Civil Service Numerical Reasoning Test Cheat Sheet 2026

The 30 highest-yield Civil Service Numerical Reasoning Test facts, distilled from real exam questions. Print it, save it as a PDF, or study it here — free, no sign-up.

1. A pie chart shows that 40% of a council's £500,000 budget is spent on social services. How much is spent on social services? → £200,000
2. An international procurement is quoted at $42,500 USD. The exchange rate is £1 = $1.25. What is the cost in sterling? → £34,000
3. A train leaves at 07:55 and arrives at 11:20. The journey includes a 15-minute stop. What is the actual travel time (excluding the stop)? → 3 hours 10 minutes
4. A data set contains: 3, 3, 7, 7, 7, 9, 9. Which measure of average is 7? → Mean, median, and mode are all 7
5. A pump drains 45 litres per minute. How long does it take to drain a 2,700-litre tank? → 60 minutes
6. A table shows that Department A processed 240 applications and Department B processed 160. What fraction of applications did Department A process? → 3/5
7. Find the mode of: 4, 7, 2, 7, 9, 4, 7, 1. → 7
8. In a survey, 120 out of 400 people agreed with a policy. What percentage agreed? → 30%
9. What is the missing number: 1, 4, 16, 64, __, 1024? → 256
10. A train travels 240 miles at an average speed of 80 mph. How long does the journey take? → 3 hours
11. A line graph shows four data points: 15, 22, 19, 28. What is the range? → 13
12. A department's budget increased from £90,000 to £99,000. What was the percentage increase? → 10%
13. Find the missing number: 1, 2, 4, 7, 11, 16, __? → 22
14. Find the range of: 45, 12, 67, 33, 89, 21. → 77
15. A product is sold for £336 after a 40% mark-up on cost. What was the original cost? → £240
16. Two departments receive budgets in a 3:7 ratio. The smaller department receives £135,000. What is the combined total budget? → £450,000
17. Eight values: 3, 7, 7, 9, 11, 13, 15, 19. What is the median? → 10
18. A class of 30 students has a mean test score of 64. What is the total of all scores? → 1,920
19. A bar chart shows monthly sales: Jan £24,000; Feb £18,000; Mar £30,000. What is the average monthly sales over this period? → £24,000
20. Customer satisfaction scores for five regional offices are: 72, 85, 68, 91, 74. The mean is 78. What is the sample standard deviation? → 9.6
21. A staff member receives a bonus of 8% of their £27,500 salary. What is the bonus amount? → £2,200
22. A loan of £15,000 is taken out at 6% simple interest for 3 years. What is the total amount repaid? → £17,700
23. A line graph shows a value starting at 400 in Year 1 and ending at 550 in Year 5. Assuming constant annual increase, how much does it increase each year? → 37.5
24. Workers A and B share a bonus in a ratio of 5:3. Worker A receives £625. What does Worker B receive? → £375
25. Data set: 4, 8, 15, 16, 23, 42. What is the median? → 15.5
26. A train travels at 90 mph. How far does it travel in 40 minutes? → 60 miles
27. A business earns £2,400 per day. How much does it earn in a 5-day working week? → £12,000
28. Find the missing term: 3, 6, 11, 18, 27, __? → 38
29. Temperatures over 5 days: 14°C, 17°C, 11°C, 20°C, 13°C. What is the range? → 9°C
30. A retail outlet's monthly costs are: rent £3,500, wages £8,200, utilities £600, stock £12,000. Monthly revenue is £28,000. What is the monthly profit? → £3,700