The math section is everyday arithmetic set in police work: patrol miles, the value of stolen property, overtime hours, averages and simple percent. You get 20 min for 20 items and a sheet of scratch paper. The 18 questions below drill the same kinds of problem.
20items on the test
20 minsection time
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18questions on this page
What the math items ask
From the item types in the test owner’s study guide, in our words:
Totals and differences: add up a list of stolen items or cash, or find the total except one item.
Averages: total ÷ count, including the “average of the other days” once one day is taken out.
Rates: fuel per 100 miles, cost per case, visits per week across a year with weeks off.
Time: shift length, overtime, response times and spans that cross midnight.
Percent and money: a fee or tax on a charge, a discount, a share of a total.
The slips the wrong answers are built on
Every wrong option here comes from a mistake people make under time:
stopping one step early, so the intermediate total shows up as an option;
dividing by every day when the question leaves one out;
a decimal one place off: 1.4 or 140 gallons instead of 14;
a $100 carry slip in the hundreds column;
using a number from the story that the question never asks about.
At 20 min for 20 items you have about a minute each. Write each step on scratch paper, and check the last line against what the question asks before you answer.
18 math questions
0 of 18 answered · 0 correct
Question 1 of 18 · Mathematics · 20 itemsNot answered
An officer drives a patrol vehicle to a district training center at an average speed of 40 mph, completing the trip in 45 minutes. If the officer returns using the same route but maintains an average speed of 50 mph, how much time will the return trip take?
Answer explanations
A
Correct: 36 minutes: the first leg is three quarters of an hour at forty miles per hour, or thirty miles, and thirty miles at 50 mph takes 0.6 hour.
B
Incorrect: 60 comes from reading 0.6 hour as 60 minutes.
C
Incorrect: 45 minutes assumes the trip takes the same time at a higher speed.
D
Incorrect: 30 is the distance in miles, not the time.
E
Incorrect: 40 minutes is how long the return would take at forty-five miles per hour, not at 50 mph.
Question 2 of 18 · Mathematics · 20 itemsNot answered
A cleaning solution must be mixed in a ratio of 1:7 (1 part chemical concentrate to 7 parts water). If an officer needs to prepare exactly 40 gallons of the total mixture, how many gallons of the chemical concentrate are required?
Answer explanations
A
Incorrect: 7 is the water's share of the ratio, not an amount in gallons.
B
Incorrect: 5 5/7 gallons divides 40 by 7 instead of by the 8 total parts.
C
Incorrect: 35 gallons is the water, the seven parts.
D
Incorrect: 8 is the number of parts, not the gallons of concentrate.
E
Correct: A 1:7 mix has 8 parts; 40 ÷ 8 = 5 gallons per part, and the concentrate is one part.
Question 3 of 18 · Mathematics · 20 itemsNot answered
Response times to a priority call over five shifts were 4, 5, 5, 26, and 6 minutes. The 26-minute response occurred during a road closure and is left out. What is the average of the other four response times?
Answer explanations
A
Incorrect: 11.5 minutes divides the full 46 by 4, so the 26 was not removed.
B
Incorrect: 9.2 is the average of all five times, including the one to be left out.
C
Correct: Without the 26, the times add to 20, and 20 ÷ 4 = 5 minutes.
D
Incorrect: 6.5 minutes divides the 26 by 4 instead of averaging the other times.
E
Incorrect: 4 minutes divides 20 by 5, though only four times remain.
Question 4 of 18 · Mathematics · 20 itemsNot answered
A patrol car gets 25 miles per gallon. How many gallons of fuel will it use on a 120-mile patrol?
Answer explanations
A
Incorrect: 3,000 gallons multiplies 120 by 25 instead of dividing.
B
Incorrect: 95 gallons subtracts 25 from 120.
C
Correct: Gallons = miles ÷ miles per gallon: 120 ÷ 25 = 4.8.
D
Incorrect: 0.21 gallon divides 25 by 120, which is upside down.
E
Incorrect: 48 misplaces the decimal point.
Question 5 of 18 · Mathematics · 20 itemsNot answered
A patrol log shows that an officer spent 3.4 hours on a stakeout. How long is this in hours and minutes?
Answer explanations
A
Incorrect: 20 minutes would be one third of an hour, or about 0.33 hour.
B
Correct: 0.4 hour × 60 = 24 minutes, so 3.4 hours is 3 hours 24 minutes.
C
Incorrect: 36 minutes is the rest of the hour (60 − 24), not the part worked.
D
Incorrect: This reads the .4 as 4 minutes.
E
Incorrect: This reads the .4 as 40 minutes; an hour has 60 minutes, not 100.
Question 6 of 18 · Mathematics · 20 itemsNot answered
Captain Miller is reviewing quarterly clearance rates for five detective squads. The North Squad cleared 19 of 32 assigned cases. The South Squad cleared 11 of 20. The East Squad cleared 3 of 5. The West Squad cleared 7 of 12. The Central Squad cleared 9 of 16. Which squad achieved the highest clearance rate?
Answer explanations
A
Incorrect: Central Squad cleared 9 of 16, or about 56%.
B
Incorrect: West Squad cleared 7 of 12, or about 58%.
C
Incorrect: South Squad cleared 11 of 20, or 55%.
D
Incorrect: North Squad cleared the most cases, but 19 of 32 is only about 59%.
E
Correct: East Squad cleared 3 of 5, or 60%, the highest rate of the five.
Question 7 of 18 · Mathematics · 20 itemsNot answered
A water leak at a precinct is losing water at a rate of 10 gallons per hour. If the municipality charges $0.05 per gallon for water usage, what is the cost of the water lost over a full 24-hour day?
Answer explanations
A
Incorrect: $10.50 is the cost of 210 gallons, which is only 21 hours of leaking.
B
Incorrect: $50.00 is the cost of 1,000 gallons, far more than the 240 gallons lost in a day.
C
Incorrect: $24.00 charges 10 cents per gallon instead of 5.
D
Incorrect: $12.50 is the cost of 250 gallons, one hour more than a full day.
Question 8 of 18 · Mathematics · 20 itemsNot answered
An item costs $120.00 before tax. The sales tax rate is 8.25%. What is the total cost including tax?
Answer explanations
A
Incorrect: $129.60 uses 8% and drops the extra 0.25%.
B
Incorrect: $219.00 treats 8.25% as 82.5%.
C
Incorrect: $9.90 is the tax alone, not the total.
D
Correct: $129.90 is $120.00 plus 8.25% tax (8% is $9.60 and 0.25% is $0.30).
E
Incorrect: $130.90 adds an extra dollar.
Question 9 of 18 · Mathematics · 20 itemsNot answered
The price of a replacement light bar was raised 40%. Later the raised price was cut by 25%. Compared with the price before either change, what is the net change?
Answer explanations
A
Incorrect: A 40% increase forgets the later 25% cut.
B
Incorrect: A 5% decrease is wrong: the final price is above the starting price.
C
Incorrect: A 15% increase just subtracts 25 from 40, but the cut is taken from the higher price.
D
Correct: +40% turns $100 into $140, and 25% off $140 leaves $105: a 5% increase.
E
Incorrect: "No change" assumes the two changes cancel, but they do not.
Question 10 of 18 · Mathematics · 20 itemsNot answered
An evidence room holds 360 items. One-third of them are narcotics. Of the remaining items, three-eighths are weapons. How many items are neither narcotics nor weapons?
Answer explanations
A
Correct: 150 items: a third of 360 are narcotics, and 3/8 of the rest are weapons, leaving 5/8 of the remaining items.
B
Incorrect: 240 is what remains after the narcotics, before the weapons are removed.
C
Incorrect: 105 items takes 3/8 of all 360 items instead of 3/8 of the remainder.
D
Incorrect: 90 is the number of weapons.
E
Incorrect: 120 is the number of narcotics.
Question 11 of 18 · Mathematics · 20 itemsNot answered
A monthly report lists incidents by category: assault 12, theft 8, vandalism 5, and drug activity 15. What percent of all the incidents were thefts?
Answer explanations
A
Incorrect: 25% divides 8 by 32, the incidents other than thefts.
B
Incorrect: 12.5% is the vandalism share (5 of 40).
C
Incorrect: 37.5% is the drug-activity share (15 of 40).
D
Incorrect: 8% reads the count of thefts as a percent.
E
Correct: There are 40 incidents in all, and 8 ÷ 40 = 20%.
Question 12 of 18 · Mathematics · 20 itemsNot answered
A radio is priced at $200. It is marked down 25%, and the department then applies a $20 coupon to the reduced price. What is the final price?
Answer explanations
A
Incorrect: $175 subtracts $25 instead of 25%.
B
Incorrect: $150 is the price before the coupon is applied.
C
Correct: $130 takes 25% off $200 first and then subtracts the $20 coupon.
D
Incorrect: $70 is the total amount saved, not the final price.
E
Incorrect: $135 applies the coupon first and then takes 25% off $180, the reverse order.
Question 13 of 18 · Mathematics · 20 itemsNot answered
Officer Ruiz walked a foot patrol of 2 miles and then walked another 2,640 feet to reach a call. How many feet did he walk in all? (1 mile = 5,280 feet)
Answer explanations
A
Incorrect: 7,920 feet is 1.5 miles; it counts only one of the two miles plus the extra distance.
B
Incorrect: 2,642 feet adds 2 to 2,640, as if the miles were feet.
C
Incorrect: 10,560 feet is the two miles alone, without the extra 2,640 feet.
D
Incorrect: 15,840 feet counts the 2,640 feet as another full mile.
E
Correct: 13,200 feet is 2 × 5,280 feet plus the extra 2,640 feet.
Question 14 of 18 · Mathematics · 20 itemsNot answered
The evidence-room custodian started the month with $1,250.50 in the supply account. She spent $500.50 on evidence bags and $149.00 on labels. How much money is left in the account?
Answer explanations
A
Incorrect: $1,900.00 adds the purchases to the balance instead of subtracting them.
B
Incorrect: $701.00 is $100 too high, a slip when borrowing in the hundreds.
C
Correct: $601.00 is $1,250.50 minus both purchases: $500.50 + $149.00 = $649.50.
D
Incorrect: $1,101.50 subtracts only the $149.00 for labels.
E
Incorrect: $750.00 subtracts only the $500.50 for evidence bags.
Question 15 of 18 · Mathematics · 20 itemsNot answered
A security team must estimate the crowd in a fenced viewing zone that covers 6,000 square feet. The safety plan estimates 1 person for every 5 square feet. What is the estimated number of people in the zone?
Answer explanations
A
Incorrect: 12,000 has an extra zero; 6,000 ÷ 5 gives a number ten times smaller.
B
Incorrect: 30,000 multiplies by 5 instead of dividing.
C
Incorrect: 600 divides by 10 square feet per person instead of 5.
D
Incorrect: 1,500 divides by 4 square feet per person instead of 5.
E
Correct: 1,200 people is 6,000 square feet ÷ 5 square feet per person.
Question 16 of 18 · Mathematics · 20 itemsNot answered
An officer spends 1/3 of a shift processing paperwork and 1/4 of the same shift in court. What fraction of the total shift has been spent on these two tasks combined?
Answer explanations
A
Incorrect: 2/7 adds the tops and the bottoms straight across, which is not how fractions add.
B
Incorrect: 2/12 adds the numerators without first finding a common denominator.
C
Correct: 7/12 is 1/3 + 1/4 written as 4/12 + 3/12.
D
Incorrect: 1/12 subtracts 1/4 from 1/3 instead of adding.
E
Incorrect: 5/12 is the part of the shift left after the two tasks, not the part spent on them.
Question 17 of 18 · Mathematics · 20 itemsNot answered
A trust fund seized in an investigation held $800.00 that earned simple interest at 5% per year for 2 years. How much interest did the fund earn?
Answer explanations
A
Incorrect: $40.00 is one year of interest, but the fund earned interest for 2 years.
B
Correct: $80.00 is 5% of $800 ($40) for each of the 2 years.
C
Incorrect: $160.00 doubles the rate as well as the years.
D
Incorrect: $880.00 is the balance after 2 years, not the interest earned.
E
Incorrect: $8.00 uses 0.5% instead of 5%, a decimal slip.
Question 18 of 18 · Mathematics · 20 itemsNot answered
Officer Patel earned $900 for working a 40-hour week. What is Officer Patel's hourly rate of pay?
Answer explanations
A
Incorrect: $25.00 would be $900 ÷ 36 hours, not 40.
B
Incorrect: $225.00 divides by 4 instead of by 40.
C
Incorrect: $22.00 drops the 50 cents left over in the division.
D
Correct: $22.50 is $900 ÷ 40 hours.
E
Incorrect: $2.25 misplaces the decimal point.
Answer every question to see your score
!
Myth: the math includes algebra and geometry
Some prep sets pad the section with equations, area and volume. Salt Lake City and the Utah Highway Patrol describe it as general and money arithmetic, with no algebra or geometry, and no calculator is allowed. Spend your time on clean, fast arithmetic instead.
Arithmetic with police details: adding and subtracting money, averages, rates, clock time and simple percent. Numbers are small enough to work by hand.
Can I use a calculator on the NPOST math section?
No. Scratch paper is your tool, so practice long multiplication and division on paper.