36 Mathematics Practice Questions & Answers

1. 1. On an entrance exam you must evaluate: 7 + 6 x 4 - 9. What is the correct value?

   • A.52
   • B.43
   • C.22✓ Answer
   • D.31

   Order of operations (PEMDAS) requires multiplication before addition or subtraction: 6 x 4 = 24, then 7 + 24 = 31, then 31 - 9 = 22. Working strictly left to right gives the trap value 43 (7 + 6 = 13, 13 x 4 = 52, 52 - 9 = 43); 31 is the result of stopping before the subtraction, and 52 stops one step earlier still.

   Ref QB-K2RWHKSource: Order of operations (PEMDAS); FCTC/Cal-JAC written test, Solve Mathematical Problems section (addition, subtraction, multiplication, division)Report a problem with this question

2. 2. A preplan drawing shows a triangular gable end wall with a base of 24 feet and a height of 9 feet. What is the area of that triangular wall?

   • A.216 square feet
   • B.33 square feet
   • C.108 square feet✓ Answer
   • D.54 square feet

   The area of a triangle is one half the base times the height, because a triangle is exactly half of the rectangle that encloses it: A = 1/2 x 24 x 9 = 1/2 x 216 = 108 square feet. Answer 216 is the enclosing rectangle (forgetting the 1/2 factor), 33 comes from adding 24 + 9 instead of multiplying, and 54 halves the result twice.

   Ref QB-3JJRXJSource: Area of a triangle A = 1/2 x base x height; FCTC math content area 'Area'Report a problem with this question

3. 3. An engine's water tank is 3/8 full. The crew adds water equal to 1/4 of the tank's total capacity. What fraction of the tank is now full?

   • A.1/3
   • B.3/32
   • C.1/8
   • D.5/8✓ Answer

   Fractions can only be added after they are written over a common denominator, so 1/4 must be rewritten as 2/8: 3/8 + 2/8 = 5/8. Answer 1/3 comes from the classic error of adding numerators and denominators separately (3+1 over 8+4 = 4/12), 3/32 comes from multiplying the fractions instead of adding, and 1/8 comes from subtracting.

   Ref QB-J2DKCJSource: Addition of fractions with unlike denominators (common denominator rule); FCTC math content area 'Fractions/Decimals'Report a problem with this question

4. 4. Of the 8 self-contained breathing apparatus cylinders on an apparatus, 5 have been refilled after a working fire. What percent of the cylinders have been refilled?

   • A.62.5%✓ Answer
   • B.58%
   • C.12.5%
   • D.37.5%

   A fraction is converted to a percent by dividing the part by the whole and multiplying by 100: 5 / 8 = 0.625, and 0.625 x 100 = 62.5%. Answer 37.5% is the percent NOT refilled (the complement), 12.5% is the value of a single cylinder (1/8), and 58% simply misreads the digits of 5 and 8.

   Ref QB-2J7ESHSource: Fraction-to-percent conversion (part / whole x 100); FCTC math content areas 'Fractions/Decimals' and 'Percentages'Report a problem with this question

5. 5. A 750-gallon booster tank is full at the start of an incident. During the attack, 480 gallons are discharged. What percent of the tank's water REMAINS?

   • A.56%
   • B.27%
   • C.64%
   • D.36%✓ Answer

   The question asks for the water remaining, so the part must be found first: 750 - 480 = 270 gallons left, and 270 / 750 = 0.36 = 36%. Answer 64% is the percent USED (480 / 750), the standard complement trap; 56% divides 270 by 480 instead of by the full tank, and 27% drops the decimal placement.

   Ref QB-H2297HSource: Percent of a total: part / whole x 100; percent used vs. percent remaining (complement rule); FCTC math content area 'Percentages'Report a problem with this question

6. 6. A station's monthly call volume rose from 240 calls to 300 calls. What was the percent increase?

   • A.20%
   • B.25%✓ Answer
   • C.125%
   • D.60%

   Percent change is always measured against the ORIGINAL value: (new - old) / old x 100 = (300 - 240) / 240 = 60 / 240 = 0.25 = 25%. Answer 20% is the most common error, dividing the 60-call increase by the new value 300; 60 is the raw increase, not a percent; and 125% is the new total expressed as a percent of the old (300 / 240).

   Ref QB-ZHU3MGSource: Percent increase = (new - old) / old x 100 (denominator is the original value); FCTC math content area 'Percentages'Report a problem with this question

7. 7. During a 24-hour shift, a company spends a total of 4 hours and 48 minutes committed to emergency calls. What percent of the shift was spent on calls?

   • A.20%✓ Answer
   • B.19%
   • C.80%
   • D.2%

   Unlike units must be converted before dividing: 48 minutes is 48/60 = 0.8 of an hour, so the committed time is 4.8 hours. Then 4.8 / 24 = 0.2 = 20%. Answer 19% comes from writing the time as 4.48 hours (treating minutes as decimals), 80% is the percent of the shift NOT on calls, and 2% misplaces the decimal by a factor of ten.

   Ref QB-G2PWZFSource: Unit conversion (1 hour = 60 minutes) combined with percent of a total; FCTC math content areas 'Percentages' and word-problem formatReport a problem with this question

8. 8. On a training worksheet you are told that, for a given supply layout, each additional inch of hose diameter delivers 84 more gallons per minute (GPM). A 2-inch line is currently in use, and the incident commander needs 252 GPM MORE than that line delivers. What diameter hose is needed?

   • A.A 5-inch hose✓ Answer
   • B.A 4-inch hose
   • C.A 3-inch hose
   • D.A 6-inch hose

   Set up the rate as a proportion: 252 GPM needed / 84 GPM per inch = 3 additional inches of diameter. The question asks for the resulting hose size, not the increase, so 2 + 3 = a 5-inch hose. Answer '3-inch' is the classic stop-one-step-early trap (reporting the increment instead of the final size); 4-inch and 6-inch correspond to adding 2 or 4 inches.

   Ref QB-YHGREFSource: Unit rate and proportional reasoning (given rate x quantity); Ergometrics/NTN FireTEAM math component: 'proportions'Report a problem with this question

9. 9. A nozzle flows 150 gallons per minute. If it is opened for 12 minutes without interruption, how many gallons of water are discharged?

   • A.1,800 gallons✓ Answer
   • B.18,000 gallons
   • C.180 gallons
   • D.162 gallons

   Total volume equals flow rate multiplied by time, because gallons per minute times minutes leaves gallons: 150 x 12 = 1,800 gallons. Answer 180 drops a factor of ten (150 x 12 is not 15 x 12), 18,000 adds one, and 162 comes from adding 150 + 12 instead of multiplying.

   Ref QB-F2BKUESource: Rate x time = quantity (gallons per minute x minutes = gallons); FCTC math content: multiplication word problemsReport a problem with this question

10. 10. An engine carries a 750-gallon water tank and has a pump rated at 1,250 GPM. A crew flows a nozzle at 250 GPM using tank water only. How long will the tank water last?

    • A.5 minutes
    • B.3 minutes✓ Answer
    • C.0.6 minutes
    • D.30 minutes

    Time equals volume divided by the rate actually being used: 750 gallons / 250 GPM = 3 minutes. The pump's 1,250 GPM rating is extraneous information because the nozzle, not the pump capacity, sets the flow; using it wrongly gives 750 / 1,250 = 0.6 minutes or 1,250 / 250 = 5 minutes, and 30 minutes misplaces the decimal.

    Ref QB-V7SZ55Source: Volume / rate = time; identification of extraneous data in word problems (FCTC sample-item convention)Report a problem with this question

11. 11. During a long response, an apparatus used 24 gallons of fuel to travel 180 miles. At the same rate of consumption, how many gallons would it use to travel 300 miles?

    • A.2,250 gallons
    • B.12.5 gallons
    • C.40 gallons✓ Answer
    • D.80 gallons

    Set the two trips as a proportion, 24 gallons / 180 miles = x / 300 miles, and cross-multiply: x = 24 x 300 / 180 = 7,200 / 180 = 40 gallons. Answer 2,250 multiplies by the 7.5 miles-per-gallon figure instead of dividing by it, 12.5 divides 300 by 24 (the reciprocal rate), and 80 doubles the correct value.

    Ref QB-DQX6R5Source: Proportion and unit rate (cross-multiplication); Ergometrics/NTN FireTEAM math component: 'proportions'Report a problem with this question

12. 12. A ground ladder is rated for a maximum total load of 1,050 pounds. Three firefighters whose combined weight is 600 pounds will climb it at the same time, each carrying an equal amount of equipment. What is the maximum weight of equipment each firefighter may carry without exceeding the rating?

    • A.200 pounds
    • B.150 pounds✓ Answer
    • C.450 pounds
    • D.350 pounds

    First find the load still available, then divide it among the climbers: 1,050 - 600 = 450 pounds available, and 450 / 3 = 150 pounds each. Answer 450 is the stop-one-step-early trap (the total remaining capacity, not the per-person share), 350 divides 1,050 by 3 without subtracting the firefighters, and 200 divides 600 by 3.

    Ref QB-U7EPY3Source: Two-step linear equation: (limit - fixed load) / number of shares; FCTC math content area 'Algebra/Geometry'Report a problem with this question

13. 13. A hose lay is built from an unknown number of 50-foot sections plus one 25-foot section. The finished lay measures 375 feet. How many 50-foot sections were used?

    • A.7.5
    • B.7✓ Answer
    • C.6
    • D.8

    Translate the words into an equation and isolate the unknown with inverse operations: 50x + 25 = 375, so 50x = 350 and x = 7 sections. Answer 7.5 comes from dividing 375 by 50 without first removing the 25-foot section, 8 rounds that figure up, and 6 subtracts twice.

    Ref QB-CQKUJ4Source: Solving a two-step linear equation (ax + b = c); FCTC math content area 'Algebra/Geometry'Report a problem with this question

14. 14. For a training exercise you are told that water weighs 8.34 pounds per gallon. How much does the water in a full 400-gallon tank weigh?

    • A.48 pounds
    • B.33,360 pounds
    • C.333.6 pounds
    • D.3,336 pounds✓ Answer

    Substituting into the supplied relationship weight = 8.34 pounds per gallon x gallons gives 8.34 x 400 = 3,336 pounds; multiplying by 4 and then by 100 keeps the decimal in the right place. Answers 333.6 and 33,360 are decimal-placement errors by a factor of ten, and 48 comes from dividing 400 by 8.34 instead of multiplying.

    Ref QB-X7GPG7Source: Substitution into a formula supplied in the stem; decimal multiplication (FCTC study guide: task-specific formulas are taught on the job, never required on the exam)Report a problem with this question

15. 15. A warehouse is made of two attached rectangular sections. Both sections are 48 feet deep. One section has a 85-foot frontage and the other has a 115-foot frontage. Approximately how many square feet of floor area does the building have?

    • A.20,000 square feet
    • B.14,000 square feet
    • C.6,000 square feet
    • D.10,000 square feet✓ Answer

    Because both parts share the same 48-foot depth, the frontages can be added first: 85 + 115 = 200 feet, and 48 x 200 = 9,600 square feet, which rounds to approximately 10,000. Answer 6,000 is one section only (48 x 115 = 5,520), 14,000 comes from using a wrong common side, and 20,000 doubles the building.

    Ref QB-FQNU38Source: Composite area by factoring a common side (A = L x W); estimation/rounding convention for 'approximately' items; FCTC math content area 'Area'Report a problem with this question

16. 16. A preplan lists a two-story residence with a footprint of 28 feet by 45 feet. Both floors have the same dimensions. What is the total floor area of the residence?

    • A.2,520 square feet✓ Answer
    • B.630 square feet
    • C.146 square feet
    • D.1,260 square feet

    The area of one floor is length times width, 28 x 45 = 1,260 square feet, and the question asks for the whole building, so both stories count: 1,260 x 2 = 2,520 square feet. Answer 1,260 is the classic one-floor trap, 146 is the perimeter (2 x 28 + 2 x 45) rather than the area, and 630 halves one floor.

    Ref QB-W75CB6Source: Rectangle area A = L x W applied per story; perimeter vs. area distinction; FCTC math content area 'Area'Report a problem with this question

17. 17. A rectangular water storage tank measures 8 feet long, 5 feet wide, and 4 feet deep. You are told that 1 cubic foot holds 7.48 gallons. How many gallons does the tank hold when full?

    • A.160 gallons
    • B.1,196.8 gallons✓ Answer
    • C.119.68 gallons
    • D.21.4 gallons

    Find the volume first, then convert with the factor given in the stem: 8 x 5 x 4 = 160 cubic feet, and 160 x 7.48 = 1,196.8 gallons. Answer 160 stops at cubic feet and never converts to the units the question asks for, 119.68 misplaces the decimal by a factor of ten, and 21.4 divides by 7.48 instead of multiplying.

    Ref QB-EQAHW6Source: Rectangular volume V = L x W x H with supplied conversion 1 cubic foot = 7.48 gallons; FCTC math content area 'Volume'Report a problem with this question

18. 18. A cylindrical storage tank is 10 feet in diameter and holds 590 gallons for every foot of water depth. The tank currently contains water to a depth of 6 feet. How many gallons are in the tank?

    • A.5,900 gallons
    • B.3,540 gallons✓ Answer
    • C.98 gallons
    • D.1,770 gallons

    When a capacity per unit of depth is supplied, the volume is simply that rate times the depth: 590 x 6 = 3,540 gallons. The 10-foot diameter is extraneous information and must not be used to recompute the tank; multiplying by it gives the trap 5,900, 1,770 uses a 3-foot depth, and 98 divides 590 by 6.

    Ref QB-VYABGTSource: Capacity-per-unit-depth rate x depth; extraneous-data convention in official firefighter math sample items; FCTC math content area 'Volume'Report a problem with this question

19. 19. A cylindrical tank has a diameter of 6 feet and a height of 10 feet. Using the formula V = pi x r^2 x h with pi = 3.14, what is the volume of the tank?

    • A.188.4 cubic feet
    • B.1,130.4 cubic feet
    • C.282.6 cubic feet✓ Answer
    • D.94.2 cubic feet

    The formula uses the radius, which is half the diameter, so r = 3 feet: V = 3.14 x 3^2 x 10 = 3.14 x 9 x 10 = 282.6 cubic feet. Answer 1,130.4 is the classic diameter-for-radius error (3.14 x 36 x 10), 94.2 omits the squaring, and 188.4 is the circumference times height rather than a volume.

    Ref QB-DGGG3USource: Cylinder volume V = pi r^2 h with radius = diameter / 2; FCTC math content area 'Volume'Report a problem with this question

20. 20. A ground ladder is raised against a vertical wall so that it forms a 75-degree angle with the level ground. What is the angle between the ladder and the wall at the point where the ladder touches the wall?

    • A.105 degrees
    • B.25 degrees
    • C.90 degrees
    • D.15 degrees✓ Answer

    The ladder, the wall, and the ground form a triangle whose interior angles must total 180 degrees; the wall meets level ground at 90 degrees, so 180 - 90 - 75 = 15 degrees at the wall. Answer 105 is the supplement of 75 (the angle on the other side of the straight ground line), 90 is the ground-to-wall angle itself, and 25 has no basis in the triangle.

    Ref QB-UUZ4NESource: Interior angles of a triangle sum to 180 degrees; supplementary angles on a straight line; FCTC math content area 'Angles'Report a problem with this question

21. 21. A 25-foot ladder is placed with its base 7 feet out from the base of a wall. Using a^2 + b^2 = c^2, how far up the wall does the top of the ladder reach?

    • A.18 feet
    • B.26 feet
    • C.32 feet
    • D.24 feet✓ Answer

    The ladder is the hypotenuse of a right triangle, so the vertical leg is found by rearranging the relation: 25^2 - 7^2 = 625 - 49 = 576, and the square root of 576 is 24 feet. Answer 18 subtracts the lengths directly (25 - 7), 32 adds them, and 26 treats the ladder as a leg instead of the hypotenuse.

    Ref QB-BCUX2ESource: Pythagorean relation a^2 + b^2 = c^2 for ladder base-and-reach geometry; FCTC math content area 'Algebra/Geometry'Report a problem with this question

22. 22. A unit is out of service for maintenance for 2 hours and 38 minutes. How many seconds is that?

    • A.9,480 seconds✓ Answer
    • B.9,600 seconds
    • C.15,800 seconds
    • D.158 seconds

    Convert each unit before adding, since 1 hour = 3,600 seconds and 1 minute = 60 seconds: 2 x 3,600 = 7,200 and 38 x 60 = 2,280, so 7,200 + 2,280 = 9,480 seconds. Answer 158 is the time in minutes only, 15,800 multiplies those minutes by 100 instead of 60, and 9,600 rounds 38 minutes up to 40.

    Ref QB-TUNSFDSource: U.S. customary time conversion: 1 hour = 60 minutes = 3,600 seconds; NWCG 'Firefighter Math' units-of-measure moduleReport a problem with this question

23. 23. A company logs five response times, in minutes: 6.2, 4.8, 7.5, 5.0, and 6.5. What is the average (mean) response time?

    • A.6.2 minutes
    • B.7.5 minutes
    • C.6.0 minutes✓ Answer
    • D.30.0 minutes

    The mean is the sum of the values divided by how many values there are: 6.2 + 4.8 + 7.5 + 5.0 + 6.5 = 30.0, and 30.0 / 5 = 6.0 minutes. Answer 30.0 is the sum without dividing, 6.2 is the median (the middle value when sorted), and 7.5 is the longest single time, not an average.

    Ref QB-ACGMVCSource: Arithmetic mean = sum of values / number of values; mean vs. median distinction; FCTC math content: word problems with decimalsReport a problem with this question

24. 24. A monthly run report lists: Station 1 - 142 EMS runs and 18 fire runs; Station 2 - 96 EMS runs and 24 fire runs; Station 3 - 130 EMS runs and 30 fire runs. How many FIRE runs did the three stations make in total?

    • A.440 runs
    • B.72 runs✓ Answer
    • C.160 runs
    • D.368 runs

    Table questions are answered by selecting only the rows and column the question names, so add just the fire runs: 18 + 24 + 30 = 72. Answer 368 totals the EMS column instead (142 + 96 + 130), 440 adds every number in the table, and 160 is Station 1's combined total (142 + 18).

    Ref QB-SUAFACSource: Data interpretation: selecting only the required values from a table; Louisiana Office of State Examiner firefighter test, Math and Reasoning componentReport a problem with this question

25. 25. A fire department has 36 members assigned to its training division, and those 36 members make up 24% of the department's total membership. How many members does the department have in total?

    • A.864 members
    • B.150 members✓ Answer
    • C.45 members
    • D.144 members

    To find the whole when a part and its percent are known, divide the part by the percent written as a decimal: 36 ÷ 0.24 = 150. Choosing 144 treats 24% as if it were 25% (36 × 4), and 864 comes from multiplying 36 by 24 without converting the percent to a decimal.

    Ref QB-9C5AQBSource: FCTC Written Test Study Guide — mathematical reasoning: percentages (finding the whole from a given part)Report a problem with this question

26. 26. At shift change, an engine's 800-gallon water tank is 35% full. How many gallons of water are in the tank?

    • A.280 gallons✓ Answer
    • B.240 gallons
    • C.2,800 gallons
    • D.520 gallons

    Percent of a quantity means multiply: 0.35 × 800 = 280 gallons. The 520-gallon answer is the empty portion of the tank (65%), 240 uses 30% instead of 35%, and 2,800 comes from misplacing the decimal point when converting the percent.

    Ref QB-RUX45BSource: FCTC Written Test Study Guide — mathematical reasoning: percent of a quantityReport a problem with this question

27. 27. On a wildland assignment, a crew hikes 1 1/2 miles to a lookout, then 3/4 mile along a ridge, and finally 5/8 mile down to the fire edge. What total distance does the crew hike?

    • A.2 7/8 miles✓ Answer
    • B.2 1/2 miles
    • C.3 1/8 miles
    • D.2 3/4 miles

    Fractions must share a common denominator before adding: 1 1/2 = 12/8 and 3/4 = 6/8, so 12/8 + 6/8 + 5/8 = 23/8 = 2 7/8 miles. The 2 1/2-mile answer comes from adding 3/4 as if it were 3/8 — combining numerators without first converting everything to eighths.

    Ref QB-8CSXHASource: FCTC Written Test Study Guide — mathematical reasoning: adding fractions with unlike denominatorsReport a problem with this question

28. 28. An incident lasted 3 1/2 hours from dispatch to termination, and overhaul accounted for 2/7 of the total time. How many hours were spent on overhaul?

    • A.1 1/4 hours
    • B.1 hour✓ Answer
    • C.12 1/4 hours
    • D.6/7 hour

    A fraction 'of' a quantity means multiplication: convert 3 1/2 to the improper fraction 7/2, then 7/2 × 2/7 = 1 hour. Dividing by the fraction instead of multiplying gives 12 1/4 hours, and multiplying only the whole number 3 by 2/7 gives 6/7 hour.

    Ref QB-YUEFBKSource: FCTC Written Test Study Guide — mathematical reasoning: multiplying fractions and mixed numbersReport a problem with this question

29. 29. Class A foam is batch-mixed at a ratio of 1 gallon of foam concentrate for every 25 gallons of water. How many gallons of concentrate are needed for 200 gallons of water?

    • A.25 gallons
    • B.10 gallons
    • C.4 gallons
    • D.8 gallons✓ Answer

    Set up the proportion 1/25 = x/200 and solve: x = 200 ÷ 25 = 8 gallons. Choosing 4 assumes a 1:50 ratio, 10 comes from dividing 200 by 20, and 25 simply repeats the number given in the ratio.

    Ref QB-FC9ARJSource: FCTC Written Test Study Guide — mathematical reasoning: ratios and proportionsReport a problem with this question

30. 30. An engine responds to an incident 6 miles from the station and averages 30 miles per hour through traffic. How many minutes does the response take?

    • A.5 minutes
    • B.12 minutes✓ Answer
    • C.10 minutes
    • D.20 minutes

    Time equals distance divided by speed: 6 ÷ 30 = 0.2 hour, and 0.2 × 60 = 12 minutes. Reading 0.2 hour directly as 20 minutes skips the conversion (an hour has 60 minutes, not 100), and 5 comes from dividing the speed by the distance.

    Ref QB-RSZX4BSource: NTN FireTEAM math section — time/distance/rate problems (time = distance ÷ speed)Report a problem with this question

31. 31. An SCBA cylinder is rated to last 45 minutes at a standard work rate. During heavy exertion, a firefighter consumes air at 1.5 times the standard rate. About how long will the cylinder last?

    • A.22.5 minutes
    • B.30 minutes✓ Answer
    • C.15 minutes
    • D.67.5 minutes

    Using air 1.5 times faster means the same supply is exhausted in 1/1.5 of the rated time, so divide: 45 ÷ 1.5 = 30 minutes. Multiplying instead gives 67.5 minutes, and 22.5 treats '1.5 times the rate' as if consumption had doubled.

    Ref QB-9A75QBSource: NTN FireTEAM math section — rate problems (duration = rated time ÷ consumption multiplier)Report a problem with this question

32. 32. An attack line must reach a doorway 210 feet from the engine, and hose is available only in 50-foot sections. What is the minimum number of full sections the crew must connect?

    • A.3 sections
    • B.4 sections
    • C.5 sections✓ Answer
    • D.6 sections

    Dividing gives 210 ÷ 50 = 4.2 sections, but hose comes only in whole sections, and 4 sections reach just 200 feet — 10 feet short. In coverage problems a partial result must be rounded up, so 5 sections (250 feet) is the minimum that reaches the doorway.

    Ref QB-SSCAACSource: FCTC Written Test Study Guide — mathematical reasoning: division word problems (rounding up to whole units)Report a problem with this question

33. 33. Each pump service on an apparatus uses 6 quarts of oil. Given that 1 gallon = 4 quarts, how many complete services can be performed from a 15-gallon drum of oil?

    • A.2 services
    • B.60 services
    • C.12 services
    • D.10 services✓ Answer

    Convert first, then divide: 15 gallons × 4 = 60 quarts, and 60 ÷ 6 = 10 complete services. Dividing 15 by 6 without converting gives 2, 12 assumes 5 quarts per gallon, and 60 comes from converting to quarts but forgetting to divide by the 6 quarts each service uses.

    Ref QB-AAJFVCSource: U.S. customary units: 1 gallon = 4 quarts — FCTC/FireTEAM unit-conversion word problemsReport a problem with this question

34. 34. A training worksheet gives the formula W = 45 + 12n for the loaded weight of a hose pack in pounds, where n is the number of hose sections in the pack. If a pack weighs 105 pounds, how many sections does it hold?

    • A.5 sections✓ Answer
    • B.12 sections
    • C.60 sections
    • D.8 sections

    Solve the equation in two steps: subtract 45 from both sides to get 12n = 60, then divide by 12 to get n = 5. Dividing 105 by 12 without first subtracting the 45-pound base gives about 8, and stopping after the subtraction step gives 60.

    Ref QB-PSAAS8Source: FCTC Written Test Study Guide — mathematical reasoning: algebra (two-step linear equations)Report a problem with this question

35. 35. A rectangular salvage cover measures 12 feet by 16 feet, and rope is to be sewn along its entire outside edge. How many feet of rope are required?

    • A.56 feet✓ Answer
    • B.40 feet
    • C.28 feet
    • D.192 feet

    The distance all the way around a rectangle is its perimeter: P = 2 × (12 + 16) = 56 feet. Choosing 192 confuses perimeter with area (12 × 16 square feet), 28 adds the two different sides only once, and 40 leaves out one of the four sides.

    Ref QB-7AGFC9Source: FCTC Written Test Study Guide — mathematical reasoning: geometry (perimeter of a rectangle, P = 2(l + w))Report a problem with this question

36. 36. A station's weekly training log shows: Monday 12 hours, Tuesday 9 hours, Wednesday 15 hours, Thursday not recorded, and Friday 10 hours. The log states the five-day total is 60 hours. How many hours were trained on Thursday?

    • A.13 hours
    • B.12 hours
    • C.16 hours
    • D.14 hours✓ Answer

    Add the four recorded days (12 + 9 + 15 + 10 = 46) and subtract from the stated total: 60 − 46 = 14 hours. Choosing 12 mistakes the answer for the daily average (60 ÷ 5), and 16 results from mis-adding the known days as 44.

    Ref QB-QSNMX9Source: NYS Civil Service Firefighter Series Test Guide — Basic Arithmetic (finding a missing value in a number table)Report a problem with this question

Practice questions modeled on the common domains of firefighter written entrance exams (reading, math, mechanical reasoning, spatial orientation). Not affiliated with or endorsed by any fire department or testing vendor. Departments use different exams — check your department's announcement for its specific format. U.S. Fire Administration →