Numerical Reasoning

Crime statistics for Metropolis Police: Burglary 2024: 450 incidents, Burglary 2025: 540 incidents. What is the percentage increase?

• A22%
• B18%
• C20%✓
• D25%

Answer: Increase = 540 - 450 = 90. Percentage = (90/450) × 100 = 20%

A police shift has 24 officers. If 3 are on sick leave and 5 are on training, what percentage of the shift is available for duty?

• A79%
• B71%
• C75%
• D67%✓

Answer: Available officers = 24 - 3 - 5 = 16. Percentage = (16/24) × 100 = 66.67%, approximately 67%.

A town's population is 200,000. Crime survey shows 15% experienced crime in the past year. How many people experienced crime?

• A15,000
• B20,000
• C25,000
• D30,000✓

Answer: 15% of 200,000 = 0.15 × 200,000 = 30,000

Police response times: Day shift average 12 minutes, Night shift average 18 minutes. What is the ratio of day to night response time?

• A2:3✓
• B4:5
• C3:5
• D3:4

Answer: Day:night = 12:18. Divide both parts by their highest common factor, 6: 12 ÷ 6 = 2 and 18 ÷ 6 = 3, so the ratio is 2:3.

Police force budget allocation: Frontline policing 55%, Administration 25%, Specialist units 20%. If total budget is £100 million, how much is allocated to specialist units?

• A£30 million
• B£15 million
• C£25 million
• D£20 million✓

Answer: 20% of £100 million = 0.20 × £100 million = £20 million

Training course attendance: Day 1 - 45 officers, Day 2 - 42 officers, Day 3 - 39 officers. What is the average attendance?

• A40
• B41
• C42✓
• D43

Answer: (45 + 42 + 39) / 3 = 126 / 3 = 42

Vehicle theft comparison: North division 180 thefts (2024), South division 240 thefts (2024). What percentage more thefts occurred in South compared to North?

• A40%
• B33%✓
• C25%
• D50%

Answer: Difference = 240 - 180 = 60. Percentage more = (60/180) × 100 = 33.3%, approximately 33%.

Arrest outcomes: Charged with offence 35%, Released on bail 40%, Released without charge 25%. If 200 people were arrested, how many were released without charge?

• A25
• B40
• C50✓
• D70

Answer: 25% of 200 = 0.25 × 200 = 50

Sick leave statistics: Officers absent due to illness: Week 1 - 8, Week 2 - 12, Week 3 - 10, Week 4 - 6. What is the median number of absences?

• A9✓
• B10
• C11
• D12

Answer: Sorted: 6, 8, 10, 12. With four values the median is the mean of the middle two: (8 + 10) / 2 = 18 / 2 = 9. Simply picking the larger middle value gives 10, and averaging the middle two of the unsorted list (12 and 10) gives 11 - both are wrong.

Community policing officer workload: Officer A - 15 community events, Officer B - 12 community events, Officer C - 18 community events. Total workload hours: 240 hours. What is the average hours per event?

• A6.7 hours
• B6.2 hours
• C5.3 hours✓
• D5.7 hours

Answer: Total events = 15 + 12 + 18 = 45. Hours per event = 240 ÷ 45 = 5.33, approximately 5.3 hours.

Domestic abuse calls: Year 1 - 2,500 calls, Year 2 - 2,750 calls. What is the percentage increase?

• A15%
• B5%
• C12%
• D10%✓

Answer: Increase = 2,750 - 2,500 = 250. Percentage = (250/2,500) × 100 = 10%

Crimes reported per 10,000 population: City A - 420, City B - 350. What is the ratio of crime in City A to City B?

• A4:3
• B3:2
• C5:4
• D6:5✓

Answer: Ratio = 420:350. Divide both by 70 = 6:5

Police misconduct complaints: Substantiated 45, Not substantiated 135, Withdrawn 20. What percentage were substantiated?

• A22.5%✓
• B25%
• C20%
• D28%

Answer: Total complaints = 45 + 135 + 20 = 200. Percentage substantiated = (45/200) × 100 = 22.5%. The denominator is every complaint received, not just the 180 that reached a substantiated/not-substantiated decision.

Officer shift sizes recorded over four days: Monday 32 officers, Tuesday 28 officers, Wednesday 18 officers, Thursday 32 officers. What is the mode (most common shift size)?

• A18
• B26
• C28
• D32✓

Answer: The mode is the value that occurs most often. The four shift sizes are 32, 28, 18 and 32. 32 occurs twice and every other size occurs once, so the mode is 32.

Overtime costs: Month 1 - £8,000, Month 2 - £10,500, Month 3 - £9,200. What is the average monthly overtime cost?

• A£9,900
• B£9,233✓
• C£9,500
• D£9,000

Answer: (8,000 + 10,500 + 9,200) / 3 = 27,700 / 3 = 9,233.33, approximately £9,233

Prosecution outcomes: Guilty 68%, Not guilty 12%, Acquitted 20%. Of 500 cases, how many resulted in guilty verdicts?

• A300
• B320
• C340✓
• D360

Answer: 68% of 500 = 0.68 × 500 = 340

Evidence storage: Items stored 2024: 1,200, Items stored 2025: 1,500. What is the percentage increase?

• A30%
• B20%
• C25%✓
• D15%

Answer: Increase = 1,500 - 1,200 = 300. Percentage = (300/1,200) × 100 = 25%

Police partnership funding: Police contribution £500,000, Health service contribution £300,000, Local authority contribution £200,000. What percentage is the police contribution?

• A60%
• B45%
• C55%
• D50%✓

Answer: Total budget = 500,000 + 300,000 + 200,000 = 1,000,000. Police percentage = (500,000/1,000,000) × 100 = 50%.

Victim support contact: Telephone 1,200 contacts, In-person 400 contacts, Online 800 contacts. What ratio of contacts were telephone vs in-person?

• A2:1
• B4:1
• C1:3
• D3:1✓

Answer: Ratio = 1,200:400. Divide both by 400 = 3:1

Performance metrics: Crimes detected 2024: 3,600, Crimes detected 2025: 3,960. What is the percentage increase in detection?

• A10%✓
• B15%
• C8%
• D12%

Answer: Increase = 3,960 - 3,600 = 360. Percentage = (360/3,600) × 100 = 10%

Youth crime figures: Age 10-14: 450 offences, Age 15-17: 720 offences, Age 18-20: 380 offences. What is the average offences per age group?

• A516
• B517✓
• C518
• D519

Answer: (450 + 720 + 380) / 3 = 1,550 / 3 = 516.67, approximately 517

Stop and search data: Resulted in arrest 45, Did not result in arrest 855. What percentage resulted in arrest?

• A5.3%
• B5.8%
• C5%✓
• D5.5%

Answer: Total = 45 + 855 = 900. Percentage = (45/900) × 100 = 5%

Custody suite occupancy: Morning 8 cells occupied out of 20, Afternoon 14 cells out of 20, Evening 18 cells out of 20. What is the average occupancy percentage?

• A55%
• B66.7%✓
• C50%
• D60%

Answer: Average occupancy = [(8/20) + (14/20) + (18/20)] / 3 = [0.4 + 0.7 + 0.9] / 3 = 2.0 / 3 = 0.667 = 66.7%. The aggregate figure agrees: 40 occupied cells out of 60 cell-slots = 66.7%.

Fines issued: Speeding 1,200, Parking violations 800, Other 400. Total collected: £180,000. What is the average fine amount?

• A£100
• B£75✓
• C£90
• D£50

Answer: Total fines issued = 1,200 + 800 + 400 = 2,400. Average = £180,000 / 2,400 = £75

Drug seizures: Cocaine 50kg, Heroin 30kg, Cannabis 120kg. What percentage of total seizure was cocaine?

• A30%
• B25%✓
• C20%
• D35%

Answer: Total = 50 + 30 + 120 = 200kg. Cocaine percentage = (50/200) × 100 = 25%

Promotion board results: Passed 24, Failed 56. What is the pass rate?

• A35%
• B25%
• C40%
• D30%✓

Answer: Total candidates = 24 + 56 = 80. Pass rate = (24/80) × 100 = 30%.

Policing areas: Urban population 2 million, Rural population 500,000, Suburban population 1.5 million. Total officers: 6,000. What is the average population per officer?

• A583
• B600
• C617
• D667✓

Answer: Total population = 2,000,000 + 500,000 + 1,500,000 = 4,000,000. Population per officer = 4,000,000 ÷ 6,000 = 666.67, approximately 667.

Incident response times in minutes: Call 1 - 8, Call 2 - 14, Call 3 - 11, Call 4 - 9, Call 5 - 13. What is the median response time?

• A10
• B11✓
• C12
• D13

Answer: Sorted: 8, 9, 11, 13, 14. Median (middle value) = 11

Complaint handling duration: Case A - 45 days, Case B - 52 days, Case C - 48 days, Case D - 50 days, Case E - 55 days. What is the mean duration?

• A51 days
• B48 days
• C52 days
• D50 days✓

Answer: Mean = (45 + 52 + 48 + 50 + 55) ÷ 5 = 250 ÷ 5 = 50 days.

Diversity statistics: Male officers 75%, Female officers 25%. If force has 4,000 officers total, how many are female?

• A1,000✓
• B2,000
• C3,000
• D4,000

Answer: 25% of 4,000 = 0.25 × 4,000 = 1,000. Assuming an even split would give 2,000, 3,000 is the number of male officers (75%), and 4,000 is the whole force.

Vehicle maintenance costs: Police car A - £2,400/year, Police car B - £1,800/year, Police car C - £2,200/year. Average maintenance cost per vehicle?

• A£2,133✓
• B£2,000
• C£2,300
• D£2,200

Answer: (2,400 + 1,800 + 2,200) / 3 = 6,400 / 3 = 2,133.33, approximately £2,133

Crime prevention investment: Community schemes £500,000, CCTV systems £800,000, Policing £1,200,000. What percentage is spent on CCTV?

• A32%✓
• B20%
• C30%
• D35%

Answer: Total = 500,000 + 800,000 + 1,200,000 = 2,500,000. CCTV share = (800,000 / 2,500,000) x 100 = 32%.

Call volume analysis: Emergency calls (Grade 1) 5,000, Urgent calls (Grade 2) 8,000, Non-urgent calls (Grade 3) 12,000. What percentage are non-urgent?

• A50%
• B55%
• C48%✓
• D40%

Answer: Total = 5,000 + 8,000 + 12,000 = 25,000. Non-urgent percentage = (12,000 / 25,000) x 100 = 48%.

Training participation rates: Course A enrolled 120, completed 96. Course B enrolled 150, completed 135. What is the overall completion rate?

• A85.6%✓
• B90%
• C92%
• D88%

Answer: Total enrolled = 120 + 150 = 270. Total completed = 96 + 135 = 231. Overall completion rate = (231/270) × 100 = 85.56%, which rounds to 85.6%. This is the aggregate rate (total completed / total enrolled), not the average of the two course rates.

Resource allocation by district: North 35 officers, South 42 officers, East 38 officers, West 45 officers. What percentage of total officers are in the South district?

• A26%✓
• B22%
• C20%
• D24%

Answer: Total = 35 + 42 + 38 + 45 = 160. South percentage = (42/160) × 100 = 26.25%, approximately 26%

Repeat offenders: First-time offenders 1,200, Repeat offenders (2-5 times) 400, Multiple repeat offenders (6+ times) 100. What percentage are first-time offenders?

• A75%
• B70.6%✓
• C85%
• D80%

Answer: Total = 1,200 + 400 + 100 = 1,700. First-time percentage = (1,200/1,700) × 100 = 70.59%, which rounds to 70.6%.

Sickness absence: Officers absent 0 days - 300, Officers absent 1-5 days - 250, Officers absent 6-10 days - 80, Officers absent 11+ days - 20. What is the total number of officers?

• A600
• B650✓
• C700
• D750

Answer: Total = 300 + 250 + 80 + 20 = 650

Witness interviews: Completed same day 80, Completed within 3 days 180, Completed within 1 week 220, Not yet completed 120. What percentage were completed same day?

• A13.3%✓
• B12%
• C20%
• D24%

Answer: Total = 80 + 180 + 220 + 120 = 600. Same-day percentage = (80 / 600) x 100 = 13.3%.

Promotion eligibility: Years of service 5-10 years - 450 eligible, 10-15 years - 600 eligible, 15+ years - 300 eligible. What is the mode (most common group)?

• A15+ years
• B10-15 years✓
• CEqual
• D5-10 years

Answer: The group with highest count is 10-15 years (600), so that's the mode.

Forensic lab backlog: Month 1 - 450 cases pending, Month 2 - 420 cases pending, Month 3 - 380 cases pending. What is the trend (average reduction per month)?

• A25 cases/month
• B30 cases/month
• C40 cases/month
• D35 cases/month✓

Answer: Month 1 to 2 reduction: 450 - 420 = 30. Month 2 to 3 reduction: 420 - 380 = 40. Average reduction = (30 + 40) / 2 = 35 cases/month.