Civil Service Numerical Reasoning Test — Questions and Answers

Question 1: Find the mean of: 14, 18, 22, 10, 16.

16 (Correct answer)
18
15
17

Correct answer: 16

Sum = 14 + 18 + 22 + 10 + 16 = 80. Mean = 80 ÷ 5 = 16.

Question 2: What is 120% of £350?

£385
£420 (Correct answer)
£400
£450

Correct answer: £420

120% of £350 = 1.20 × 350 = £420.

Question 3: What is the next term: 3, 7, 15, 31, __?

63 (Correct answer)
55
61
67

Correct answer: 63

Each term = (previous term × 2) + 1. 3→7: (3×2)+1=7. 7→15: (7×2)+1=15. 15→31: (15×2)+1=31. 31→63.

Question 4: A 100% stacked bar chart shows transport mode shares for commuting civil servants: Car 45%, Train 28%, Bus 12%, Cycling 9%, Walking 6%. If 3,200 civil servants were surveyed, how many commute by train or bus combined?

1,216
1,344
1,152
1,280 (Correct answer)

Correct answer: 1,280

Train + Bus = 28% + 12% = 40%. Number of commuters = 40% of 3,200 = 0.40 x 3,200 = 1,280.

Question 5: A table shows that a region's population was 240,000 in 2010 and 264,000 in 2020. What was the percentage increase?

15%
10% (Correct answer)
8%
12%

Correct answer: 10%

Increase = 24,000. (24,000 ÷ 240,000) × 100 = 10%.

Question 6: Find the next number: 4, 9, 16, 25, 36, __?

45
42
49 (Correct answer)
50

Correct answer: 49

These are perfect squares: 2², 3², 4², 5², 6², 7². Next = 7² = 49.

Question 7: What is the next term: 100, 50, 25, 12.5, __?

7.5
10
5
6.25 (Correct answer)

Correct answer: 6.25

Each term is halved: 12.5 ÷ 2 = 6.25.

Question 8: Quarterly revenue: Q1 £110,000; Q2 £130,000; Q3 £95,000; Q4 £140,000. What is the average quarterly profit if total costs for the year were £360,000?

£28,750 (Correct answer)
£25,000
£30,000
£27,500

Correct answer: £28,750

Total revenue = £475,000. Annual profit = £475,000 − £360,000 = £115,000. Quarterly average = £115,000 ÷ 4 = £28,750.

Question 9: A car's value depreciates by 15% per year. It is currently worth £20,000. What will it be worth after one year?

£15,000
£16,000
£18,000
£17,000 (Correct answer)

Correct answer: £17,000

15% of £20,000 = £3,000. Value after one year = £20,000 − £3,000 = £17,000.

Question 10: What is the missing number: 7, 14, __, 56, 112?

35
28 (Correct answer)
42
21

Correct answer: 28

Each term is doubled: 7, 14, 28, 56, 112.

Question 11: A spreadsheet shows 3 rows of data being added every 2 minutes. How many rows are added in one hour?

90 (Correct answer)
60
120
75

Correct answer: 90

60 minutes ÷ 2 minutes per set = 30 sets. 30 × 3 rows = 90 rows.

Question 12: Find the missing number: 81, 27, 9, __, 1?

2
6
4
3 (Correct answer)

Correct answer: 3

Each term is divided by 3: 81 ÷ 3 = 27, 27 ÷ 3 = 9, 9 ÷ 3 = 3, 3 ÷ 3 = 1.

Question 13: A trend graph shows NHS waiting times (in weeks) at four points: Jan 18.2, Apr 16.5, Jul 15.1, Oct 17.8. Between which two consecutive data points was the largest change observed?

Apr to Jul
Jul to Oct (Correct answer)
Jan to Apr
All changes were equal

Correct answer: Jul to Oct

Changes: Jan to Apr = 1.7 weeks decrease; Apr to Jul = 1.4 weeks decrease; Jul to Oct = 2.7 weeks increase. The largest change (2.7 weeks) occurred between July and October.

Question 14: A pump drains 45 litres per minute. How long does it take to drain a 2,700-litre tank?

45 minutes
60 minutes (Correct answer)
90 minutes
30 minutes

Correct answer: 60 minutes

Time = 2,700 ÷ 45 = 60 minutes.

Question 15: A project was completed with a spend of £84,000 against a budget of £105,000. What percentage of the budget was used?

70%
75%
80% (Correct answer)
85%

Correct answer: 80%

(84,000 ÷ 105,000) × 100 = 80%.

Question 16: An IT infrastructure budget allows £18,000 per server and the department can spend up to £150,000. What is the maximum number of servers the department can purchase?

9 servers
10 servers
7 servers
8 servers (Correct answer)

Correct answer: 8 servers

8 × £18,000 = £144,000 ≤ £150,000, but 9 × £18,000 = £162,000 > £150,000, so the maximum is 8 servers.

Question 17: A business earns £2,400 per day. How much does it earn in a 5-day working week?

£14,000
£9,600
£12,000 (Correct answer)
£10,000

Correct answer: £12,000

£2,400 × 5 = £12,000.

Question 18: A report states that absenteeism fell by 30% to 140 days. What was the original number of days?

180
200 (Correct answer)
175
220

Correct answer: 200

If the current value is 70% of the original, then original = 140 ÷ 0.70 = 200.

Question 19: Total costs are split: fixed costs £12,000 and variable costs £8,400. Revenue is £26,000. What is the profit?

£6,000
£4,600
£5,600 (Correct answer)
£7,000

Correct answer: £5,600

Total costs = £20,400. Profit = £26,000 − £20,400 = £5,600.

Question 20: An item originally costs £200. It is discounted by 12.5%. What is the sale price?

£175 (Correct answer)
£170
£180
£185

Correct answer: £175

12.5% of £200 = £25. Sale price = £200 − £25 = £175.

Question 21: What is the range of the values 3.5, 7.2, 1.8, 9.4, 5.6?

5.9
6.4
8.2
7.6 (Correct answer)

Correct answer: 7.6

Range = 9.4 − 1.8 = 7.6.

Question 22: A business paid £240,000 in wages. Wages represent 60% of total costs. What are the total costs?

£400,000 (Correct answer)
£420,000
£440,000
£360,000

Correct answer: £400,000

Total costs = £240,000 ÷ 0.60 = £400,000.

Question 23: What is the missing number: 2, 5, 10, 17, __, 37?

24
26 (Correct answer)
22
28

Correct answer: 26

Differences: +3, +5, +7, +9, +11. Next term = 17 + 9 = 26. The differences increase by 2 each time.

Question 24: A workforce of 500 is 60% female. How many male workers are there?

250
150
300
200 (Correct answer)

Correct answer: 200

If 60% are female, 40% are male. 40% of 500 = 200.

Question 25: What is the next term: 0.5, 1, 2, 4, 8, __?

10
20
12
16 (Correct answer)

Correct answer: 16

Each term is doubled: 8 × 2 = 16.

Question 26: A store buys 200 items at £4.50 each and sells 180 of them at £7.00 each. What is the overall profit?

£270
£450
£540
£360 (Correct answer)

Correct answer: £360

Cost = 200 × £4.50 = £900. Revenue = 180 × £7.00 = £1,260. Profit = £1,260 − £900 = £360.

Question 27: A business made a loss of £9,000 on a deal. This represents 12% of the original investment. What was the original investment?

£90,000
£72,000
£75,000 (Correct answer)
£80,000

Correct answer: £75,000

£9,000 = 12% of investment. Investment = £9,000 ÷ 0.12 = £75,000.

Question 28: What is the missing number: 100, 91, 83, 76, 70, __?

64
63
65 (Correct answer)
66

Correct answer: 65

Differences: −9, −8, −7, −6, −5. Next = 70 − 5 = 65.

Question 29: A price was reduced from £80 to £68. What percentage discount was applied?

20%
10%
15% (Correct answer)
12%

Correct answer: 15%

Reduction = £12. (12 ÷ 80) × 100 = 15%.

Question 30: A graph shows revenue for three products over one year. Product X: £150,000; Y: £90,000; Z: £60,000. What percentage of total revenue does Product X represent?

45%
55%
40%
50% (Correct answer)

Correct answer: 50%

Total = £300,000. X's share = 150,000 ÷ 300,000 = 0.5 = 50%.

Question 31: Profits fell from £200,000 to £170,000. What was the percentage decrease?

10%
12%
20%
15% (Correct answer)

Correct answer: 15%

Decrease = £30,000. (30,000 ÷ 200,000) × 100 = 15%.

Question 32: A team of 25 completes a project in 12 days. How many days would a team of 15 take to complete the same project (assuming the same work rate)?

20 (Correct answer)
18
16
24

Correct answer: 20

Total work = 25 × 12 = 300 person-days. Time for 15 people = 300 ÷ 15 = 20 days.

Question 33: An employee's tax bill is 20% on income above £12,570. Their income is £28,570. How much tax do they pay?

£4,000
£5,714
£2,800
£3,200 (Correct answer)

Correct answer: £3,200

Taxable income = £28,570 − £12,570 = £16,000. Tax = 20% of £16,000 = £3,200.

Question 34: A charity receives donations totalling £48,000. Administration costs take 12.5%. How much is available for charitable activities?

£44,000
£36,000
£42,000 (Correct answer)
£40,000

Correct answer: £42,000

Admin costs = 12.5% of £48,000 = £6,000. Available = £48,000 − £6,000 = £42,000.

Question 35: A project has 3 phases: Phase 1 takes 2 weeks, Phase 2 takes 3 weeks, Phase 3 takes 1.5 weeks. If Phase 2 starts 1 week after Phase 1 ends, what is the total elapsed time from start to finish?

8 weeks
6.5 weeks
7 weeks
7.5 weeks (Correct answer)

Correct answer: 7.5 weeks

Phase 1 ends at Week 2. Phase 2 starts at Week 3 (1-week gap) and ends at Week 6. Phase 3 starts at Week 6 and ends at Week 7.5. Total = 7.5 weeks.

Question 36: An area chart shows cumulative spending across four programmes over 12 months. Programme C reaches £3.1m by month 12 and was at £1.5m at month 6. What fraction of Programme C's total spending occurred in the second half of the year?

Approximately 52% (Correct answer)
Approximately 44%
Approximately 56%
Approximately 48%

Correct answer: Approximately 52%

Programme C second half spending = £3.1m minus £1.5m = £1.6m. As a fraction of total: (£1.6m / £3.1m) x 100 = 51.6%, approximately 52%.

Question 37: A cyclist travels 36 km in 1.5 hours. What is their average speed?

30 km/h
27 km/h
24 km/h (Correct answer)
18 km/h

Correct answer: 24 km/h

Speed = Distance ÷ Time = 36 ÷ 1.5 = 24 km/h.

Question 38: A table shows that Department A processed 240 applications and Department B processed 160. What fraction of applications did Department A process?

2/5
3/5 (Correct answer)
1/3
2/3

Correct answer: 3/5

Total = 240 + 160 = 400. Department A's share = 240/400 = 3/5.

Question 39: A chart shows sales grew from 800 units to 1,000 units. By what percentage did sales grow?

15%
20%
30%
25% (Correct answer)

Correct answer: 25%

Increase = 200 units. Percentage growth = (200 ÷ 800) × 100 = 25%.

Question 40: Three people share a prize in a ratio of 2:3:5. The total prize is £4,000. How much does the person with the largest share receive?

£2,000 (Correct answer)
£1,200
£1,600
£800

Correct answer: £2,000

Total parts = 10. Largest share (5 parts) = (5/10) × £4,000 = £2,000.

Civil Service Numerical Reasoning Test

The Civil Service Numerical Reasoning Test (CSNT) is an aptitude assessment used in UK Civil Service recruitment to evaluate candidates' ability to interpret numerical data from graphs, tables, and charts, and perform calculations involving percentages, ratios, number sequences, and financial concepts.

Questions

30 min

Time Limit

70%

To Pass

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