An 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?
Basic Arithmetic And Fractions
Question · Hard
IQ test: finish the series
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In Public Appointments Service (PAS / publicjobs) recruitment competitions, what is the critical difference between an 'Order of Merit' and an 'Appointment Panel'?
PAS Assessment & Test Strategy
Flashcard
A 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?
Question · Medium
Chapter 1: Test Overview, Structure & Assessment Strategies
1.1 Test Overview, Structure & Administration
Study guide
Cheat sheet
A 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?
Question · Easy
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How is an average item pacing benchmark calculated for a timed numerical reasoning test with a fixed duration and shared clock?
Two 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 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?
Under a standard scoring model (+1 for correct, 0 for incorrect or blank), what is the expected score of an educated guess when 2 options can be eliminated from 5?
A 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?
1.2 Pacing, Time Management & Exam Strategies
A 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.)
In civil service psychometric numerical reasoning, when is the option 'Cannot Say' (or 'Insufficient Information') mathematically required?
A 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 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?
What official guidance governs permitted aids (calculators and rough scrap paper) for online publicjobs assessments?
In 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?
1.3 Assessment Interfaces, Tabbed Layouts & 'Cannot Say' Logic
A fictional national park spans 24,000 hectares. A land-cover audit records 11,450 hectares of upland heath, 3,850 hectares of blanket bog, and 2,700 hectares of exposed rock and water bodies, with the remaining area classified as native woodland. How many hectares of native woodland are in the park?
What is the recommended 3-step 'Route Diagnosis' procedure before beginning calculations on complex numerical tables?
A weather log says that 4 days had more than 10 mm of rain. Those days were exactly one fifth of all rainy days, and rainy days accounted for two thirds of the observation period. How many days were in the observation period?
A research vessel leaves port on 5 July and returns on 17 July. For its daily allowance, every calendar day from departure through return is counted, including both dates. What is the total allowance at €70 per counted day?
What is the formula for Percentage Change (Increase or Decrease), and which value must always be placed in the denominator?
Percentages & Index Numbers
A laboratory needs 180 sample bottles, each holding 750 millilitres. Empty bottles are sold only in sealed packs of 16. What is the minimum number of packs that must be ordered?
Chapter 2: Core Arithmetic, Fractions & Decimals
2.1 Order of Operations & Mental Arithmetic Techniques
A food-export spreadsheet lists 2.5 thousand tonnes of product at €2,400 per tonne and a separate shipment worth €0.5 million. What is the combined export value in millions of euros?
How do you calculate the Original Value before a percentage increase or decrease using the Reverse Percentage multiplier method?
A sample county register lists 3,200 farms. If 1/8 of these farms are organic, and they plan to increase the number of organic farms by 1/4 of their current count next year, what will be the new number of organic farms?
A local authority winter-maintenance depot holds 45 metric tonnes of rock salt. Crews spread 13.6 metric tonnes on national primary routes and 1,400 kilograms on regional link roads, then pack the remaining salt into 1-kilogram bags for footpath gritting. Given that 1 metric tonne equals 1,000 kilograms, how many 1-kilogram bags are filled?
What is the mathematical distinction between 'Percentage Points' and 'Percentage Change'?
Under a central digital-services framework, an agency pays €3.25 million per quarter across all 4 quarters of the year for cloud hosting, plus a one-off migration fee of €1.40 million, and then deducts €6.40 million in shared-service reimbursements from partner bodies. What is the agency's net annual expenditure?
2.2 Fractions & Rational Numbers in Public Administration
A Heritage Council conservation fund of €120,000 is divided among three projects: museum preservation, historic town walls, and archive digitisation. Historic town walls receive twice the amount allocated to museum preservation, while archive digitisation receives €12,000 more than museum preservation. What amount is allocated to museum preservation?
How are successive (compound) percentage changes calculated using decimal multipliers?
Survey returns over five working days averaged 6,000 per day. The first four daily totals were 5,400, 6,200, 6,100 and 5,800. How many returns were received on the fifth day?
A hospital vacancy rate fell from 20% to 15%. What was the relative percentage reduction in the vacancy rate?
Percentages And Ratios
What is the formula for an Index Number, and what does an index figure represent relative to its base period?
In a staffing exercise, Garda District A has 60 Gardaí for 30,000 residents, while Garda District B has 80 Gardaí for 48,000 residents. What is the ratio of Gardaí per 1,000 residents in District A to District B in its simplest form?
2.3 Decimals, Rounding & Unit Conversions
A sample council housing plan proposed to build 1,500 social housing units. If they successfully completed 1,125 units in the first year, what percentage of the planned units was built?
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