publicjobs Numerical Reasoning Test Practice
A question asks for cases per employee after a staff transfer. The table still shows the old headcount. Divide by that figure and you get a perfectly believable answer to the wrong question.
That is what this practice set works on: reading the question, choosing the figures and checking the result. There are five questions, starting with a table lookup and building to a comparison of two budgets before cuts. Each worked answer explains the wrong options as well as the right one.
Download the question paper and worked answers (PDF) · Take the interactive numerical test
Try these five questions
Have a calculator and paper beside you. For a timed attempt, allow eight minutes for the whole set, keep the answers closed and note your time when you finish. If you are relearning the methods, leave the timer off for now.
These are original PSP exercises with fictional figures. Eight minutes is a practice target, not a publicjobs test specification.
1. Grant approvals
The table shows grant applications received and the approval rate by county. How many applications were approved in Cavan?
| County | Applications received | % approved |
|---|---|---|
| Louth | 2,000 | 40% |
| Meath | 900 | 25% |
| Cavan | 700 | 80% |
| Monaghan | 1,800 | 25% |
Check answer 1 and see the working
D: 560. Stay in the Cavan row. The question asks for approvals, so use 80% of the 700 applications received.
700 x 80% = 560 approved.
Where the other answers come from
- 140 is the 20% that were not approved.
- 450 uses Monaghan’s figures: 1,800 at 25%.
- 175 mixes Cavan’s total with Monaghan’s approval rate.
A useful check: Put a finger or cursor beside the row you need. Keep the total and its percentage together.
2. Applications per 1,000 people
The table shows housing support applications and population by county. How many applications per 1,000 population were made in Clare? Round to one decimal place.
| County | Applications | Population |
|---|---|---|
| Meath | 1,526 | 62,000 |
| Cavan | 1,935 | 67,000 |
| Louth | 1,858 | 127,000 |
| Clare | 1,790 | 65,000 |
Check answer 2 and see the working
A: 27.5 per 1,000 people. Use Clare’s 1,790 applications and population of 65,000. Multiply the fraction by 1,000 to express it for a group of 1,000 people.
1,790 / 65,000 x 1,000 = 27.5 per 1,000 people.
Where the other answers come from
- 275.4 uses a multiplier of 10,000.
- 5.6 divides Clare’s applications by the population of all four counties.
- 24.6 uses the Meath row.
A useful check: Read the unit attached to the answer. A percentage means per 100; this question asks for per 1,000.
3. A staff transfer
The table shows each unit’s weekly caseload and staffing. 2 staff transfer from the Passport Office to the Motor Tax Office, and both units keep the weekly caseloads shown. Working a 52-week year, how many cases will each member of the enlarged Motor Tax Office team handle in a year? Assume an equal share of the work and round to the nearest whole case.
| Unit | Cases per week | Staff |
|---|---|---|
| Social Protection Branch | 182 | 13 |
| Passport Office | 330 | 30 |
| Motor Tax Office | 400 | 20 |
| Planning Section | 238 | 14 |
Check answer 3 and see the working
A: 945 cases. Motor Tax receives two staff, but no extra cases. Update its headcount to 22 before dividing. Then spread the annual workload across that team.
The Motor Tax Office still handles 400 cases a week, so 400 x 52 = 20,800 a year. The team is now 20 + 2 = 22 staff. 20,800 / 22 = 945 cases.
Where the other answers come from
- 1,156 takes two staff away: 20,800 divided by 18.
- 1,725 transfers the Passport Office’s caseload as well as its staff.
- 1,040 uses the old headcount of 20.
A useful check: More people share the same workload, so the answer per person must fall.
4. An invoice with VAT included
The table shows amounts payable to suppliers with VAT included, and the VAT rate applied to each. What is the VAT-exclusive (net) amount on the Ennis Office Supplies invoice?
| Supplier | Amount payable (VAT included) | VAT rate |
|---|---|---|
| Ennis Office Supplies | €86,100 | 23% |
| Boyne IT Services | €35,970 | 9% |
| Ardee Facilities Ltd | €61,500 | 23% |
| Fingal Catering Ltd | €102,150 | 13.5% |
Check answer 4 and see the working
D: €70,000. The Ennis invoice includes 23% VAT. Its total represents 123% of the price before VAT. Divide by 1.23 to recover that original price.
The €86,100 is 123% of the net amount, not 100%. Net = €86,100 / 1.23 = €70,000.
Where the other answers come from
- €53,900 removes 23% again from the correct net price.
- €16,100 is the VAT amount, not the net price.
- €66,297 subtracts 23% of the gross invoice. VAT was added to the net price, so that uses the wrong base.
A useful check: Rebuild the invoice: multiply your net answer by 1.23. You should get the original total.
5. Compare budgets before a cut
The table shows each council’s roads maintenance allocation AFTER a budget cut, and the size of the cut applied. How much larger was Meath County Council’s allocation than Kerry County Council’s before the cuts were applied?
| Council | Roads allocation after cut | Cut applied |
|---|---|---|
| Kerry County Council | €2,025,000 | 25% |
| Wexford County Council | €1,980,000 | 10% |
| Meath County Council | €2,660,000 | 5% |
| Sligo County Council | €2,125,000 | 15% |
Check answer 5 and see the working
D: €100,000. The table gives the amounts left after the cuts. Recover Meath’s original allocation using 95%, and Kerry’s using 75%. Then compare the original amounts.
Meath County Council before = €2,660,000 / 0.95 = €2,800,000. Kerry County Council before = €2,025,000 / 0.75 = €2,700,000. Difference = €100,000.
Where the other answers come from
- €635,000 compares the figures as printed, after the cuts.
- €261,750 adds 5% and 25% back to the reduced amounts. Those percentages now act on smaller bases.
- €2,700,000 is Kerry’s original allocation, not the difference between the two.
A useful check: Finish the question. Finding both original budgets is the working; subtracting them gives the requested answer.
What to do with your result
Right answer, slow working: look for a shorter setup. For the staffing question, you only need one row and the transfer instruction. Calculating the other units’ totals costs time without helping you answer.
Wrong answer, sensible calculation: check what you divided by. The invoice and budget questions both require you to recover an original amount. Subtracting a percentage from the figure in front of you will not do that.
You understood the solution as soon as you saw it: close it and write the calculation again from a blank sheet. Being able to follow an explanation is useful; being able to choose the method yourself is the next step.
When those methods are clear, try five different numerical questions in the free taster. It gives you a score and explains missed answers. No account or card is needed. It has no enforced countdown, so use your own timer if you want to practise pace.
CO and EO: check your competition instructions
For official practice, start with the Clerical Officer self-assessment or Executive Officer self-assessment, both linked from publicjobs test advice.
Your competition’s familiarisation material gives the live test’s question count, time limit, calculator rules and navigation. The public advice page does not give one current numerical time limit that applies to every CO or EO competition. Check whether you can return to a question before practising a skip-and-return approach.
For a test with one overall timer, divide the available minutes by the question count to get an average pace. Treat that as a checkpoint: a table used by several questions may deserve more time on the first read. If each question has its own timer, follow that limit instead.
More numerical practice
- Question types and worked examples
- Working faster without losing accuracy
- Verbal reasoning practice for the reading side of your preparation
The free material lets you check the methods before paying for more. Compare the practice plans if you need further questions; Premium is €39 per month until cancelled.
Sources and updates
Official test advice and its CO/EO self-assessment links checked on 15 September 2026. PublicServicePathway is an independent preparation service, not part of publicjobs.
15 September 2026: replaced the introductory worksheet with a graduated five-question set, individual solutions and explanations of the wrong answers. The PDF contains the same questions, with the answers on separate pages.
Try five interactive numerical questions
Practise reading data and choosing the right calculation. See your score and explanations for missed answers, with no account or card required.