ASVAB Arithmetic Reasoning Practice & Word Problems Guide
Arithmetic Reasoning (AR) tests your ability to solve real-world mathematical word problems using basic arithmetic principles, ratios, percentages, and algebraic logic.
What to Expect in Arithmetic Reasoning
Unlike Mathematics Knowledge, which presents pure formulas and algebra, Arithmetic Reasoning presents math in story form. You must extract the relevant numerical information, identify the required mathematical operation, and calculate the solution accurately without a calculator.
Enters raw composite directly: $2(VE) + AR + MK$
Scratch paper and pencils provided
60–90 seconds target per question
Walkthrough Practice Problems
A military transport convoy travels at an average speed of 60 mph. How far will it travel in 2.5 hours?
Step 1: Identify the formula: Distance = Speed × Time.
Step 2: Substitute given values: Distance = 60 mph × 2.5 hours.
Step 3: Perform the calculation: 60 × 2 = 120; 60 × 0.5 = 30; 120 + 30 = 150 miles.
If a soldier earns $2,400 per month and saves 15% of it, how much does the soldier save each month?
Step 1: Convert percentage to decimal: 15% = 0.15.
Step 2: Multiply salary by percentage: $2,400 × 0.15.
Step 3: Quick mental math: 10% of $2,400 = $240; 5% = $120; $240 + $120 = $360.
If 4 workers can assemble a supply shelter in 6 hours, how many hours will it take 8 workers working at the same rate?
Step 1: Determine total worker-hours needed: 4 workers × 6 hours = 24 worker-hours.
Step 2: Divide total worker-hours by the new team size: 24 ÷ 8 workers = 3 hours.
Explore the Other 3 AFQT Subtests
Put Your Arithmetic Skills to the Test
Our free 20-question diagnostic exam includes 5 timed Arithmetic Reasoning word problems with step-by-step explanations for every question.
Launch Free Diagnostic TestFrequently Asked Questions
What is the difference between Arithmetic Reasoning (AR) and Mathematics Knowledge (MK)?
Arithmetic Reasoning evaluates your ability to solve practical word problems using arithmetic and logical reasoning (e.g., speed, time, rate of work, percentages). Mathematics Knowledge tests your knowledge of high-school mathematical principles (e.g., algebra equations, exponents, and geometric theorems).
Can I use scratch paper during the Arithmetic Reasoning section?
Yes. Scratch paper and pencils are provided at Military Entrance Processing Stations (MEPS) and MET sites. Because calculators are prohibited, you should practice setting up word problems and working through calculations entirely on paper.
What are the most common formulas tested in Arithmetic Reasoning?
The most frequent formulas include Distance = Rate × Time (d = rt), Work Done = Rate × Time, Percentage Change = (Change / Original) × 100%, and Averages = Sum of Values / Number of Values.