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Free Practice Questions for Irish Numerical Reasoning

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Sample Irish Numerical Reasoning Practice Questions

Try these sample questions to review concepts for the Irish Numerical Reasoning exam. Each question includes a detailed explanation. Start the interactive quiz above for the full 124+ question experience with AI tutoring.

1An illustrative education budget of €240,000 is distributed as follows: 1/3 goes to science equipment, 1/4 to arts programs, and 1/8 to sports equipment. The remainder is allocated to IT infrastructure. What is the euro amount allocated to IT infrastructure?
A.€70,000
B.€80,000
C.€90,000
D.€100,000
Explanation: The total fraction spent on science, arts, and sports is 1/3 + 1/4 + 1/8 = (8 + 6 + 3) / 24 = 17/24. The fraction remaining for IT is 1 - 17/24 = 7/24. The euro amount is 240,000 * 7 / 24 = €70,000.
2A hospital needs 200 nursing hours covered on a weekend. Each additional nurse can cover one 7.5-hour shift. What is the smallest number of additional nurses needed to cover all 200 hours?
A.24 nurses
B.27 nurses
C.28 nurses
D.30 nurses
Explanation: 200 / 7.5 = 26 2/3 shifts. Because a fraction of a nurse cannot cover a separate full shift, round up to 27 nurses; 27 shifts provide 202.5 hours.
3A bus timetable lists a 54-minute outward journey and a 46-minute return journey. A driver must also take a 20-minute break between complete round trips. Starting at 09:00, when will the driver finish three round trips, with no break required after the final trip?
A.14:00
B.14:20
C.14:40
D.15:00
Explanation: Each round trip takes 54 + 46 = 100 minutes. Three take 300 minutes, with two 20-minute breaks adding 40 minutes. A total of 340 minutes is 5 hours 40 minutes, so the finish time is 14:40.
4Two mail-sorting machines work simultaneously at constant rates of 900 and 600 letters per minute. They start with 150,000 letters, and manual staff remove 30,000 letters for separate processing before the machines begin. How long do the two machines take to sort their remaining workload?
A.60 minutes
B.80 minutes
C.100 minutes
D.120 minutes
Explanation: The machine workload is 150,000 - 30,000 = 120,000 letters. Their combined rate is 900 + 600 = 1,500 per minute, so they take 120,000 / 1,500 = 80 minutes.
5A conservation project uses 6 workers, each contributing 7 hours per day for 10 days. A second team must provide the same total worker-hours in 5 days, with each worker contributing 6 hours per day. How many workers does the second team need?
A.10 workers
B.12 workers
C.14 workers
D.16 workers
Explanation: The first team provides 6 * 7 * 10 = 420 worker-hours. Each second-team worker provides 6 * 5 = 30 hours, so 420 / 30 = 14 workers are needed.
6A farm uses 4/9 of its 360 hectares for dairy research. It then allocates 1/4 of the remaining land to tillage. How many hectares remain for forestry?
A.100 hectares
B.150 hectares
C.160 hectares
D.200 hectares
Explanation: Dairy uses 360 * 4/9 = 160 hectares, leaving 200. Tillage uses one quarter of that remainder, or 50 hectares. Forestry therefore receives 200 - 50 = 150 hectares.
7A 42 km road is shown on a map at a scale of 1:200,000. What length should represent the road on the map? (There are 100,000 centimetres in one kilometre.)
A.18 cm
B.21 cm
C.24 cm
D.42 cm
Explanation: Convert 42 km to 4,200,000 cm. Dividing by the map scale gives 4,200,000 / 200,000 = 21 cm.
8A rail-maintenance team completed 40 inspections in the first week and 60 in the second. The average inspection took 80 minutes in Week 1 and 60 minutes in Week 2. What was the mean time per inspection across both weeks?
A.60 minutes
B.65 minutes
C.68 minutes
D.70 minutes
Explanation: Total inspection time is 40 * 80 + 60 * 60 = 6,800 minutes for 100 inspections. The weighted mean is 6,800 / 100 = 68 minutes.
9A tax-information survey received 45,000 responses. Of these, 25,000 respondents had used the online guidance and 13,500 had used a telephone helpline. A total of 32,000 had used at least one of the two services. How many respondents had used both?
A.4,500
B.5,500
C.6,500
D.13,000
Explanation: Adding the two service totals counts people who used both twice. The overlap is therefore 25,000 + 13,500 - 32,000 = 6,500.
10In a hypothetical civil service recruitment stage, 8,000 candidates sat the initial assessments. If 3/5 met the qualifying standard on the numerical reasoning test, and 3/8 of that qualifying group also met the qualifying standard on the verbal reasoning test, how many candidates met the qualifying standard on both tests?
A.1,500
B.1,800
C.2,100
D.2,400
Explanation: Candidates meeting the numerical standard: 8,000 * 3/5 = 4,800. Candidates of that group also meeting the verbal standard: 4,800 * 3/8 = 1,800.

About the Irish Numerical Reasoning Exam

Independent numerical reasoning practice for Irish public service recruitment. publicjobs assessments and eligibility vary by competition. The topics below are practice categories, not a universal official weighted syllabus.

Exam sponsor: Public Appointments Service (publicjobs.ie). The requirements and fees below concern the certification or admission exam, separate from our free practice resources.

Assessment

Numerical reasoning assessment used in recruitment; typically multiple-choice. Follow the instructions for your competition.

Time Limit

Specified in the competition assessment and familiarisation material.

Passing Score

Competition-specific qualifying scores and order-of-merit rules; no universal 70% pass mark.

Exam / Certification Fees

See the information booklet for the relevant recruitment competition.

Exam sponsor website

Reported exam pass rate: Not published across competitions. No universal pass rate is published for all recruitment competitions. Exam sponsor website

Fees, eligibility, and exam policies can change. Confirm them with the exam sponsor before applying or paying.

Official sources

Our practice resources: topics covered

We aim to reflect publicly available exam outlines and topic information in our study resources. Coverage, format, and difficulty may differ from the actual exam, and we cannot guarantee that every detail is accurate or current. Confirm exam requirements, fees, and policies with the official exam sponsor.

Practice topic; no universal official weight

Basic Arithmetic & Fractions

Fractional calculations, decimals, and basic equations.

Practice topic; no universal official weight

Percentages & Ratios

Percentage change, reverse percentages, ratios and weighted rates.

Practice topic; no universal official weight

Data Interpretation & Charts

Reading and analysing information from graphs, charts, and tables.

Practice topic; no universal official weight

Financial Computations

Budget variances, unit costs, supplied tax rates and price-index calculations.

Practice topic; no universal official weight

Numerical Series & Estimation

Optional number-pattern practice plus estimation and answer checks; not a universal publicjobs syllabus.

Preparing for the Irish Numerical Reasoning Exam

What You Need to Know

  • Passing score: Competition-specific qualifying scores and order-of-merit rules; no universal 70% pass mark.
  • Assessment: Numerical reasoning assessment used in recruitment; typically multiple-choice. Follow the instructions for your competition.
  • Time limit: Specified in the competition assessment and familiarisation material.
  • Exam / certification fees: See the information booklet for the relevant recruitment competition. Official sources

Using Our Practice Resources

  • Work through all 124 available questions
  • Review every answer and explanation
  • Track weak areas and revisit them
  • Use our AI tutor for tough concepts

Frequently Asked Questions

Is Irish public service numerical reasoning one fixed certification exam?

No. publicjobs may use numerical reasoning during recruitment to assess how candidates interpret numerical information. Selection stages depend on the competition. This independent guide is preparation across competitions, not an official certification syllabus.

What score is needed, and does passing create a place on a final panel?

There is no single published pass mark covering all publicjobs competitions. Qualifying standards and stage order of merit depend on the competition. Meeting an initial test standard does not itself establish final panel membership: the recruitment process describes panels for candidates successful at the final stage.

Which numerical skills does this guide teach?

The guide teaches arithmetic, percentages, ratios, tables and charts, followed by hypothetical financial applications and estimation. Number patterns are optional extension practice. These categories are not official topic weights or evidence of which questions occur most frequently; your competition material determines the actual scope.