22 Basic Mathematics Practice Questions & Answers

1. 1. An evidence clerk counts cash seized from three suspects and records it in this table: Suspect | $100 bills | $50 bills | $20 bills Alvarez | 14 | 6 | 9 Brooks | 8 | 3 | 12 Chen | 5 | 10 | 4 How much cash was counted for ALVAREZ only?

   • A.$1,190
   • B.$4,150
   • C.$1,700
   • D.$1,880✓ Answer

   With a denomination table, each cell must be multiplied by the value of its column and only the requested row may be summed. For Alvarez: 14 × $100 = $1,400, 6 × $50 = $300, 9 × $20 = $180, and $1,400 + $300 + $180 = $1,880. $1,190 is the Brooks row, $4,150 is all three rows added together, and $1,700 leaves out the $20 column.

   Source: Police entrance exam blueprint — Basic Math: cash/denomination table, row-selective total (DART Police & Ocean City PD study-guide sample format)Report a problem with this question

2. 2. A property report lists each item with a code (S = Stolen, D = Damaged): S — laptop — $725.50 D — window — $180.25 S — 2 bicycles — $410.00 D — mailbox — $96.75 S — toolbox — $132.00 What is the total value of ALL property listed on the report?

   • A.$1,267.50
   • B.$1,447.75
   • C.$1,544.50✓ Answer
   • D.$277.00

   The word ALL means no code filter applies, so every line is added with the decimal points aligned: $725.50 + $180.25 + $410.00 + $96.75 + $132.00 = $1,544.50. $1,267.50 is only the S-coded rows, $277.00 is only the D-coded rows, and $1,447.75 drops the $96.75 line.

   Source: Police entrance exam blueprint — Basic Math: report-table reading, unfiltered decimal money totalReport a problem with this question

3. 3. Using the same property report: S — laptop — $725.50 D — window — $180.25 S — 2 bicycles — $410.00 D — mailbox — $96.75 S — toolbox — $132.00 (S = Stolen, D = Damaged.) What is the total value of the STOLEN property only?

   • A.$277.00
   • B.$1,135.50
   • C.$1,267.50✓ Answer
   • D.$1,544.50

   A conditional total requires selecting rows by code first and adding second, so only the three S lines count: $725.50 + $410.00 + $132.00 = $1,267.50. $1,544.50 is every row, $277.00 is the D rows, and $1,135.50 forgets the $132.00 toolbox.

   Source: Police entrance exam blueprint — Basic Math: code-filtered (conditional) table totalReport a problem with this question

4. 4. A judge sets bond at $18,000 for a defendant, and the court requires 10% of that amount to be posted in cash. How much cash must be posted?

   • A.$1,080
   • B.$1,800✓ Answer
   • C.$180
   • D.$18

   Percent of an amount means multiplying the whole by the rate written as a decimal: 10% = 0.10, so $18,000 × 0.10 = $1,800. Because 10% simply moves the decimal point one place left, $180 and $18 are decimal-placement errors, the most commonly graded mistake on this item type.

   Source: Police entrance exam blueprint — Basic Math: percent of an amount (part = whole × rate), decimal placementReport a problem with this question

5. 5. A precinct logged 400 burglary reports in the first quarter. In the second quarter the count fell 20% from the first-quarter figure, and in the third quarter it rose 10% above the second-quarter figure. How many reports were logged in the third quarter?

   • A.320
   • B.352✓ Answer
   • C.360
   • D.440

   Successive percent changes must be applied one at a time, each to the value that exists at that moment, never added together. First: 400 × 0.80 = 320. Then the 10% increase applies to 320, not to 400: 320 × 1.10 = 352. Chaining the percents additively (−20% + 10% = −10%) gives the trap answer 360.

   Source: Police entrance exam blueprint — Basic Math: successive percent change (apply each change to the new base)Report a problem with this question

6. 6. A weekly citation tally shows: Officer A 45, Officer B 30, Officer C 60, Officer D 15. What percent of the week's citations were issued by Officer C?

   • A.60%
   • B.40%✓ Answer
   • C.33%
   • D.25%

   A percent of a total requires the whole first, so add every entry: 45 + 30 + 60 + 15 = 150. Then divide the part by the whole and multiply by 100: 60 ÷ 150 = 0.40 = 40%. The choice 60% simply repeats the raw count as if it were already a percent, and 25% comes from dividing by four officers instead of by the total.

   Source: Police entrance exam blueprint — Basic Math: tally-table reading combined with part ÷ whole percentReport a problem with this question

7. 7. A department pays overtime at 1.5 times an officer's regular hourly rate. An officer whose regular rate is $28.00 per hour works 6 hours of overtime. How much overtime pay is earned?

   • A.$252✓ Answer
   • B.$420
   • C.$168
   • D.$336

   The premium rate must be computed before multiplying by hours, because the 1.5 multiplier applies to the hourly rate, not to the total: $28.00 × 1.5 = $42.00 per overtime hour, and $42.00 × 6 = $252.00. $168 ignores the 1.5 multiplier entirely and $336 uses a 2× multiplier instead of 1.5×.

   Source: Police entrance exam blueprint — Basic Math: multi-step money problem, premium (1.5×) rate then hoursReport a problem with this question

8. 8. An officer drives a personal vehicle 145 miles on department business. The department reimburses $0.40 per mile. What is the total reimbursement?

   • A.$36.25
   • B.$580.00
   • C.$5.80
   • D.$58.00✓ Answer

   A per-unit rate is applied by multiplying the rate by the number of units: 145 × $0.40 = $58.00. A quick sanity check confirms the decimal point, since $0.40 is a little under half a dollar and 145 miles should therefore yield a little under $72.50, which rules out $5.80 and $580.00 as decimal-placement errors.

   Source: Police entrance exam blueprint — Basic Math: unit-rate money problem (rate × quantity), decimal placementReport a problem with this question

9. 9. Nine patrol units are dispatched toward a scene 40 miles away. Seven units reach the scene, while two units are recalled after covering 25% of the distance. How many miles in total did the nine units drive toward the scene?

   • A.300✓ Answer
   • B.290
   • C.360
   • D.280

   The two groups must be computed separately and then added, because they did not travel the same distance: 7 × 40 = 280 miles, and each recalled unit drove 40 × 0.25 = 10 miles, so 2 × 10 = 20 miles. The total is 280 + 20 = 300 miles. 360 assumes all nine completed the trip and 280 ignores the recalled units entirely.

   Source: Police entrance exam blueprint — Basic Math: multi-step composite (multiplication + percent-of + addition)Report a problem with this question

10. 10. An officer's regular shift runs from 4:00 p.m. to midnight. At 11:40 p.m. the officer is dispatched to a disturbance and does not clear the scene until 1:15 a.m. How much time PAST the end of the regular shift did the officer work?

    • A.35 minutes
    • B.1 hour 15 minutes✓ Answer
    • C.1 hour 35 minutes
    • D.2 hours 15 minutes

    Overtime is measured from the moment the shift ends, not from the dispatch time, so the count starts at midnight and runs to 1:15 a.m., which is 1 hour 15 minutes. The 11:40 p.m. dispatch is a deliberate distractor: measuring from the call gives 1 hour 35 minutes, which is total time on the call rather than time past the shift.

    Source: Police entrance exam blueprint — Basic Math: elapsed time across midnight, overtime measured from shift endReport a problem with this question

11. 11. During one shift an officer issued 3 times as many written warnings as citations. The warnings and citations together totaled 96. How many citations did the officer issue?

    • A.48
    • B.24✓ Answer
    • C.72
    • D.32

    Let c be the number of citations; the warnings are 3c, and the two quantities together give the equation c + 3c = 96, so 4c = 96 and c = 24 (with 72 warnings, which checks: 24 + 72 = 96). The trap 32 comes from dividing 96 by 3 instead of by the 4 total parts, and 72 answers for warnings rather than citations.

    Source: Police entrance exam blueprint — Basic Math: solving for one unknown (total split into equal parts)Report a problem with this question

12. 12. A dispatch log shows an officer began a shift at 2200 hours and was relieved at 0630 hours the next morning. How long was the shift?

    • A.9 hours 30 minutes
    • B.15 hours 30 minutes
    • C.8 hours 30 minutes✓ Answer
    • D.7 hours 30 minutes

    When a shift crosses midnight the interval is split in two and the pieces are added: 2200 to 2400 is 2 hours, and 0000 to 0630 is 6 hours 30 minutes, giving 8 hours 30 minutes. Subtracting 0630 from 2200 directly produces the trap 15 hours 30 minutes, because clock time restarts at midnight rather than continuing upward.

    Source: Police entrance exam blueprint — Basic Math: elapsed time on the 24-hour clock, crossing midnightReport a problem with this question

13. 13. A police report must record times using the 24-hour (military) clock. An incident occurred at 9:45 p.m. How should that time be written in the report?

    • A.2145✓ Answer
    • B.0945
    • C.1945
    • D.2045

    On the 24-hour clock, times from 1:00 p.m. onward are converted by adding 12 to the hour, so 9 p.m. becomes 9 + 12 = 21 and the minutes are unchanged: 2145. Choosing 0945 keeps the a.m. hour, while 1945 and 2045 come from adding 10 or 11 instead of 12.

    Source: Police entrance exam blueprint — Basic Math: 24-hour (military) time conversion for report writingReport a problem with this question

14. 14. Responding to a call, a patrol car travels 3 miles on one street, 11 miles on a highway, and 16 miles on a rural road. If the car averages 60 miles per hour for the entire route, how long does the trip take?

    • A.30 minutes✓ Answer
    • B.16 minutes
    • C.1 hour
    • D.45 minutes

    The legs must be added before the rate is applied, because time = total distance ÷ speed: 3 + 11 + 16 = 30 miles, and 30 ÷ 60 = 0.5 hour = 30 minutes. At exactly 60 mph each mile takes one minute, which is the fastest pencil-and-paper check; the choice 16 minutes uses only the final leg.

    Source: Police entrance exam blueprint — Basic Math: rate-time-distance, sum route legs before applying the rateReport a problem with this question

15. 15. A suspect vehicle traveling 70 mph is 2 miles ahead of a patrol car traveling 80 mph on the same straight highway. If both hold their speeds, how long until the patrol car catches the suspect vehicle?

    • A.24 minutes
    • B.1.5 minutes
    • C.8 minutes
    • D.12 minutes✓ Answer

    A pursuit closes at the difference between the two speeds, not at either car's own speed: 80 − 70 = 10 mph of closing rate. Time = gap ÷ closing speed = 2 ÷ 10 = 0.2 hour, and 0.2 × 60 = 12 minutes. Using the patrol car's full 80 mph gives the trap 1.5 minutes.

    Source: Police entrance exam blueprint — Basic Math: relative (closing) speed in pursuit problemsReport a problem with this question

16. 16. An officer measures a skid mark as 7 feet 5 inches. The accident report requires the length to be entered in inches only. Given that 12 inches = 1 foot, what figure goes in the report?

    • A.96 inches
    • B.75 inches
    • C.89 inches✓ Answer
    • D.84 inches

    A compound measurement is converted by changing the larger unit and then adding the leftover smaller unit: 7 × 12 = 84 inches, plus the 5 loose inches, equals 89 inches. The choice 84 drops the extra inches and 96 rounds the measurement up to a full 8 feet, which the report would not permit.

    Source: Police entrance exam blueprint — Basic Math: compound unit conversion (12 in = 1 ft), report in a single unitReport a problem with this question

17. 17. A seized package is weighed at 3 pounds 9 ounces. The evidence log requires the weight in ounces only. Given that 16 ounces = 1 pound, what weight is logged?

    • A.39 ounces
    • B.64 ounces
    • C.48 ounces
    • D.57 ounces✓ Answer

    Converting down to a single unit means multiplying the pounds by the conversion factor and then adding the loose ounces: 3 × 16 = 48 ounces, plus 9 ounces, equals 57 ounces. The choice 48 forgets the extra ounces and 64 rounds up to a full 4 pounds.

    Source: Police entrance exam blueprint — Basic Math: compound unit conversion (16 oz = 1 lb)Report a problem with this question

18. 18. An item of evidence weighs 2,500 grams. Using the conversions 1 kilogram = 1,000 grams and 1 kilogram = 2.2 pounds, what is the weight in pounds?

    • A.5.5 pounds✓ Answer
    • B.55 pounds
    • C.1.14 pounds
    • D.2.5 pounds

    A two-step conversion moves through the shared unit: 2,500 ÷ 1,000 = 2.5 kilograms, then 2.5 × 2.2 = 5.5 pounds. Dividing by 2.2 instead of multiplying gives 1.14, the classic wrong-direction error, and 2.5 stops after the first step without converting to pounds.

    Source: Police entrance exam blueprint — Basic Math: metric-to-customary conversion with the factor suppliedReport a problem with this question

19. 19. Over four shifts an officer averaged 12 calls per shift. The first three shifts produced 10, 14, and 11 calls. How many calls occurred on the fourth shift?

    • A.15
    • B.12
    • C.13✓ Answer
    • D.11

    Because an average is the total divided by the count, the total can be recovered by multiplying: 12 × 4 = 48 calls across all four shifts. The three known shifts account for 10 + 14 + 11 = 35, so the fourth shift had 48 − 35 = 13 calls. Answering 12 assumes the missing value must equal the average, which is only true when every value is identical.

    Source: Police entrance exam blueprint — Basic Math: recovering a missing value from an average (total = average × count)Report a problem with this question

20. 20. A length of evidence rope measures 8 1/4 feet. An officer cuts off and books 2 5/8 feet of it. How much rope remains?

    • A.6 5/8 feet
    • B.5 5/8 feet✓ Answer
    • C.6 3/8 feet
    • D.5 3/8 feet

    Mixed numbers must share a denominator before subtracting, so 8 1/4 becomes 8 2/8. Since 2/8 is smaller than 5/8, borrow one whole foot: 8 2/8 = 7 10/8. Then 7 10/8 − 2 5/8 = 5 5/8 feet. The trap 6 3/8 comes from subtracting the smaller fraction from the larger one instead of borrowing.

    Source: Police entrance exam blueprint — Basic Math: mixed-number subtraction with common denominators and borrowingReport a problem with this question

21. 21. A department's staffing plan calls for sworn officers and civilian employees in a 3:5 ratio. If the department has 320 employees in total, how many are sworn officers?

    • A.192
    • B.96
    • C.120✓ Answer
    • D.200

    A 3:5 ratio is part-to-part, so the total is divided into 3 + 5 = 8 shares and officers make up 3 of every 8 employees: 320 ÷ 8 = 40 per share, and 3 × 40 = 120 officers. Treating 3:5 as part-to-whole and taking 3/5 of 320 gives the trap 192, while 200 is the civilian count.

    Source: Police entrance exam blueprint — Basic Math: ratio and proportion, part-to-part vs part-to-wholeReport a problem with this question

22. 22. A warehouse floor measures 90 feet by 60 feet. Investigators tape off a rectangular section measuring 40 feet by 30 feet. Using Area = length × width, how many square feet of the floor are OUTSIDE the taped-off section?

    • A.5,400 square feet
    • B.3,000 square feet
    • C.1,200 square feet
    • D.4,200 square feet✓ Answer

    A remaining-area problem takes two areas and subtracts: the whole floor is 90 × 60 = 5,400 square feet and the taped section is 40 × 30 = 1,200 square feet, so the area outside it is 5,400 − 1,200 = 4,200 square feet. The listed 1,200 answers for the taped section instead of the area asked for. (Geometry is agency-dependent: CWH-format municipal exams include rectangular area, while the NPOST states it has no geometry problems.)

    Source: Police entrance exam blueprint — Basic Math: rectangular area with a remaining-area step (CWH-format agencies; excluded from the NPOST)Report 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 →