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ASVAB Arithmetic Reasoning practice test

10 free questions · scored as you go · every answer explained

Word problems: rates, percents, ratios, money and time. On the computer-based ASVAB you get 15 Arithmetic Reasoning questions in 55 minutes, about 3.7 minutes per question. It is one of the four subtests that make up your AFQT, the score that decides whether you can enlist.

AR practice test 10 questions

  1. ARArithmetic ReasoningAFQT1 of 10

    At the exchange you buy items costing $3.45, $2.80 and $6.25. You pay with a $20 bill. How much change should you get?

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    Answer: B. $7.50

    Add the purchases first: 3.45 + 2.80 + 6.25 = 12.50. Then subtract from the payment: 20.00 − 12.50 = 7.50. Lining up decimal points when adding prevents the most common slip.

  2. ARArithmetic ReasoningAFQT2 of 10

    A field jacket normally sells for $80 and is marked 25% off. What is the sale price?

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    Answer: B. $60

    25% of 80 is 0.25 × 80 = 20, so the price drops to 80 − 20 = 60. Shortcut: paying after 25% off means paying 75%, and 0.75 × 80 = 60.

  3. ARArithmetic ReasoningAFQT3 of 10

    A convoy must travel 180 miles at an average speed of 45 miles per hour. How long will the trip take?

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    Answer: C. 4 hours

    Time equals distance divided by speed: 180 ÷ 45 = 4 hours. Keep the triangle in mind: distance = speed × time, so time = distance ÷ speed and speed = distance ÷ time.

  4. ARArithmetic ReasoningAFQT4 of 10

    A student scores 78, 85, 92 and 89 on four practice tests. What is the average score?

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    Answer: A. 86

    Add the scores: 78 + 85 + 92 + 89 = 344. Divide by the number of tests: 344 ÷ 4 = 86. An average is always the total divided by the count.

  5. ARArithmetic ReasoningAFQT5 of 10

    A truck's 48-gallon fuel tank is three-quarters full. How many gallons are in the tank?

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    Answer: A. 36

    Three-quarters of 48 is (3 ÷ 4) × 48 = 36 gallons. 'Of' with a fraction means multiply. The tank has 12 gallons of space left, which is the trap answer.

  6. ARArithmetic ReasoningAFQT6 of 10

    One painter can paint a barracks room in 6 hours. Another can do it in 3 hours. Working together, how long will the room take?

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    Answer: D. 2 hours

    Add rates, not times. The first paints 1/6 of the room per hour, the second 1/3. Together: 1/6 + 1/3 = 1/2 per hour, so the whole room takes 2 hours. Averaging the times (4.5) is the classic mistake.

  7. ARArithmetic ReasoningAFQT7 of 10

    A mess-hall recipe uses flour and sugar in a 3-to-2 ratio. If a batch uses 12 cups of flour, how much sugar does it need?

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    Answer: B. 8 cups

    Set up the proportion 3/2 = 12/x. Cross-multiply: 3x = 24, so x = 8. Each 'part' is 4 cups because 12 cups of flour is 3 parts.

  8. ARArithmetic ReasoningAFQT8 of 10

    A mechanic earns $18 per hour for a 40-hour week and time-and-a-half for overtime. How much does he earn in a week with 5 overtime hours?

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    Answer: C. $855

    Regular pay: 40 × 18 = 720. Overtime rate: 18 × 1.5 = 27, and 5 × 27 = 135. Total: 720 + 135 = 855.

  9. ARArithmetic ReasoningAFQT9 of 10

    Jake is twice as old as Sam, and their ages add up to 36. How old is Jake?

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    Answer: D. 24

    Let Sam be x, so Jake is 2x. Then x + 2x = 36, so 3x = 36 and x = 12. Jake is 2 × 12 = 24. Answering Sam's age (12) is the common trap.

  10. ARArithmetic ReasoningAFQT10 of 10

    A rectangular training field measures 40 yards by 60 yards. How much fencing is needed to enclose it completely?

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    Answer: A. 200 yards

    Perimeter of a rectangle is 2 × (length + width) = 2 × (40 + 60) = 200 yards. Multiplying 40 × 60 gives 2,400, which is the area in square yards, not the fence length.

What Arithmetic Reasoning covers

The facts and methods behind the questions, from the app's study notes. Questions on test day are different, but they test the same things.

Numbers and operations

Multi-step arithmetic in context: order of operations, and what remainders, factors and multiples mean in a story.

  • Order of operations. Parentheses, exponents, multiply/divide, add/subtract. In stories: price each group of items before adding groups together.
  • Remainders in the real world. Covering a need rounds UP (1,000 rounds in boxes of 64 → 16 boxes). Fitting into a limit rounds DOWN. Repeating cycles use the remainder: 100 days from Monday is 100 ÷ 7 → remainder 2 → Wednesday.
  • LCM and GCF. Events that repeat align at the least common multiple (6 s and 8 s flashers → 24 s). Splitting groups evenly uses the greatest common factor (24 and 36 → squads of 12).
  • Estimate first. Round the numbers, predict the ballpark, then compute. The ASVAB’s wrong answers are built from skipped steps and misplaced decimals.

Fractions, percents and ratios

Fractions, percents and ratios as they appear in word problems: discounts, tax, interest, percent change, proportions and scale.

  • Percent moves. "Of" means multiply: 30% of 240 = 72. Build from 10%. Discounts: pay (100 − d)%. Stacked discounts multiply (×0.8 then ×0.9 = 72%, not 70%). Tax adds: ×1.08.
  • Percent change. (new − old) ÷ old. The divisor is always the ORIGINAL — 150→120 is a 20% drop, not 25%.
  • Ratios. A 5:4 split has 9 parts — divide the total by 9 first. Proportions cross-multiply: 3/2 = 12/x → x = 8. Map scales are proportions: 1 inch = 25 miles → 3.5 inches = 87.5 miles.
  • Fractions of amounts. 3/4 of 48 = 36. A fraction OF a fraction multiplies: half of two-thirds = one-third. Simple interest: principal × rate × years.

Rates, time and money

Rates: speed and distance, combined work, unit prices, wages and elapsed time (including the 24-hour clock).

  • d = s × t. Moving apart, speeds add; chasing, they subtract (close a 30-mile gap at 10 mph → 3 hours). Convert hours to minutes at the END (0.75 h = 45 min).
  • Work rates. Add rates, never times: 1/6 + 1/3 = 1/2 job per hour → 2 hours together. A pump’s rate is amount ÷ time.
  • Money rates. Unit price = pack price ÷ count. Overtime is usually 1.5× the hourly rate past 40 hours. Tiered plans: charge only the amount OVER the included allowance.
  • Military time. Split elapsed time at midnight: 2145→0615 is 2 h 15 m + 6 h 15 m = 8 h 30 m.

Setting up problems

Turning words into equations: averages and needed scores, mixtures, coin problems, consecutive numbers, and geometry in stories.

  • Averages. Average = total ÷ count, so total = average × count. A needed score is the required total minus points so far. Weighted average: multiply each value by its count before dividing.
  • Mixtures. Track the pure stuff: 2 L of 30% + 3 L of 10% = 0.9 L antiseptic in 5 L → 18%. Blends: total cost ÷ total weight.
  • Classic setups. Ages: let the smaller be x. Consecutive numbers: n, n+1, n+2 (middle = sum ÷ 3). Coins: value equation in cents, 25q + 10(12 − q) = 225.
  • Geometry in words. Fencing = perimeter 2(l + w); paint = area; boxes = volume l×w×h. Triangle area takes the HALF: ½ × base × height.

Keep going in the app. All 62 Arithmetic Reasoning questions, practice that brings back the ones you miss, and full exams timed subtest by subtest like the real test.

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These are original practice questions; real ASVAB items are confidential. Practice scores are estimates, not official ASVAB scores. ASVAB Test is not affiliated with the U.S. Department of Defense or any military branch.