ASVAB Arithmetic Reasoning Practice Test

25 practice questions

Choose an answer, then check it under Show answer.

1. Question 1 of 25Easy

   A mechanic completed safety inspections on 18 vehicles, which accounted for exactly 30% of the motor pool fleet. How many total vehicles are in the fleet?

   1. AA. 90
   2. BB. 54
   3. CC. 60
   4. DD. 72
   Show answer to question 1

   Answer: C. 60

   To find the total, divide the known portion (18) by the percentage expressed as a decimal (0.30), which yields 60 vehicles. A common error is multiplying 18 by 3 to get 54, confusing division by 0.30 with multiplication.

2. Question 2 of 25Easy

   A recipe uses 0.25 cup of oil. What percent of a cup is that amount?

   1. AA. 250%
   2. BB. 0.25%
   3. CC. 2.5%
   4. DD. 25%
   Show answer to question 2

   Answer: D. 25%

   0.25 equals 25 hundredths, which is 25%. The value 2.5% is tempting if the decimal is moved only one place instead of two.

3. Question 3 of 25Medium

   A mechanic purchases 4 quarts of motor oil at $6 per quart, 2 oil filters at $11 each, and 1 air filter for $18. If the mechanic pays with a $100 bill, how much change should he receive?

   1. AA. $36
   2. BB. $64
   3. CC. $47
   4. DD. $46
   Show answer to question 3

   Answer: A. $36

   The total cost of the items is $24 for the oil (4 times $6), $22 for the oil filters (2 times $11), and $18 for the air filter, totaling $64. Subtracting $64 from $100 leaves $36 in change. The distractor $64 represents the total cost rather than the change received, while $46 is a common subtraction error when regrouping from 100.

4. Question 4 of 25Hard

   A warehouse has 14 cartons. Each carton contains 12 small boxes, and each small box contains 8 markers. If 25 markers are damaged, how many markers are not damaged?

   1. AA. 1344
   2. BB. 1369
   3. CC. 1144
   4. DD. 1319
   Show answer to question 4

   Answer: D. 1319

   Multiply through the equal groups: 14 cartons times 12 boxes times 8 markers equals 1,344 markers. Then subtract the 25 damaged markers to get 1,319. The value 1,344 is the total before the damaged markers are removed.

5. Question 5 of 25Easy

   A commissary sells laundry detergent in two sizes. A 32-ounce bottle costs $8.00, and a 64-ounce bottle costs $12.80. How much less does the detergent cost per ounce when purchasing the 64-ounce bottle?

   1. AA. $0.20
   2. BB. $0.15
   3. CC. $0.10
   4. DD. $0.05
   Show answer to question 5

   Answer: D. $0.05

   Dividing the total cost by the number of ounces gives $0.25 per ounce for the 32-ounce bottle and $0.20 per ounce for the 64-ounce bottle. The difference between the two rates is $0.05 per ounce. Selecting $0.20 mistakes the unit price of the larger bottle for the amount saved.

6. Question 6 of 25Easy

   A motor pool mechanic inspected 80 military trucks. If 15% of the trucks needed new brake pads, how many trucks needed new brake pads?

   1. AA. 12
   2. BB. 16
   3. CC. 15
   4. DD. 8
   Show answer to question 6

   Answer: A. 12

   To find 15% of 80, multiply 80 by 0.15, which gives 12 trucks. The number 8 is incorrect because it represents only 10% of the trucks.

7. Question 7 of 25Easy

   A security guard starts a shift at 8:45 a.m. and finishes at 2:15 p.m. If the guard takes a 45-minute unpaid lunch break during the shift, how many total hours and minutes did the guard work?

   1. AA. 5 hours 30 minutes
   2. BB. 4 hours 45 minutes
   3. CC. 4 hours 15 minutes
   4. DD. 5 hours 00 minutes
   Show answer to question 7

   Answer: B. 4 hours 45 minutes

   The total duration between 8:45 a.m. and 2:15 p.m. is 5 hours and 30 minutes. Subtracting the 45-minute lunch break leaves 4 hours and 45 minutes of actual working time. The value of 5 hours 30 minutes is incorrect because it fails to deduct the break time.

8. Question 8 of 25Medium

   A freight train leaves a station traveling at 30 miles per hour. Two hours later, a passenger train leaves the same station on a parallel track, traveling in the same direction at 50 miles per hour. How many miles from the station will the passenger train overtake the freight train?

   1. AA. 100 miles
   2. BB. 90 miles
   3. CC. 150 miles
   4. DD. 250 miles
   Show answer to question 8

   Answer: C. 150 miles

   The freight train gains a 60-mile lead during its 2-hour head start. With a relative closing speed of 20 miles per hour, the passenger train requires 3 hours to overtake it, traveling a total distance of 150 miles at 50 miles per hour. The option of 90 miles is incorrect because it reflects the distance the freight train covers during the 3 hours of chasing, omitting its initial 60-mile head start.

9. Question 9 of 25Easy

   Marcus buys 3 t-shirts for $12 each and 1 jacket for $45. He pays the cashier with a $100 bill. How much change should he receive?

   1. AA. $19
   2. BB. $29
   3. CC. $55
   4. DD. $43
   Show answer to question 9

   Answer: A. $19

   The total cost is calculated by multiplying 3 shirts by $12 ($36) and adding the $45 jacket, which totals $81. Subtracting $81 from the $100 bill leaves $19 in change. The value $43 is incorrect because it reflects subtracting only a single shirt and the jacket from $100.

10. Question 10 of 25Medium

    A package has a mass of 3.2 kilograms. After 450 grams are removed, what is the remaining mass in kilograms?

    1. AA. 3.155 kg
    2. BB. 2.75 kg
    3. CC. 2.65 kg
    4. DD. 2.95 kg
    Show answer to question 10

    Answer: B. 2.75 kg

    The remaining mass is 2.75 kilograms because 3.2 kilograms is 3,200 grams, and 3,200 - 450 = 2,750 grams, which is 2.75 kilograms. The 3.155 kg choice would result from treating 450 grams as 0.045 kilograms instead of 0.45 kilograms.

11. Question 11 of 25Hard

    Three platoons took a physical readiness test. Platoon A has 25 soldiers and averaged 80 points. Platoon B has 15 soldiers and averaged 84 points. Platoon C has 10 soldiers and averaged 94 points. What was the combined average score for all 50 soldiers?

    1. AA. 82 points
    2. BB. 85 points
    3. CC. 84 points
    4. DD. 86 points
    Show answer to question 11

    Answer: C. 84 points

    Because the groups have different sizes, a weighted average must be calculated. The platoons earned 2,000 points, 1,260 points, and 940 points respectively, for a grand total of 4,200 points. Dividing 4,200 points across the 50 total soldiers gives a combined average of 84 points. An answer of 86 points comes from incorrectly averaging the three platoon averages directly without weighting them by platoon size.

12. Question 12 of 25Medium

    A truck uses 12 gallons of fuel to travel 180 miles. At the same rate, how many gallons will it need to travel 300 miles?

    1. AA. 24 gallons
    2. BB. 18 gallons
    3. CC. 20 gallons
    4. DD. 25 gallons
    Show answer to question 12

    Answer: C. 20 gallons

    The truck gets 180 ÷ 12 = 15 miles per gallon, so 300 miles requires 300 ÷ 15 = 20 gallons. The choice 25 gallons comes from dividing 300 by 12, which incorrectly uses gallons as if they were miles per gallon.

13. Question 13 of 25Medium

    A field kitchen uses 6 pounds of flour to bake 45 loaves of bread. At this rate, how many pounds of flour are needed to bake 120 loaves of bread?

    1. AA. 18 pounds
    2. BB. 14 pounds
    3. CC. 20 pounds
    4. DD. 16 pounds
    Show answer to question 13

    Answer: D. 16 pounds

    Setting up the proportion 6 / 45 = x / 120 reduces to 2 / 15 = x / 120. Solving for x gives (2 * 120) / 15 = 16 pounds. The distractor 20 pounds comes from mistakenly dividing the new loaf total (120) by the original flour quantity (6).

14. Question 14 of 25Medium

    A mechanic takes out an $1,800 personal loan to purchase diagnostic equipment. The loan has an annual simple interest rate of 8%. If the entire balance is repaid in a single payment after 6 months, what is the total amount repaid?

    1. AA. $2,016
    2. BB. $1,872
    3. CC. $1,944
    4. DD. $1,848
    Show answer to question 14

    Answer: B. $1,872

    Six months is equal to 0.5 years. The interest owed is $1,800 multiplied by 0.08 multiplied by 0.5, which is $72, making the total repayment $1,800 plus $72, or $1,872. The figure $1,944 mistakenly calculates interest for an entire full year instead of half a year.

15. Question 15 of 25Hard

    A fuel depot has three pumps connected to a single storage tank. Working alone, Pump A can empty the tank in 3 hours, Pump B can empty it in 4 hours, and Pump C can empty it in 6 hours. If all three pumps run at the same time, how many minutes will it take to completely empty the tank?

    1. AA. 75 minutes
    2. BB. 90 minutes
    3. CC. 60 minutes
    4. DD. 80 minutes
    Show answer to question 15

    Answer: D. 80 minutes

    Adding the individual rates of 4/12, 3/12, and 2/12 gives a combined pumping rate of 9/12, or 3/4 of the tank per hour. Taking the reciprocal gives 4/3 hours, which multiplied by 60 minutes yields 80 minutes. The distractor of 75 minutes comes from incorrectly converting 4/3 hours as 1.25 hours instead of 1 hour and 20 minutes.

16. Question 16 of 25Easy

    A landscaper is laying sod to cover a circular lawn that has a radius of 10 feet. How many square feet of sod are needed? (Use 3.14 for pi.)

    1. AA. 62.8
    2. BB. 628
    3. CC. 1,256
    4. DD. 314
    Show answer to question 16

    Answer: D. 314

    To find the circular area, square the radius and multiply by pi: 10 squared is 100, and 100 multiplied by 3.14 equals 314 square feet. The value 62.8 is incorrect because it calculates the circumference of the circle (2 * pi * r) rather than the area.

17. Question 17 of 25Medium

    A cylindrical chemical tank has a diameter of 6 feet and a height of 5 feet. Using 3.14 for pi, what is the volume of the tank in cubic feet?

    1. AA. 47.1 cubic feet
    2. BB. 565.2 cubic feet
    3. CC. 141.3 cubic feet
    4. DD. 94.2 cubic feet
    Show answer to question 17

    Answer: C. 141.3 cubic feet

    To find the volume, first determine the radius by dividing the diameter by 2, which gives 3 feet. Using the formula V = pi * r^2 * h, compute 3.14 * 3^2 * 5 = 3.14 * 45 = 141.3 cubic feet. The option 565.2 cubic feet is incorrect because it mistakenly uses the diameter of 6 feet as the radius instead of dividing it by 2.

18. Question 18 of 25Hard

    Six soldiers agree to rent an off-base storage unit and split the monthly cost equally. When two soldiers are deployed and stop paying, the remaining four soldiers divide the total monthly cost equally among themselves, increasing each person's share by $25 per month. What is the total monthly rental cost of the unit?

    1. AA. $240
    2. BB. $300
    3. CC. $100
    4. DD. $150
    Show answer to question 18

    Answer: B. $300

    The 4 remaining soldiers absorb a combined increase of 4 times $25, which equals $100. Because that $100 represents the original combined share of the 2 deployed soldiers, each original share was $50 ($100 divided by 2). Multiplying the original $50 share by all 6 soldiers gives a total monthly rent of $300. The distractor $150 results from multiplying the $25 increase by 6 soldiers instead of determining the full original share.

19. Question 19 of 25Hard

    A convoy travels 120 miles at an average speed of 60 mph, halts for a 1-hour scheduled maintenance stop, and then travels the final 100 miles at an average speed of 50 mph. What is the average speed of the convoy for the overall journey, including the stop?

    1. AA. 44 mph
    2. BB. 50 mph
    3. CC. 58 mph
    4. DD. 55 mph
    Show answer to question 19

    Answer: A. 44 mph

    The overall average speed requires dividing the total distance of 220 miles by the total elapsed time of 5 hours (2 hours driving, 1 hour stopped, and 2 hours driving), resulting in 44 mph. The value of 55 mph is incorrect because it omits the 1-hour stop from the calculation (dividing 220 miles by only 4 driving hours) or incorrectly averages the driving rates directly.

20. Question 20 of 25Hard

    A homeowner is installing a fence around a backyard that measures 50 feet wide and 30 feet deep. The back wall of the house covers one 50-foot side, so no fence is needed there. A 4-foot-wide gate is installed on one side, which costs a flat $120. The rest of the fencing costs $15 per foot. What is the total cost of the project?

    1. AA. $1,770
    2. BB. $2,460
    3. CC. $1,710
    4. DD. $1,590
    Show answer to question 20

    Answer: C. $1,710

    The three sides requiring enclosure total 110 feet. Subtracting the 4-foot gate leaves 106 feet of fencing, which costs $1,590 at $15 per foot. Adding the $120 gate yields a total cost of $1,710. The distractor $1,770 results from forgetting to subtract the 4-foot gate width from the linear fencing footage before calculating cost.

21. Question 21 of 25Hard

    A tactical jacket originally priced at $150 was discounted by 20%. During a holiday promotion, the store took an additional 10% off the discounted price. What was the final price of the jacket?

    1. AA. $108
    2. BB. $105
    3. CC. $120
    4. DD. $118
    Show answer to question 21

    Answer: A. $108

    The first 20% discount lowers the price by $30 to $120. The second 10% discount applies to the newly reduced price of $120, taking off another $12 to give a final price of $108. Adding the discounts together to take 30% off the original price yields $105, which fails to account for the sequential compounding of the reductions.

22. Question 22 of 25Medium

    A mechanic prepares an engine coolant solution using a ratio of 3 parts antifreeze to 7 parts water. How many quarts of antifreeze are needed to make 60 quarts of this mixture?

    1. AA. 42
    2. BB. 18
    3. CC. 20
    4. DD. 24
    Show answer to question 22

    Answer: B. 18

    The mixture consists of 10 total parts (3 parts antifreeze plus 7 parts water), so each part equals 6 quarts (60 divided by 10). Multiplying the 3 parts of antifreeze by 6 quarts yields 18 quarts. The value 42 quarts is the amount of water required rather than antifreeze.

23. Question 23 of 25Medium

    A rectangular living room measures 18 feet by 24 feet. How many square yards of carpet are required to cover the entire floor?

    1. AA. 28
    2. BB. 48
    3. CC. 432
    4. DD. 144
    Show answer to question 23

    Answer: B. 48

    To find square yards, either convert the dimensions to yards first (6 yards by 8 yards) to get 48 square yards, or divide the total area of 432 square feet by 9. The value of 144 square yards is a common error resulting from dividing square feet by 3 instead of 9. The value of 432 represents the area in square feet without converting to square yards.

24. Question 24 of 25Medium

    A base motor pool receives a delivery of 24 boxes of spark plugs, with each box containing 12 spark plugs. Over the course of two weeks, mechanics use 88 spark plugs for vehicle maintenance and discard 8 cracked plugs that cannot be used. How many spark plugs remain in inventory?

    1. AA. 192
    2. BB. 168
    3. CC. 200
    4. DD. 208
    Show answer to question 24

    Answer: A. 192

    Multiplying 24 boxes by 12 plugs per box gives an initial total of 288 plugs. Mechanics then removed a combined total of 96 plugs (88 used plus 8 damaged), leaving 288 - 96 = 192 plugs in stock. An answer of 200 results from subtracting only the 88 used plugs while forgetting to deduct the 8 damaged plugs.

25. Question 25 of 25Medium

    A restaurant bill is $65.00 before tip. The customer leaves a 20% tip. What is the total amount paid?

    1. AA. $84.50
    2. BB. $66.30
    3. CC. $71.50
    4. DD. $78.00
    Show answer to question 25

    Answer: D. $78.00

    Twenty percent of $65.00 is $13.00, so the total is $65.00 plus $13.00, or $78.00. The tempting $71.50 comes from using a 10% tip instead of 20%.

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The full ASVAB bank has 715 Arithmetic Reasoning questions. See plans