EPSO Numerical Reasoning Practice

This week’s five questions, with the answers

Real questions from the bank, free and with no account. The set is the same for everyone all week and rotates every Monday.

1. Question 1 of 5Difficulty 4/5
   Table 1 — Public expenditure on education by country

   Country	Population (million) in 2021	Population (million) in 2022
   Austria	8.93	8.98
   Bulgaria	6.53	6.48
   Germany	83.16	83.24
   Ireland	5.07	5.15
   Portugal	10.39	10.42

   Table 2 — Public expenditure on education (€ million)

   Country	Public expenditure on education (€ million) in 2021	Public expenditure on education (€ million) in 2022
   Austria	19,905.3	21,300.8
   Bulgaria	3,103.5	3,374.3
   Germany	163,747.3	174,061.3
   Ireland	11,794.7	12,924.2
   Portugal	10,153.6	10,807.3

   Which country's public expenditure on education per inhabitant grew the most in percentage terms between 2021 and 2022?

   • AIreland
   • BGermany
   • CAustria
   • DBulgaria
   • ENone of the above
   Show the answer and the reasoning

   Correct answer: D — Bulgaria

   Why

   Compare percentage changes, each against its own starting figure: Bulgaria 9.6%; Ireland 7.9%; Austria 6.4%; Germany 6.2%; Portugal 6.1%. Bulgaria leads. The largest rise in € million belongs to Germany (+10,314.0), not to Bulgaria, and per inhabitant the population has to come out first. It takes both tables: population (million) from Table 1 and public expenditure on education (€ million) from Table 2.

   Option by option

   • AYou get Ireland by working with the total instead of the amount per inhabitant. Compare percentage changes, each against its own starting figure: the biggest jump in the table's units is not necessarily the fastest growth.
   • BGermany is what you get by picking the steepest line, which is the largest increase in absolute terms and not in percentage terms. Compare percentage changes, each against its own starting figure: the biggest jump in the table's units is not necessarily the fastest growth.
   • CAustria results from reading the right column of the wrong country. Compare percentage changes, each against its own starting figure: the biggest jump in the table's units is not necessarily the fastest growth.
   • DThat's the one. Compare percentage changes, each against its own starting figure: the biggest jump in the table's units is not necessarily the fastest growth.
   • EThe exact answer, Bulgaria, is listed, so "None of the above" does not apply.
2. Question 2 of 5Difficulty 4/5
   Public expenditure on education by country

   Country	2019		2023
   	Public expenditure on education (% of GDP)	Public expenditure on education (€ million)	Public expenditure on education (% of GDP)	Public expenditure on education (€ million)
   Croatia	5.19	2,894.3	5.26	4,165.2
   Cyprus	5.15	1,205.1	4.95	1,605.7
   Estonia	5.96	1,696.9	6.31	2,407.8
   Latvia	5.94	1,755.8	6.10	2,408.0
   Lithuania	4.54	2,251.6	5.03	3,799.6

   Country indicators, 2023

   Country	Croatia	Cyprus	Estonia	Latvia	Lithuania
   Population (million) in 2023	3.85	0.95	1.37	1.90	2.86
   Area (thousand km²)	56.6	9.3	45.3	64.6	65.3
   Population density (inhabitants per km²) in 2023	68.0	102.2	30.2	29.4	43.8

   By how many percentage points did Estonia's share of the combined public expenditure on education of the 5 countries change between 2019 and 2023, to two decimal places?

   • A-3.30
   • B-0.64
   • C-0.61
   • D-0.57
   • ENone of the above
   Show the answer and the reasoning

   Correct answer: D — -0.57

   Why

   A share is a part over the total of the same year, and a change in percentage points is the difference of two shares. 2019: 1,696.9 ÷ 9,803.7 × 100 = 17.3088%. 2023: 2,407.8 ÷ 14,386.3 × 100 = 16.7368%. 16.7368 − 17.3088 = -0.57 points. The share itself changed by -3.3%, a percentage change, not points. The second table, country indicators, 2023, is not needed.

   Option by option

   • AYou get -3.30 by giving the percentage change of the share instead of its change in percentage points. Work out the share in each year against that year's own total, then subtract. A change in percentage points is a difference of two shares, not a percentage change.
   • BNo standard calculation on this data gives -0.64, close as it is: work it through again and watch the rounding.
   • C-0.61 sits near the answer but does not come from the data by any standard route: recompute step by step and check the rounding.
   • DCorrect. Work out the share in each year against that year's own total, then subtract. A change in percentage points is a difference of two shares, not a percentage change.
   • E-0.57 is among the options: there is no need for "None of the above".
3. Question 3 of 5Difficulty 5/5
   Table 1 — Defence expenditure (€ million) and population

   Country	Population (million) in 2019	Defence expenditure (€ million) in 2019	Population (million) in 2021	Defence expenditure (€ million) in 2021
   Finland	5.52	2,814.5	5.53	2,885.7
   Italy	59.82	23,043.6	59.24	25,006.0
   Latvia	1.92	579.4	1.89	803.6
   Romania	19.41	2,752.1	19.20	3,476.1
   Sweden	10.23	5,737.9	10.38	7,155.0

   Table 2 — Defence expenditure (% of GDP)

   Country	Finland	Italy	Latvia	Romania	Sweden
   2019	1.18	1.28	1.96	1.24	1.21
   2020	1.34	1.36	2.55	1.87	1.35
   2021	1.16	1.36	2.49	1.45	1.34

   By what percentage did GDP per inhabitant in Sweden change between 2019 and 2021 (to two decimal places)?

   • A-9.89%
   • B11.13%
   • C12.60%
   • D22.90%
   • ENone of the above
   Show the answer and the reasoning

   Correct answer: E — None of the above

   Why

   Recover GDP first (amount ÷ % of GDP × 100). Per inhabitant in each year: 2019 46,354.51 €, 2021 51,440.77 €. (51,440.77 ÷ 46,354.51 − 1) × 100 = 10.973%, i.e. 10.97%. The total grew by 12.6%, but the population changed too. The exact figure, 10.97%, is not among the options, so the answer is "None of the above".

   Option by option

   • A-9.89% results from taking the later year as the base of the percentage change, not the earlier one. Work out the amount per inhabitant in each year first: the total and the population both move.
   • B11.13% is what you get by subtracting the population's percentage change from the total's instead of dividing the per-inhabitant figures. Work out the amount per inhabitant in each year first: the total and the population both move.
   • C12.60% comes from working with the total instead of the amount per inhabitant. Work out the amount per inhabitant in each year first: the total and the population both move.
   • DYou get 22.90% by comparing the printed absolute figures instead of the quantity they imply. Work out the amount per inhabitant in each year first: the total and the population both move.
   • ECorrect. The exact figure, 10.97%, is not among the options, so the answer is "None of the above". Trust a result you have checked rather than picking the nearest figure.
4. Question 4 of 5Difficulty 5/5
   Health expenditure by country

   Country	Finland	Germany	Hungary	Italy	Romania
   Population (million) in 2023	5.56	83.12	9.60	59.00	19.06
   Health expenditure (€ million) in 2023	28,555.4	495,273.9	12,626.2	179,265.4	18,490.4
   Health expenditure publicly funded (%) in 2023	81.0	85.7	73.7	73.0	76.2
   Health expenditure (% of GDP) in 2023	10.47	11.64	6.40	8.37	5.76

   Between 2020 and 2021, Finland's health expenditure rose by 7.5%; between 2021 and 2022 it rose by €1,223.7 million; and between 2022 and 2023 it rose by 10.4%, to the 2023 figure in the table. What was it in 2020, in € million (to one decimal place)?

   • A22,534.8
   • B22,922.5
   • C23,182.1
   • D24,060.8
   • ENone of the above
   Show the answer and the reasoning

   Correct answer: B — 22,922.5

   Why

   Write the 2020 figure as X: (X × 1.075 + 1,223.7) × 1.104 = 28,555.4. Undo the steps from the last one back: 28,555.4 ÷ 1.104 = 25,865.40; 25,865.40 − 1,223.7 = 24,641.70; 24,641.70 ÷ 1.075 = 22,922.51, i.e. 22,922.5. Each percentage is undone by dividing by its own factor, at its own place in the chain; adding the two percentages or skipping the fixed amount lands on a trap.

   Option by option

   • A22,534.8 results from applying the percentage to the later figure (taking it off, or adding it back) instead of dividing by the growth factor. Write the chain as an equation in X and undo it from the last step back: a fixed amount is added back or taken off, a percentage is undone by dividing by its own factor.
   • BThat's the one. Write the chain as an equation in X and undo it from the last step back: a fixed amount is added back or taken off, a percentage is undone by dividing by its own factor.
   • C23,182.1 is what you get by adding the two percentage changes instead of chaining them. Write the chain as an equation in X and undo it from the last step back: a fixed amount is added back or taken off, a percentage is undone by dividing by its own factor.
   • DYou get 24,060.8 by undoing the percentages but forgetting the fixed amount. Write the chain as an equation in X and undo it from the last step back: a fixed amount is added back or taken off, a percentage is undone by dividing by its own factor.
   • E22,922.5 is among the options: there is no need for "None of the above".
5. Question 5 of 5Difficulty 5/5
   Rail network length (km)

   Year	Romania	Finland	Czechia	Germany
   2007	7,102	6,308	6,286	28,610
   2010	7,271	6,276	6,394	28,446
   2013	7,076	6,237	6,419	28,312
   2016	7,251	6,373	6,304	27,669

   In 2013, what was Romania's rail freight per km of network, in million tonne-km (to two decimal places)?

   • A0.24
   • B1.95
   • C2.50
   • D2.68
   • ENone of the above
   Show the answer and the reasoning

   Correct answer: E — None of the above

   Why

   This per-unit question joins the chart (freight) and the table (network length). Romania's 2013 freight is 16.7 billion tonne-km, i.e. 16,700 million tonne-km, and its 2013 network is 7,076 km, so 16,700 ÷ 7,076 = 2.3601, i.e. 2.36 million tonne-km per km. That is not listed, so the answer is 'None of the above'. 🎯 A result that is exactly ten times too small or too large almost always means a lost conversion factor.

   Option by option

   • A0.24 has the right digits but loses a factor of ten in the conversion from billion to million tonne-km. One billion is 1,000 million, so 16.7 billion becomes 16,700 million before you divide.
   • B1.95 divides 13.8, Romania's 2016 freight, by the correct 2013 network length of 7,076. Check that the bar you read carries the year in the question; both figures must be for 2013.
   • C2.50 is a nearby figure that a rounding or reading slip lands on, for example misreading the network length. The exact inputs are 16,700 million tonne-km and 7,076 km, and 16,700 ÷ 7,076 = 2.36, so 2.50 is too high.
   • D2.68 divides Romania's 2013 freight by 6,237, which is Finland's 2013 network length in the next column. When you move from the chart to the table, confirm the column heading says Romania.
   • ECorrect. Romania's 2013 freight is 16.7 billion tonne-km (16,700 million) and its 2013 network is 7,076 km; 16,700 ÷ 7,076 = 2.3601, i.e. 2.36. No option shows 2.36, so 'None of the above' is the answer; your calculation, not the nearest option, decides.