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Arithmetic Reasoning (AR) AFQT

Arithmetic Reasoning tests how well you turn real-world word problems into math and solve them. It is one of the four AFQT subtests, so your score here directly affects whether you qualify to enlist.

Practice questions

Original Arithmetic Reasoning questions in the ASVAB style. Pick an answer for instant feedback and an explanation, then keep going in the app.

  1. A car travels 210 miles using 7 gallons of gas. At the same rate of fuel efficiency, how many miles can it travel on 12 gallons?

    1. 300 miles
    2. 350 miles
    3. 360 miles
    4. 420 miles

    The car gets 210 / 7 = 30 miles per gallon. On 12 gallons it travels 30 x 12 = 360 miles.

  2. A jacket originally priced at $80 is marked down 25%. At the register, an additional 10% is taken off the sale price. What is the final price?

    1. $48.00
    2. $52.00
    3. $54.00
    4. $56.00

    After 25% off: 80 x 0.75 = $60. Then 10% off $60: 60 x 0.90 = $54. The two discounts are applied one after the other, not added together.

  3. One pump can fill a water tank in 6 hours, and a second pump can fill the same tank in 3 hours. Working together, how long will it take to fill the tank?

    1. 2 hours
    2. 3 hours
    3. 4.5 hours
    4. 9 hours

    The pumps fill 1/6 + 1/3 = 1/6 + 2/6 = 3/6 = 1/2 of the tank per hour. At half a tank per hour, the full tank takes 2 hours.

  4. On her first three math tests a student scored 82, 90, and 76. What score does she need on the fourth test to have an average of exactly 85 across all four tests?

    1. 88
    2. 90
    3. 92
    4. 94

    An 85 average over 4 tests requires 85 x 4 = 340 total points. Her first three tests total 82 + 90 + 76 = 248, so she needs 340 - 248 = 92.

  5. A cookie recipe uses 3 cups of flour to make 24 cookies. Keeping the same proportions, how many cups of flour are needed to make 40 cookies?

    1. 3.75 cups
    2. 4.5 cups
    3. 5 cups
    4. 6 cups

    Each cookie needs 3 / 24 = 0.125 cup of flour. For 40 cookies: 0.125 x 40 = 5 cups.

  6. Two trains start at the same time from stations 300 miles apart and travel toward each other. One travels at 60 mph and the other at 40 mph. How long until they meet?

    1. 2.5 hours
    2. 3 hours
    3. 4 hours
    4. 5 hours

    Moving toward each other, they close the gap at 60 + 40 = 100 mph. The 300-mile gap closes in 300 / 100 = 3 hours.

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What it measures

Arithmetic Reasoning (AR) measures your ability to read a word problem, figure out what math it is really asking for, and solve it correctly. It is less about heavy computation and more about reasoning: choosing the right operation, setting up the problem, and working through it step by step.

AR is one of the four AFQT subtests (along with Mathematics Knowledge, Word Knowledge, and Paragraph Comprehension). The AFQT score is what determines whether you qualify to enlist and which branches and bonuses you are eligible for, so AR carries real weight. A strong AR score can meaningfully raise your overall AFQT.

What's on it

Topics and skills you will see

  • Basic operations in context: addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals
  • Percentages: discounts, tax, tips, interest, and percent increase or decrease
  • Ratios and proportions: scaling recipes, mixtures, map scales, and unit pricing
  • Rate, time, and distance problems (distance = rate x time)
  • Work and production rates: how long a job takes at a given pace
  • Averages (means) and finding a missing value from an average
  • Unit conversion: hours to minutes, feet to inches, dollars to cents
  • Multi-step problems that combine two or more of the skills above

How to study it

Translate before you calculate. The hardest part of AR is usually setup, not arithmetic. Read the whole problem, underline what it asks for, and write down the numbers with labels (miles, hours, dollars). Turn phrases into math: "per" signals division or a rate, "of" often means multiply, "how many more" means subtract.

Master the core formulas cold. Distance = rate x time, and its rearrangements, shows up constantly. So do percent (part = percent x whole) and average (sum divided by count). If these are automatic, you free up time for the reasoning.

Estimate to catch errors. Before choosing, ask whether your answer is reasonable. If a discounted price comes out higher than the original, or a trip "takes" a negative time, you made a setup mistake. Rounding to sanity-check will eliminate answer choices fast.

Common mistakes to avoid: mixing up units (adding minutes to hours, or feet to inches) is the number-one error, so convert everything to the same unit first. Watch for answer choices that represent a partial step rather than the final answer, especially in multi-step problems where the test bank includes the intermediate number as a trap. Do not rush the reading; a single misread word ("less" vs. "more," "each" vs. "total") changes the whole problem. Practice without a calculator, since the paper version does not allow one and mental fluency helps everywhere.

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