AR tests your ability to solve word problems using basic math. It directly affects your AFQT and GT scores — two of the most important numbers for enlistment.
Ability to solve mathematical word problems involving percentages, ratios, distance/rate/time, work problems, and basic algebra applied to everyday scenarios.
Arithmetic Reasoning is less about difficult computation than translating a short story into the right operation. Train yourself to name the unknown, ignore extra details, estimate the answer range, and then calculate without a calculator.
Turn phrases such as “per,” “of,” “difference,” and “total” into equations before touching the numbers.
Use equivalent ratios for scale problems and convert percent language into a part-whole relationship.
Recognize motion questions and decide whether rates combine, differ, or stay constant.
Apply unit rates to jobs, purchases, wages, discounts, tax, and mean values.
Use basic area, perimeter, and volume formulas in real-world settings while keeping units consistent.
Open a question to review the choices, correct answer, and a short explanation.
Why: 18 ÷ 24 = 0.75, and 0.75 × 100% = 75%.
Why: There are 3 + 5 = 8 equal parts. Each part is 64 ÷ 8 = 8 flags, so blue flags = 5 × 8 = 40.
Why: Distance = rate × time = 55 × 2.5 = 137.5 miles.
Why: After the discount, the price is $120 × 0.80 = $96. Tax makes the total $96 × 1.06 = $101.76.
Why: The added 18 gallons represents 4/5 − 2/5 = 2/5 of capacity. Capacity = 18 ÷ (2/5) = 45 gallons.
Translation: Translate 20 short word statements into equations without solving them.
Ratios and percents: Practice proportions, percent of a number, discounts, tax, and percent change.
Rates and motion: Solve unit-rate and distance-rate-time problems with unit conversions.
Work and averages: Practice combined work, weighted totals, and average problems.
Geometry in context: Review perimeter, area, volume, and measurement conversions.
Mixed set: Complete a mixed set slowly and write why each operation is appropriate.
Timed set: Complete 15 mixed questions under time, then sort misses by problem type.
Try Arithmetic Reasoning questions in the free AFQT practice test and review every explanation.
Free ASVAB study cheat sheet
Key formulas, composite scores, and score benchmarks in one printable PDF.