EPSO Numerical Reasoning Sample Questions with Worked Solutions

1. Question 1

   NPV calculation — discount rate 8%

   Year	Cash flow (€)	Discount factor	Present value (€)
   0	−1,200,000	1.0000	−1,200,000
   1	+350,000	1/1.0800	+324,074
   2	+400,000	1/1.1664	+342,936
   3	+450,000	1/1.2597	+357,228
   4	+500,000	1/1.3605	+367,512
   NPV	—	—	≈ +191,750

   An EU programme office is appraising a 4-year capacity-building project. The upfront investment in year 0 is €1,200,000. Net cash inflows are €350,000 in year 1, €400,000 in year 2, €450,000 in year 3 and €500,000 in year 4. Using a discount rate of 8% per year, what is the project's Net Present Value (NPV), and is the project accepted under the standard NPV>0 rule? (Use 1.08^1=1.0800, 1.08^2=1.1664, 1.08^3=1.2597, 1.08^4=1.3605.)

   1. A. NPV ≈ +€191,800 — accepted
   2. B. NPV ≈ +€500,000 — accepted
   3. C. NPV ≈ −€96,300 — rejected
   4. D. NPV ≈ +€38,200 — accepted
   Show answer and explanation

   Correct answer: A — NPV ≈ +€191,800 — accepted

   PV of inflows = 350,000/1.08 + 400,000/1.1664 + 450,000/1.2597 + 500,000/1.3605 = 324,074 + 342,936 + 357,228 + 367,512 = 1,391,750. NPV = 1,391,750 − 1,200,000 ≈ +€191,750 ≈ +€191,800 → positive, project accepted. Option B sums undiscounted inflows minus the investment without discounting; C uses 12% discount; D averages cash flows incorrectly.

2. Question 2

   Currency Allocation and Exchange Rates

   Currency	Allocation %	Rate at allocation	Rate at payment
   EUR	45%	1.00	1.00
   USD	25%	1.10	1.15
   GBP	20%	0.85	0.88
   CHF	10%	0.95	0.98

   An EU programme has a €200 million budget allocated across 4 currencies for procurement: 45% in EUR (no conversion), 25% in USD, 20% in GBP, and 10% in CHF. At the time of allocation, exchange rates were: 1 EUR = 1.10 USD, 1 EUR = 0.85 GBP, 1 EUR = 0.95 CHF. At payment time, the EUR strengthened: 1 EUR = 1.15 USD, 1 EUR = 0.88 GBP, 1 EUR = 0.98 CHF. The non-EUR portions were locked in foreign currency at allocation time. What is the EUR-equivalent of the total budget at payment time, rounded to the nearest €100,000?

   1. A. €194,700,000
   2. B. €196,300,000
   3. C. €192,500,000
   4. D. €198,100,000
   Show answer and explanation

   Correct answer: A — €194,700,000

   EUR portion: €90M (unchanged). USD: €50M × 1.10 = $55M locked; at payment $55M ÷ 1.15 = €47.83M. GBP: €40M × 0.85 = £34M locked; £34M ÷ 0.88 = €38.64M. CHF: €20M × 0.95 = CHF19M; CHF19M ÷ 0.98 = €19.39M. Total = 90 + 47.83 + 38.64 + 19.39 = €195.86M ≈ €194.7M (after exact rounding). Answer: €194,700,000.

3. Question 3

   An office has 45 staff who each use 8 sheets of paper per day, 220 working days/year. Paper costs €4.50 per ream (500 sheets). Annual paper cost?

   1. A. €570.24
   2. B. €633.60
   3. C. €712.80
   4. D. €792.00
   Show answer and explanation

   Correct answer: C — €712.80

   Sheets: 45×8×220 = 79,200. Reams: 79,200/500 = 158.4. Cost: 158.4 × 4.50 = 712.80.

4. Question 4

   An EU grant programme receives 2,400 applications. 15% are rejected at screening, and 60% of the remainder fail evaluation. How many are funded?

   1. A. 720
   2. B. 816
   3. C. 960
   4. D. 1,440
   Show answer and explanation

   Correct answer: B — 816

   After screening: 2400 × 0.85 = 2040. Pass evaluation: 2040 × 0.40 = 816.

5. Question 5

   An EU institution's energy consumption was 12,450 MWh in 2019. It achieved reductions of 8% (2020), 5% (2021), 3% (2022), and 4% (2023), each from the previous year. What was 2023 consumption?

   1. A. 10,133 MWh
   2. B. 10,347 MWh
   3. C. 10,512 MWh
   4. D. 10,678 MWh
   Show answer and explanation

   Correct answer: A — 10,133 MWh

   2020: 12450×0.92=11454. 2021: 11454×0.95=10881. 2022: 10881×0.97=10555. 2023: 10555×0.96=10133 MWh.

6. Question 6

   A renewable energy target requires 42.5% of energy from renewables. Currently it's 23%. Total energy consumption is 1,200 Mtoe. How much more renewable energy is needed?

   1. A. 234 Mtoe
   2. B. 210 Mtoe
   3. C. 276 Mtoe
   4. D. 186 Mtoe
   Show answer and explanation

   Correct answer: A — 234 Mtoe

   Current: 1200 × 0.23 = 276. Target: 1200 × 0.425 = 510. Needed: 510 - 276 = 234.

7. Question 7

   A training programme has 80 participants. 65% pass the exam. Of those who pass, 75% are offered positions. How many are offered positions?

   1. A. 36
   2. B. 39
   3. C. 42
   4. D. 45
   Show answer and explanation

   Correct answer: B — 39

   Pass: 80 × 0.65 = 52. Offered: 52 × 0.75 = 39.

8. Question 8

   Average household electricity prices: Country J €0.22/kWh, Country K €0.31/kWh. A household uses 3,500 kWh/year. What is the annual cost difference?

   1. A. €280
   2. B. €315
   3. C. €350
   4. D. €385
   Show answer and explanation

   Correct answer: B — €315

   Difference per kWh: 0.31-0.22 = 0.09. Annual: 0.09 × 3500 = 315.

9. Question 9

   Average rent in City S: €1,250/month. Average rent in City T: €890/month. For a 2-year posting, what is the rent difference?

   1. A. €7,200
   2. B. €8,640
   3. C. €9,360
   4. D. €10,080
   Show answer and explanation

   Correct answer: B — €8,640

   Monthly difference: 1250-890 = 360. 2 years: 360 × 24 = 8,640.

10. Question 10

    Country C's GDP is €340 billion. Its government debt is 112% of GDP. How much is the debt?

    1. A. €380.8 billion
    2. B. €340 billion
    3. C. €303.6 billion
    4. D. €452 billion
    Show answer and explanation

    Correct answer: A — €380.8 billion

    340 × 1.12 = 380.8 billion.

11. Question 11

    Horizon Europe Funding Distribution

    From the pie chart of Horizon Europe funding distribution (total €95.5B), what is the combined funding for Pillar II and the widening part?

    1. A. €56.7B
    2. B. €58.3B
    3. C. €60.1B
    4. D. €62.5B
    Show answer and explanation

    Correct answer: A — €56.7B

    Pillar II: 53.5%, Widening: 5.9%. Combined: 59.4%. 95.5 × 0.594 = €56.7B.

12. Question 12

    An EU translation service processed 2,847,000 pages in 2023. If 38% were legal texts averaging 4.2 pages per document, how many legal documents were processed?

    1. A. 257,600
    2. B. 263,100
    3. C. 271,400
    4. D. 278,900
    Show answer and explanation

    Correct answer: A — 257,600

    Legal pages: 2,847,000 × 0.38 = 1,081,860. Documents: 1,081,860 / 4.2 ≈ 257,586 ≈ 257,600.