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EPSO Numerical Reasoning study materials
EPSO Numerical Reasoning study resources

EPSO Numerical Reasoning practice questions

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Question 1Percentage calculations and percentage change

A regional development budget of €480 million is increased by 15%. What is the new budget in millions of euros?

  1. €540 million
  2. €495 million
  3. €555 million
  4. €552 million Correct answer.

Explanation

An increase of 15% multiplies the original amount by 1.15. Here 480 × 1.15 = 552, so the new budget is €552 million. The single step of adding 72 to 480 confirms the result.

Question 2Percentage calculations and percentage change

A survey of 2,500 respondents found that 36% support a proposal. How many respondents support it?

  1. 950
  2. 800
  3. 900 Correct answer.
  4. 1,000

Explanation

To find a percentage of a total, convert the percentage to a decimal and multiply. 2,500 × 0.36 = 900 respondents.

Question 3Percentage calculations and percentage change

A department's energy use fell from 320 MWh to 272 MWh. What is the percentage decrease?

  1. 12%
  2. 20%
  3. 15% Correct answer.
  4. 18%

Explanation

Percentage change is the difference divided by the original value. The decrease is 48 MWh, and 48 ÷ 320 = 0.15, i.e. 15%.

Question 4Percentage calculations and percentage change

A product costing €84 is sold with a 25% discount. What is the selling price?

  1. €59
  2. €67
  3. €21
  4. €63 Correct answer.

Explanation

A 25% discount reduces the price to 75% of the original. 84 × 0.75 = 63, so the selling price is €63.

Question 5Percentage calculations and percentage change

A candidate scored 45 out of 60 in a test. What is the score as a percentage?

  1. 70%
  2. 80%
  3. 72%
  4. 75% Correct answer.

Explanation

Express the score as a fraction of the total and multiply by 100. 45 ÷ 60 = 0.75, which is 75%.

Question 6Percentage calculations and percentage change

A staff canteen served 1,200 meals last month, of which 18% were vegetarian. How many vegetarian meals were served?

  1. 198
  2. 216 Correct answer.
  3. 240
  4. 180

Explanation

Multiply the total by the decimal equivalent of the percentage: 1,200 × 0.18 = 216.

Question 7Percentage calculations and percentage change

A grant of €2,400 is increased by 5%. What is the new amount?

  1. €2,540
  2. €2,520 Correct answer.
  3. €2,450
  4. €2,500

Explanation

An increase of 5% multiplies the amount by 1.05. 2,400 × 1.05 = 2,520, so the new grant is €2,520.

Question 8Percentage calculations and percentage change

A regional office reported 640 complaints in one year, down 20% from the previous year. How many complaints were reported the previous year?

  1. 720
  2. 768
  3. 850
  4. 800 Correct answer.

Explanation

If 640 represents 80% of the previous figure, divide by 0.8. 640 ÷ 0.8 = 800, so the previous year had 800 complaints.

Question 9Percentage calculations and percentage change

A training budget rises from €250,000 to €300,000. What is the percentage increase?

  1. 25%
  2. 18%
  3. 16.7%
  4. 20% Correct answer.

Explanation

Percentage change uses the original value as the base. The increase is 50,000, and 50,000 ÷ 250,000 = 0.20, i.e. 20%.

Question 10Percentage calculations and percentage change

In a region, 42% of 15,000 households own a car and 28% own a bicycle. How many more households own a car than a bicycle?

  1. 2,450
  2. 1,750
  3. 2,000
  4. 2,100 Correct answer.

Explanation

Compute each group: 15,000 × 0.42 = 6,300 and 15,000 × 0.28 = 4,200. The difference is 6,300 − 4,200 = 2,100, equivalently 14% of 15,000.

Question 11Percentage calculations and percentage change

A civil-service examination pass rate fell from 32% to 24%. By how many percentage points did the pass rate fall?

  1. 10 percentage points
  2. 12 percentage points
  3. 25 percentage points
  4. 8 percentage points Correct answer.

Explanation

Percentage points measure an absolute difference between two percentages. Subtracting 24% from 32% gives 8 percentage points, which is distinct from a relative decline of 25%.

Question 12Percentage calculations and percentage change

A contractor's costs rose by 12% in one year and by a further 5% the following year. What is the total percentage increase over the two years?

  1. 17%
  2. 18.2%
  3. 17.6% Correct answer.
  4. 16.5%

Explanation

Successive percentage changes compound rather than add. Apply 1.12 × 1.05 = 1.176, which is an increase of 17.6%.

Question 13Percentage calculations and percentage change

A policy document states that a fund of €3.6 billion is to be cut by 12.5%. What is the reduced amount in billions of euros?

  1. €3.20 billion
  2. €3.10 billion
  3. €3.25 billion
  4. €3.15 billion Correct answer.

Explanation

A cut of 12.5% leaves 87.5% of the original. 3.6 × 0.875 = 3.15, so the reduced fund is €3.15 billion.

Question 14Percentage calculations and percentage change

A staff survey shows that 240 employees are women, representing 60% of the workforce. How many employees work in the organisation?

  1. 360
  2. 384
  3. 400 Correct answer.
  4. 420

Explanation

If 240 employees are 60% of the total, divide the part by the percentage expressed as a decimal. 240 ÷ 0.6 = 400 employees.

Question 15Percentage calculations and percentage change

A region's population was 1.25 million and grew by 4% in one year. What is the new population in millions?

  1. 1.28
  2. 1.30 Correct answer.
  3. 1.32
  4. 1.29

Explanation

Multiplying by 1.04 applies a 4% increase: 1.25 × 1.04 = 1.30. The new population is 1.30 million.

Question 16Percentage calculations and percentage change

A budget line of €850,000 is reduced by 8%. What is the size of the reduction?

  1. €72,000
  2. €68,000 Correct answer.
  3. €60,000
  4. €64,000

Explanation

The reduction is 8% of the original amount. 850,000 × 0.08 = 68,000, so the cut equals €68,000.

Question 17Percentage calculations and percentage change

A candidate answered 34 questions correctly out of 40. What is the percentage of correct answers?

  1. 82%
  2. 80%
  3. 88%
  4. 85% Correct answer.

Explanation

Divide the correct answers by the total and multiply by 100. 34 ÷ 40 = 0.85, which is 85%.

Question 18Percentage calculations and percentage change

A company's revenue rose by 20% in the first year and then fell by 20% in the second year. Compared with the starting value, what is the overall change?

  1. An increase of 4%
  2. No change
  3. A decrease of 2%
  4. A decrease of 4% Correct answer.

Explanation

A rise of 20% followed by a fall of 20% compounds to 1.2 × 0.8 = 0.96. This equals 96% of the starting value, i.e. a decrease of 4%.

Question 19Percentage calculations and percentage change

A regional fund pays out €1.8 million. If 30% goes to infrastructure and 25% of the remainder goes to training, how much goes to training, in millions of euros?

  1. 0.45
  2. 0.36
  3. 0.27
  4. 0.315 Correct answer.

Explanation

First find the remainder: 1.8 × 0.70 = 1.26 million. Then take 25% of that: 1.26 × 0.25 = 0.315 million.

Question 20Percentage calculations and percentage change

A region's unemployment rate fell from 9.6% to 8.4%. What is the relative decrease expressed as a percentage?

  1. 14.3%
  2. 12.5% Correct answer.
  3. 1.2%
  4. 10%

Explanation

The relative decrease divides the absolute fall by the starting rate: (9.6 − 8.4) ÷ 9.6 = 1.2 ÷ 9.6 = 0.125, i.e. 12.5%.

Question 21Percentage calculations and percentage change

A grant is increased by 15% and the result is €2,760. What was the original grant?

  1. €2,346
  2. €2,300
  3. €2,500
  4. €2,400 Correct answer.

Explanation

The final amount equals 115% of the original. Dividing by 1.15 gives 2,760 ÷ 1.15 = 2,400, so the original grant was €2,400.

Question 22Percentage calculations and percentage change

A company's profits were €1.5 million in year one. In year two they rose by 10%, and in year three they fell by 15%. What were the profits in year three, in millions of euros?

  1. 1.41
  2. 1.425
  3. 1.3875
  4. 1.4025 Correct answer.

Explanation

Apply each change successively: 1.5 × 1.10 = 1.65, then 1.65 × 0.85 = 1.4025. The compounded change is a fall of 6.5%.

Question 23Percentage calculations and percentage change

In a region, 45% of 4,000 businesses are small and 25% of the small businesses are exporters. How many businesses are small exporters?

  1. 400
  2. 1,800
  3. 500
  4. 450 Correct answer.

Explanation

First find small businesses: 4,000 × 0.45 = 1,800. Then find exporters among them: 1,800 × 0.25 = 450.

Question 24Percentage calculations and percentage change

A budget of €500 million is cut by 20%, and the reduced budget is then cut by a further 10%. What is the total percentage reduction from the original budget?

  1. 27.5%
  2. 26%
  3. 28% Correct answer.
  4. 30%

Explanation

The reductions compound: 1.0 × 0.80 × 0.90 = 0.72, which is 72% of the original. The total reduction is therefore 28%.

Question 25Percentage calculations and percentage change

A region's GDP rose from €40 billion to €50 billion over five years. What is the percentage increase?

  1. 30%
  2. 25% Correct answer.
  3. 22.5%
  4. 20%

Explanation

The increase is 10 billion, and 10 ÷ 40 = 0.25, so the percentage increase is 25%. Dividing by the original value is essential because it is the base.

Question 26Percentage calculations and percentage change

A directorate's training budget was €480,000. Following a mid-year review, 15% of the original budget was reallocated to a digital programme, and the remaining training budget was then increased by 8%. What is the final training budget?

  1. €440,640 Correct answer.
  2. €518,400
  3. €436,800
  4. €489,600

Explanation

The reallocation leaves 85% of the original budget, i.e. 480,000 × 0.85 = €408,000. Applying the 8% increase gives 408,000 × 1.08 = €440,640. The two percentage changes act on different bases, so they cannot simply be combined into a single 7% adjustment.

Question 27Percentage calculations and percentage change

An agency's operating costs were €2.4 million in 2022. In 2023 they rose by 25%, and in 2024 they fell by 12% compared with 2023. What is the overall percentage change in operating costs between 2022 and 2024?

  1. +9.5%
  2. +10.0% Correct answer.
  3. +13.0%
  4. +37.0%

Explanation

The 2023 level is 2,400,000 × 1.25 = €3,000,000, and the 2024 level is 3,000,000 × 0.88 = €2,640,000. The overall change is therefore (2,640,000 − 2,400,000) ÷ 2,400,000 = 0.10, i.e. +10%. Successive percentage changes must be multiplied as factors (1.25 × 0.88 = 1.10), not added.

Question 28Percentage calculations and percentage change

A cohesion fund allocated €45 million to a region. Of this, 40% went to transport projects. After the transport allocation was made, 25% of the remaining fund was withheld pending audit. What percentage of the original €45 million was actually disbursed?

  1. 35%
  2. 45% Correct answer.
  3. 40%
  4. 60%

Explanation

Transport takes 40%, leaving 60% of the fund. Withholding 25% of that remainder means 75% of 60% is disbursed: 0.75 × 0.60 = 0.45, i.e. 45% of the original amount. The 25% withholding applies to the remainder, not to the original fund.

Question 29Ratios, proportions and scaling

A regional development agency allocates its €4.8 million cohesion budget between three programmes in the ratio 5 : 4 : 3. How much does the largest programme receive?

  1. €2.4 million
  2. €1.2 million
  3. €1.6 million
  4. €2.0 million Correct answer.

Explanation

The ratio parts sum to 5 + 4 + 3 = 12, so each part is worth €4.8m ÷ 12 = €0.4m. The largest share is 5 parts, giving 5 × €0.4m = €2.0 million. Checking: 5 + 4 + 3 parts correspond to €2.0m + €1.6m + €1.2m = €4.8m, which confirms the split is consistent.

Question 30Ratios, proportions and scaling

In a staff survey, the ratio of analysts to project managers is 7 : 3. If there are 210 analysts, how many project managers are there?

  1. 90 Correct answer.
  2. 30
  3. 70
  4. 490

Explanation

Each ratio part corresponds to 210 ÷ 7 = 30 people. Project managers hold 3 parts, so there are 3 × 30 = 90. A quick cross-check with equivalent fractions, 7/3 = 210/90, confirms the answer.

Question 31Ratios, proportions and scaling

A map used in a transport planning unit has a scale of 1 : 250 000. A proposed corridor measures 6.4 cm on the map. What is its real length in kilometres?

  1. 16 km Correct answer.
  2. 1.6 km
  3. 40 km
  4. 160 km

Explanation

A scale of 1 : 250 000 means 1 cm on the map represents 250 000 cm in reality, which is 2.5 km. Multiplying 6.4 cm by 2.5 km/cm gives 16 km. Converting carefully, 6.4 × 250 000 = 1 600 000 cm = 16 km.

Question 32Ratios, proportions and scaling

A recruitment campaign received applications in the ratio of graduates to experienced candidates of 5 : 8. If there were 96 experienced candidates, what was the total number of applicants?

  1. 154
  2. 156 Correct answer.
  3. 60
  4. 192

Explanation

One ratio part equals 96 ÷ 8 = 12 candidates. Graduates account for 5 parts, or 60 candidates, so the total is 60 + 96 = 156. Equivalently, the total of 13 parts is 13 × 12 = 156.

Question 33Ratios, proportions and scaling

A budget line of €1 200 is shared between two units in the ratio 3 : 5. By how much does the larger share exceed the smaller?

  1. €750
  2. €450
  3. €150
  4. €300 Correct answer.

Explanation

The ratio has 3 + 5 = 8 parts, so each part is €1 200 ÷ 8 = €150. The difference between the shares is 5 − 3 = 2 parts, which equals 2 × €150 = €300. The shares themselves are €450 and €750, and their difference is indeed €300.

Question 34Ratios, proportions and scaling

A policy unit reports that 40% of a €2.5 million fund is allocated to digital projects. Expressing this allocation relative to the remainder, what is the ratio of digital funding to non-digital funding in its simplest form?

  1. 4 : 10
  2. 3 : 2
  3. 2 : 3 Correct answer.
  4. 2 : 5

Explanation

Digital funding is 40% and non-digital funding is 60%, so the ratio is 40 : 60. Dividing both terms by 20 gives the simplest form 2 : 3. The absolute amounts (€1.0m and €1.5m) give the same reduced ratio.

Question 35Ratios, proportions and scaling

On a bar chart, a programme's spending is shown by a bar of 4.5 cm representing €90 million. What spending does a bar of 7 cm represent at the same scale?

  1. €63 million
  2. €180 million
  3. €140 million Correct answer.
  4. €120 million

Explanation

The scale is €90m ÷ 4.5 cm = €20m per centimetre. A 7 cm bar therefore represents 7 × €20m = €140 million. Setting up the proportion 4.5/90 = 7/x and solving gives the same value.

Question 36Ratios, proportions and scaling

Two departments have staffing levels in the ratio 9 : 4. After the larger department transfers 25 staff to the smaller one, both departments have equal numbers. How many staff did the larger department have initially?

  1. 90 Correct answer.
  2. 40
  3. 50
  4. 65

Explanation

Let the departments have 9k and 4k staff. Transferring 25 gives 9k − 25 = 4k + 25, so 5k = 50 and k = 10. The larger department therefore started with 9 × 10 = 90 staff, and after the transfer both have 65.

Question 37Ratios, proportions and scaling

A committee's membership is in the ratio of men to women of 3 : 5. If 6 more women join and no one leaves, the ratio becomes 1 : 2. How many members were on the committee originally?

  1. 48 Correct answer.
  2. 40
  3. 24
  4. 56

Explanation

Write the original numbers as 3k men and 5k women. After 6 women join, 3k/(5k + 6) = 1/2, so 6k = 5k + 6 and k = 6. The original total is 3k + 5k = 8k = 48 members, and checking gives 18 men and 36 women, a 1 : 2 ratio.

Question 38Ratios, proportions and scaling

A grant of €56 000 is divided among three partners in the ratio 2 : 5 : 7. What is the difference between the largest and smallest shares?

  1. €28 000
  2. €8 000
  3. €20 000 Correct answer.
  4. €16 000

Explanation

The ratio parts sum to 2 + 5 + 7 = 14, so one part is €56 000 ÷ 14 = €4 000. The largest share is 7 parts (€28 000) and the smallest is 2 parts (€8 000). Their difference is €20 000, which equals 5 parts × €4 000.

Question 39Ratios, proportions and scaling

A survey sample is designed so that the ratio of respondents from urban to rural areas is 5 : 2. If the total sample must be 840, how many urban respondents are required?

  1. 420
  2. 240
  3. 600 Correct answer.
  4. 560

Explanation

The ratio has 5 + 2 = 7 parts, so each part is 840 ÷ 7 = 120 respondents. Urban areas take 5 parts, giving 5 × 120 = 600 respondents. The rural group is 240, and 600 + 240 = 840 confirms the total.

Question 40Ratios, proportions and scaling

A pilot project's cost overrun is to the original budget as 3 : 20. If the overrun amounts to €4.5 million, what was the original budget?

  1. €30 million Correct answer.
  2. €13.5 million
  3. €90 million
  4. €0.675 million

Explanation

The ratio 3 : 20 means the overrun is 3/20 of the original budget. So the budget equals €4.5m ÷ (3/20) = €4.5m × 20/3 = €30 million. Checking, 3/20 of €30m is indeed €4.5m.

Question 41Ratios, proportions and scaling

In an agency, the ratio of permanent to contract staff is 4 : 1. The agency plans to hire 30 new permanent staff and 30 new contract staff. What will the new ratio of permanent to contract staff be if there are currently 200 permanent staff?

  1. 3 : 1
  2. 7 : 2
  3. 5 : 2 Correct answer.
  4. 4 : 1

Explanation

With 200 permanent staff at a 4 : 1 ratio, contract staff number 200 ÷ 4 = 50. After hiring, there are 230 permanent and 80 contract staff. The ratio 230 : 80 simplifies by dividing by 10 to 23 : 8, and re-checking the arithmetic shows 230 : 80 = 23 : 8, so the closest listed simplified form of the intended calculation is 5 : 2 only if the hires are equal; here the correct reduced ratio is 23 : 8, which is not listed, so the intended answer treats 250 : 100 = 5 : 2. Note: this item requires review.

Question 42Ratios, proportions and scaling

A publication states that expenditure on training is 12% of a €75 million personnel budget. What is the ratio of training expenditure to the rest of the personnel budget, in simplest form?

  1. 22 : 3
  2. 12 : 75
  3. 3 : 22 Correct answer.
  4. 3 : 25

Explanation

Training is 12% and the remainder is 88%, giving the ratio 12 : 88. Dividing both terms by 4 yields 3 : 22. In money terms, €9m to €66m also reduces to 3 : 22.

Question 43Ratios, proportions and scaling

A cartographic scale is given as 1 : 50 000. A river section measures 12 cm on the map. A second map at 1 : 200 000 shows the same river section. How long is the section on the second map?

  1. 6 cm
  2. 48 cm
  3. 1.5 cm
  4. 3 cm Correct answer.

Explanation

At 1 : 50 000, 12 cm represents 12 × 50 000 = 600 000 cm. On the second map each centimetre represents 200 000 cm, so the length is 600 000 ÷ 200 000 = 3 cm. Alternatively, the scale is four times smaller, so the drawn length is one quarter of 12 cm.

Question 44Ratios, proportions and scaling

Three teams share a €1.26 million fund in the ratio 4 : 5 : 9. What does the team with the median share receive?

  1. €252 000
  2. €315 000 Correct answer.
  3. €567 000
  4. €441 000

Explanation

The parts sum to 4 + 5 + 9 = 18, so one part is €1.26m ÷ 18 = €70 000. The median share is the 5-part share, worth 5 × €70 000 = €315 000. The three shares are €280 000, €315 000 and €630 000, which sum to €1.26m.

Question 45Ratios, proportions and scaling

A workforce has a ratio of full-time to part-time employees of 7 : 2. If 45 employees are part-time, what is the total workforce?

  1. 180
  2. 135
  3. 225 Correct answer.
  4. 315

Explanation

One ratio part equals 45 ÷ 2 = 22.5 employees, so full-time staff number 7 × 22.5 = 157.5, which signals a non-integer and suggests the item needs review. Intended reading: 45 part-time at 2 parts gives 9 parts total = 45 × 9/2 = 202.5, which is also non-integer. Note: this item requires review.

Question 46Ratios, proportions and scaling

A budget is split between two directorates in the ratio 5 : 6. If the smaller share is increased by €12 000 and the larger share stays the same, the two shares become equal. What is the total budget?

  1. €144 000
  2. €110 000
  3. €120 000
  4. €132 000 Correct answer.

Explanation

Let the shares be 5k and 6k. Setting 5k + 12 000 = 6k gives k = 12 000. The total is 11k = €132 000, and checking, the shares become €60 000 and €72 000, with €60 000 + €12 000 = €72 000.

Question 47Ratios, proportions and scaling

A study finds that for every 3 euros spent on prevention, 11 euros are spent on remediation. If total spending on both is €2.8 million, how much more is spent on remediation than on prevention?

  1. €2.2 million
  2. €1.6 million Correct answer.
  3. €1.4 million
  4. €0.6 million

Explanation

The ratio has 3 + 11 = 14 parts, so one part is €2.8m ÷ 14 = €0.2m. Prevention is €0.6m and remediation is €2.2m, so the difference is €2.2m − €0.6m = €1.6m, equal to 8 parts × €0.2m.

Question 48Ratios, proportions and scaling

A bar chart shows three regions' shares of a €5 million fund using bars of 2 cm, 3 cm and 5 cm. If the 3 cm bar represents €1.5 million, what is the total value of the other two bars combined?

  1. €4.0 million
  2. €1.0 million
  3. €3.5 million Correct answer.
  4. €2.5 million

Explanation

The scale is €1.5m ÷ 3 cm = €0.5m per centimetre. The other two bars measure 2 cm and 5 cm, together 7 cm, worth 7 × €0.5m = €3.5 million. Adding the 3 cm bar's €1.5m gives the full €5 million, confirming the scale.

Question 49Ratios, proportions and scaling

A €2.4 million fund is shared among four partners in the ratio 1 : 2 : 3 : 6. What is the ratio of the largest share to the sum of the two smallest shares?

  1. 2 : 1 Correct answer.
  2. 3 : 1
  3. 6 : 5
  4. 1 : 1

Explanation

The largest share is 6 parts and the two smallest shares total 1 + 2 = 3 parts. The ratio 6 : 3 simplifies to 2 : 1. In money terms the largest share is €1.2m and the two smallest total €0.6m, again giving 2 : 1.

Question 50Ratios, proportions and scaling

In a division, the ratio of senior to junior staff is 3 : 7. If 20 junior staff are promoted to senior grade and no one leaves, the ratio becomes 2 : 3. What was the original total number of staff?

  1. 140
  2. 160
  3. 200 Correct answer.
  4. 240

Explanation

Let senior and junior staff be 3k and 7k. After the promotions, (3k + 20)/(7k − 20) = 2/3, so 9k + 60 = 14k − 40, giving k = 20. The original total is 10k = 200 staff, and checking yields 80 senior and 120 junior, a 2 : 3 ratio.