ASVAB Arithmetic Reasoning Practice Test
Updated October 27, 2026
Arithmetic Reasoning (AR) is one of the four tests that make up your AFQT score, so it directly affects whether you can enlist. The CAT-ASVAB has 15 scored AR questions, all word problems, and calculators aren’t allowed. Try the free questions below. Each answer shows the steps.
Common Arithmetic Reasoning problem types
- Rates: distance = rate × time, and work problems
- Percents: discounts, raises, interest and tips
- Ratios and proportions: recipes, maps and mixtures
- Averages: finding the mean, or a missing value
- Unit conversions: hours and minutes, feet and inches
Free Arithmetic Reasoning practice questions
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A recruit runs 3 miles in 24 minutes. At the same pace, how long does it take to run 5 miles?Answer: CThe pace is 24 ÷ 3 = 8 minutes per mile, so 5 miles takes 5 × 8 = 40 minutes.
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A uniform costs $80. It's on sale for 15% off. What is the sale price?Answer: B15% of $80 is 0.15 × 80 = $12. The sale price is $80 − $12 = $68.
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The average of four test scores is 85. Three of the scores are 80, 90 and 82. What is the fourth score?Answer: DFour scores averaging 85 total 4 × 85 = 340. The three known scores add to 252, so the fourth is 340 − 252 = 88.
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A truck uses 6 gallons of fuel to travel 90 miles. How many gallons does it need for 240 miles?Answer: BThe truck gets 90 ÷ 6 = 15 miles per gallon, so 240 miles needs 240 ÷ 15 = 16 gallons.
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Two workers can each paint a room in 6 hours working alone. How long does it take them working together?Answer: BEach paints 1/6 of the room per hour, so together they paint 2/6 = 1/3 per hour. The whole room takes 3 hours.
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A soldier earns $2,400 a month and saves 1/8 of it. How much is saved in a year?Answer: C1/8 of $2,400 is $300 a month, and $300 × 12 = $3,600 a year.
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A map uses a scale of 1 inch = 20 miles. Two bases are 4.5 inches apart on the map. How far apart are they?Answer: D4.5 × 20 = 90 miles.
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A unit has 120 soldiers. 35% are assigned to the motor pool. How many soldiers is that?Answer: B35% of 120 = 0.35 × 120 = 42.
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A convoy travels at 45 miles per hour for 3 hours and 20 minutes. How far does it go?Answer: D3 hours 20 minutes is 3⅓ hours. 45 × 3⅓ = 135 + 15 = 150 miles.
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A box of 24 MREs costs $96. What is the cost per meal?Answer: B$96 ÷ 24 = $4.00 per meal.
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A recruit's pay rises from $2,000 to $2,300 a month. What is the percent increase?Answer: CThe increase is $300. Divide by the original pay: 300 ÷ 2,000 = 0.15, or 15%.
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Sam is 4 years older than Jo. The sum of their ages is 36. How old is Sam?Answer: CLet Jo = x, so Sam = x + 4. x + x + 4 = 36, so 2x = 32 and x = 16. Sam is 16 + 4 = 20.
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A rectangular parade field is 120 yards long and 50 yards wide. What is its perimeter?Answer: CPerimeter = 2 × (length + width) = 2 × (120 + 50) = 340 yards.
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A tank holds 80 gallons and is 3/4 full. How many gallons are needed to fill it?Answer: A3/4 of 80 is 60 gallons, so 80 − 60 = 20 gallons are needed.
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If 5 pencils cost $1.25, how much do 12 pencils cost?Answer: CEach pencil costs $1.25 ÷ 5 = $0.25, so 12 pencils cost 12 × $0.25 = $3.00.
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A ship travels 18 nautical miles in 1.5 hours. What is its speed in knots (nautical miles per hour)?Answer: BSpeed = distance ÷ time = 18 ÷ 1.5 = 12 knots.
Tips
Read the question twice and write down what it asks for before you calculate. Estimate first, then check that your answer is reasonable. See also how the AFQT is calculated and Mathematics Knowledge practice.
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