20 Basic Mathematics Practice Questions & Answers
Every Basic Mathematics practice question from the Police Officer Entrance Exam Practice Test, with the correct answer and a short explanation.
Start practice test →1. An officer writes 12 parking tickets on Monday, 8 on Tuesday, and 15 on Wednesday. How many tickets did the officer write over all three days combined?
- A.30
- B.33
- C.35✓ Answer
- D.37
Combining separate counts of the same item requires addition: 12 + 8 + 15 = 35, so the officer wrote 35 tickets across the three days.
Source: Police entrance exam blueprint — Basic Math: whole-number additionReport a problem with this question
2. A precinct began the month with 240 open cases and closed 165 of them, opening no new cases. How many cases remain open?
- A.65
- B.75✓ Answer
- C.85
- D.95
Removing a quantity from a starting total is subtraction: 240 − 165 = 75, so 75 cases remain open.
Source: Police entrance exam blueprint — Basic Math: whole-number subtractionReport a problem with this question
3. A dispatch center logged 200 calls in one shift, and 30% of them were traffic-related. How many calls were traffic-related?
- A.45
- B.50
- C.60✓ Answer
- D.70
A percentage of a total is found by multiplying: the part equals the whole times the rate, so 200 × 0.30 = 60 traffic-related calls.
Source: Police entrance exam blueprint — Basic Math: percentage of a quantity (part = whole × rate)Report a problem with this question
4. An investigator was assigned 24 cases and solved 18 of them. What percent of the cases did the investigator solve?
- A.70%
- B.72%
- C.75%✓ Answer
- D.80%
A percentage is the part divided by the whole, then multiplied by 100: 18 ÷ 24 = 0.75, which is 75%.
Source: Police entrance exam blueprint — Basic Math: finding a percentage (part ÷ whole)Report a problem with this question
5. Over five days, an officer made 4, 6, 3, 5, and 7 arrests. What was the average number of arrests per day?
- A.4
- B.5✓ Answer
- C.6
- D.7
An average (mean) is the sum of the values divided by how many there are: (4 + 6 + 3 + 5 + 7) ÷ 5 = 25 ÷ 5 = 5.
Source: Police entrance exam blueprint — Basic Math: arithmetic mean (average)Report a problem with this question
6. A patrol car travels 60 miles in 1.5 hours. What is its average speed in mph?
- A.30
- B.40✓ Answer
- C.45
- D.90
Average speed equals distance divided by time: 60 ÷ 1.5 = 40, so the car averages 40 mph.
Source: Police entrance exam blueprint — Basic Math: speed = distance ÷ timeReport a problem with this question
7. A patrol car travels at a steady 50 mph for 2.5 hours. How many miles does it cover?
- A.100
- B.115
- C.125✓ Answer
- D.150
Distance equals speed multiplied by time: 50 × 2.5 = 125 miles.
Source: Police entrance exam blueprint — Basic Math: distance = speed × timeReport a problem with this question
8. An officer must reach a scene 30 miles away while driving at 60 mph. How many minutes will the drive take?
- A.20
- B.30✓ Answer
- C.45
- D.60
Time equals distance divided by speed: 30 ÷ 60 = 0.5 hour, and 0.5 hour equals 30 minutes.
Source: Police entrance exam blueprint — Basic Math: time = distance ÷ speedReport a problem with this question
9. In a patrol unit the ratio of officers to sergeants is 8 to 1. If there are 40 officers, how many sergeants are there?
- A.4
- B.5✓ Answer
- C.6
- D.8
The ratio 8:1 means one sergeant for every 8 officers, so divide the officers by 8: 40 ÷ 8 = 5 sergeants.
Source: Police entrance exam blueprint — Basic Math: ratios and proportionsReport a problem with this question
10. A fleet keeps patrol cars and motorcycles in a ratio of 5 to 2. If there are 20 patrol cars, how many motorcycles are there?
- A.6
- B.8✓ Answer
- C.10
- D.12
20 patrol cars is 20 ÷ 5 = 4 groups of the ratio, and each group has 2 motorcycles, so 4 × 2 = 8 motorcycles.
Source: Police entrance exam blueprint — Basic Math: scaling a ratio to a totalReport a problem with this question
11. Three sealed evidence bags weigh 1.5 kg, 2.25 kg, and 0.75 kg. What is their combined weight?
- A.4.0
- B.4.25
- C.4.5✓ Answer
- D.4.75
Add the decimal weights, aligning place values: 1.5 + 2.25 + 0.75 = 4.5 kg.
Source: Police entrance exam blueprint — Basic Math: decimal additionReport a problem with this question
12. A patrol route is 3.2 miles long. If an officer drives the full route 4 times in a shift, how many miles are driven?
- A.12.2
- B.12.6
- C.12.8✓ Answer
- D.13.2
Repeating the same distance a fixed number of times is multiplication: 3.2 × 4 = 12.8 miles.
Source: Police entrance exam blueprint — Basic Math: decimal multiplicationReport a problem with this question
13. Last month a district received 120 incident reports. This month the number rose by 25%. How many reports were received this month?
- A.140
- B.145
- C.150✓ Answer
- D.160
A 25% increase adds 25% of the original to itself: 120 × 0.25 = 30, and 120 + 30 = 150 reports.
Source: Police entrance exam blueprint — Basic Math: percentage increaseReport a problem with this question
14. Reported burglaries in a neighborhood fell from 80 one year to 60 the next. What was the percent decrease?
- A.20%
- B.25%✓ Answer
- C.30%
- D.33%
Percent decrease is the drop divided by the original amount: (80 − 60) ÷ 80 = 20 ÷ 80 = 0.25, which is 25%.
Source: Police entrance exam blueprint — Basic Math: percentage decrease (change ÷ original)Report a problem with this question
15. A department assigns 156 officers evenly across 12 patrol teams. How many officers are on each team?
- A.12
- B.13✓ Answer
- C.14
- D.15
Distributing a total into equal groups is division: 156 ÷ 12 = 13 officers per team.
Source: Police entrance exam blueprint — Basic Math: whole-number divisionReport a problem with this question
16. An officer averaged 10 citations per day over a 4-day period. How many citations were issued in total?
- A.30
- B.36
- C.40✓ Answer
- D.44
Because average equals total divided by count, the total equals average times count: 10 × 4 = 40 citations.
Source: Police entrance exam blueprint — Basic Math: recovering a total from an averageReport a problem with this question
17. An officer's shift starts at 7:45 AM and ends at 4:15 PM. How many hours long is the shift?
- A.8
- B.8.5✓ Answer
- C.9
- D.9.5
From 7:45 AM to 3:45 PM is exactly 8 hours, and the extra 30 minutes to 4:15 PM adds half an hour, giving 8.5 hours.
Source: Police entrance exam blueprint — Basic Math: elapsed-time calculationReport a problem with this question
18. Over five days, the number of reports filed each day was 3, 7, 4, 9, and 5. What is the median number of reports?
- A.4
- B.5✓ Answer
- C.6
- D.7
The median is the middle value once the numbers are ordered: 3, 4, 5, 7, 9 — the center of five values is the third one, 5.
Source: Police entrance exam blueprint — Basic Math: median of a data setReport a problem with this question
19. Of 60 officers on a shift, one-quarter are assigned to traffic duty. How many officers are on traffic duty?
- A.10
- B.12
- C.15✓ Answer
- D.20
Taking one-quarter of a quantity means dividing it by 4: 60 ÷ 4 = 15 officers on traffic duty.
Source: Police entrance exam blueprint — Basic Math: fraction of a quantityReport a problem with this question
20. A suspect vehicle covers 45 miles in 45 minutes at a steady speed. What is its speed in mph?
- A.45
- B.50
- C.55
- D.60✓ Answer
Speed uses time in hours: 45 minutes is 0.75 hour, so 45 ÷ 0.75 = 60 mph. Because the trip took less than an hour, the mph value is higher than the miles traveled.
Source: Police entrance exam blueprint — Basic Math: speed with minutes converted to hoursReport a problem with this question
Practice questions modeled on the common domains of police officer written entrance exams (reading, writing/grammar, math, reasoning). Not legal advice and not affiliated with or endorsed by any law-enforcement agency or testing vendor. Agencies use different exams — check your agency's announcement for its specific format. BLS occupation profile →