to recognise the 8 core pattern families.
Ready to Practice?
Now that you understand the templates, apply your knowledge with real EPSO-style questions.
Start practicing