Oficjalne przykładowe pytania EPSO — Rozumowanie liczbowe

Klucz EPSO A — 3 040 872

Obliczenia. The table gives GDP per head, so both totals have to be built first. Eurozone: 306.70 × 20 987 = 6 436 712.9. Japan: 127.62 × 26 609 = 3 395 840.6. The difference is 3 040 872.3, which lands on option A to the last euro million. Rounding either product to three significant figures pushes you into B.

Klucz EPSO D — USA

Obliczenia. Five divisions, population over area: EU-25 116.9 · EU-15 120.8 · eurozone 124.7 · USA 30.4 · Japan 33.8. USA is lowest. The trap is Japan, which has the smallest population of the five but nowhere near the lowest density.

Klucz EPSO B — 7.42 million

Obliczenia. The only item that needs the footnotes: EU-25 is EU-15 plus ten named states, so the ten hold 454.56 − 380.36 = 74.20 million between them, and 74.20 / 10 = 7.42. Nothing in the numbered columns says the difference is ten countries; the note under the table does.

Klucz EPSO A — 7.82

Obliczenia. Two of the densities from item 2, subtracted: 124.67 − 116.85 = 7.82. The options sit 0.22 apart, so both divisions have to be carried to two decimals before subtracting. Working to one decimal gives 7.8 or 8.0 and puts A and B in play.

Klucz EPSO D — USA

Obliczenia. Population times GDP per head, in € millions: USA 8 730 829 · EU-25 8 618 458 · EU-15 8 257 616 · eurozone 6 436 713 · Japan 3 395 841. USA leads EU-25 by 1.3 percent, so this is the one item where an eyeball answer is genuinely unsafe: the population column favours the EU-25, the per head column favours the USA, and only the product settles it.

Klucz EPSO D — 3:1

Obliczenia. GDP is not in the table, but it can be recovered: R&D spend divided by R&D share of GDP. Netherlands 6 075 / 0.0182 = 333 791, Finland 3 725 / 0.0334 = 111 527. The ratio is 2.99, so 3:1. The same item appears in the AD set below with a fifth option, None of the above, which changes how safe the approximation feels.

Klucz EPSO D — 20 %

Obliczenia. History falls from 120 to 96, so 24 / 120 = 20 %. The 24 % option is the raw drop of 24 titles restated as a percentage, and the 25 % option is 24/96, the fall measured against the wrong year.

Klucz EPSO B — 162 000

Obliczenia. Three cattle rows have to be added, not one: dairy 72, beef 80, dual-purpose 10, so 162 thousand. Option 72 000 is the dairy row alone; 246 000 folds in mixed cropping and livestock, which the table lists separately.

Klucz EPSO D — 40 000

Obliczenia. The per capita column is the lever: 1 500 tonnes of fishery products is 1 500 000 kg, and at 37.50 kg a head that is 40 000 people. Reading 37.50 as thousands of inhabitants gives the 37 500 distractor.

Klucz EPSO B — 42 075 000

Obliczenia. A single addition, 24 256 000 + 17 819 000 = 42 075 000. The five options are 60 000 apart, which is where the item gets its difficulty: this is a test of adding carefully, not of adding.

Klucz EPSO D — 3:1

Obliczenia. Same item as COMP 1, with the fifth option restored. 6 075 / 0.0182 = 333 791 against 3 725 / 0.0334 = 111 527, a ratio of 2.99. Close enough to 3:1 that None of the above is a live temptation, and wrong.

Klucz EPSO C — 3:2

Obliczenia. Germany 41 100 / 0.0245 = 1 677 551, France 24 075 / 0.0215 = 1 119 767. The ratio is 1.498, so 3:2. The word approximately is doing real work here, and it is the only item in either set that uses it.

Klucz EPSO D — 4.25 %

Obliczenia. Three factors compound: GDP, the R&D share of GDP, and the government share of R&D. (1.02 × 2.52 × 31.2) / (2.45 × 31.4) = 1.0425, so 4.25 %. Adding the three percentage changes instead of multiplying them gives roughly 2.2 %, which is option B.

Klucz EPSO D — 1.41 %

Obliczenia. The same chain on Belgium’s row: (1.03 × 1.89 × 23.5) / (1.97 × 22.9) = 1.0141, so 1.41 %. Belgium’s R&D intensity fell while its government share rose, so the two effects nearly cancel and the four wrong options sit 0.10 apart.