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ASVAB Armed Services Vocational Aptitude Battery

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1 Introduction

About the ASVAB AFQT Score and Military Eligibility Line Scores and Military Jobs (MOS) How to Use This Guide

2 Verbal Domain (WK + PC)

Word Knowledge Basics Word Knowledge Practice Paragraph Comprehension Basics Paragraph Comprehension Practice

3 Mathematics Domain (AR + MK)

Number Operations Word Problems Algebra Geometry Test Strategies

4 Science & Technical Domain (GS + EI + MC)

Life Science Physical Science Electronics Fundamentals Mechanical Principles Applied Science Questions

5 Technical Skills Domain (AI + SI + AO)

Automotive Basics Automotive Systems Shop Tools and Practices Shop Safety and Materials Assembling Objects

Free exam prep ASVAB Armed Services Vocational Aptitude Battery Practice Questions 486 questions Study Guide 23 topics Cheat Sheet 120 facts Flashcards 50 cards

Word Problems

Key Takeaways Explain This Topic AI

Translate keywords to operations: 'of' means multiply, 'per' means divide, 'is' means equals.

Rate x Time = Distance (or Amount)—the fundamental formula for rate problems.

For work problems, add the rates (work per time unit), not the times.

Always identify what the question is actually asking before solving.

Check your answer by plugging it back into the original problem. Last updated: January 2026

Quick Tip: The Arithmetic Reasoning (AR) subtest is entirely word problems—16 questions in 39 minutes. That's about 2.5 minutes per question, so practice translating words to math quickly. Translating Words to Math Key Translation Words

Word/Phrase Mathematical Operation sum, total, altogether, increased by Addition (+) difference, less than, decreased by, fewer Subtraction (−) product, times, of Multiplication (×) quotient, per, divided by, ratio Division (÷) is, equals, was, will be Equals (=) what, a number Variable (x) Setting Up Equations Pattern: "[Some quantity] is [some relationship to] [another quantity]" Example: "Three more than twice a number is 17" "Twice a number" = 2 x 2x 2 x "Three more than" = 2 x + 3 2x + 3 2 x + 3 "is 17" = = 17 = 17 = 17 Equation: 2 x + 3 = 17 2x + 3 = 17 2 x + 3 = 17 Rate, Time, and Distance Problems The Fundamental Formula Distance = Rate × Time \text{Distance} = \text{Rate} \times \text{Time} Distance = Rate × Time Or rearranged: Rate = Distance Time \text{Rate} = \frac{\text{Distance}}{\text{Time}} Rate = Time Distance Time = Distance Rate \text{Time} = \frac{\text{Distance}}{\text{Rate}} Time = Rate Distance Worked Example: Basic Rate Problem Problem: A car travels at 55 mph. How far will it travel in 3 hours? Solution: Distance = Rate × Time = 55 × 3 = 165 miles \text{Distance} = \text{Rate} \times \text{Time} = 55 \times 3 = 165 \text{ miles} Distance = Rate × Time = 55 × 3 = 165 miles Worked Example: Meeting in the Middle Problem: Two cars start 360 miles apart and drive toward each other. Car A travels at 50 mph and Car B at 40 mph. When will they meet? Solution: Step 1: Combined rate = 50 + 40 = 90 mph (they're closing the gap together) Step 2: Time = Distance / Rate = 360 / 90 = 4 hours Worked Example: Catch-Up Problem Problem: A train leaves at 2 PM traveling at 60 mph. Another train leaves from the same station at 3 PM traveling at 80 mph in the same direction. When will the second train catch up? Solution: Step 1: Head start distance = 60 × 1 = 60 miles Step 2: Closing speed = 80 − 60 = 20 mph Step 3: Time to catch up = 60 / 20 = 3 hours (at 6 PM) Work Problems The Work Formula If Person A completes a job in a a a hours and Person B in b b b hours: Combined time = a b a + b \text{Combined time} = \frac{ab}{a + b} Combined time = a + b ab Or use rates: Add the work rates (job per hour): 1 a + 1 b = 1 t \frac{1}{a} + \frac{1}{b} = \frac{1}{t} a 1 + b 1 = t 1 Worked Example: Two Workers Problem: John can paint a room in 6 hours. Mary can paint the same room in 4 hours. How long will it take them working together? Solution: Method 1 (Formula): t = 6 × 4 6 + 4 = 24 10 = 2.4 hours = 2 hours 24 minutes t = \frac{6 \times 4}{6 + 4} = \frac{24}{10} = 2.4 \text{ hours} = 2 \text{ hours } 24 \text{ minutes} t = 6 + 4 6 × 4 = 10 24 = 2.4 hours = 2 hours 24 minutes Method 2 (Rates): John's rate: 1 6 \frac{1}{6} 6 1 room per hour Mary's rate: 1 4 \frac{1}{4} 4 1 room per hour Combined: 1 6 + 1 4 = 2 12 + 3 12 = 5 12 \frac{1}{6} + \frac{1}{4} = \frac{2}{12} + \frac{3}{12} = \frac{5}{12} 6 1 + 4 1 = 12 2 + 12 3 = 12 5 room per hour Time: 1 5 12 = 12 5 = 2.4 \frac{1}{\frac{5}{12}} = \frac{12}{5} = 2.4 12 5 1 = 5 12 = 2.4 hours Percentage Word Problems Common Percentage Problem Types

Type Setup Finding a percentage "What is 20% of 150?" → 0.20 × 150 0.20 \times 150 0.20 × 150 Finding what percent "15 is what percent of 60?" → 15 60 × 100 \frac{15}{60} \times 100 60 15 × 100 Finding the whole "30 is 25% of what?" → 30 0.25 \frac{30}{0.25} 0.25 30 Percent increase New − Old Old × 100 \frac{\text{New} - \text{Old}}{\text{Old}} \times 100 Old New − Old × 100 Percent decrease Old − New Old × 100 \frac{\text{Old} - \text{New}}{\text{Old}} \times 100 Old Old − New × 100 Worked Example: Discount Problem Problem: A jacket originally costs $80. It's on sale for 30% off. What is the sale price? Solution: Step 1: Discount = 80 × 0.30 = $24 Step 2: Sale price = 80 − 24 = $56 Shortcut: 30% off means you pay 70%: 80 × 0.70 = $ 56 80 \times 0.70 = \$56 80 × 0.70 = $56 Worked Example: Percent Change Problem: A stock price increased from $40 to $52. What was the percent increase? Solution: Percent increase = 52 − 40 40 × 100 = 12 40 × 100 = 30 % \text{Percent increase} = \frac{52 - 40}{40} \times 100 = \frac{12}{40} \times 100 = 30\% Percent increase = 40 52 − 40 × 100 = 40 12 × 100 = 30% Ratio and Proportion Problems Setting Up Proportions If a b = c d \frac{a}{b} = \frac{c}{d} b a = d c , then a × d = b × c a \times d = b \times c a × d = b × c (cross multiply) Worked Example: Ratio Problem Problem: The ratio of boys to girls in a class is 3:5. If there are 24 boys, how many girls are there? Solution: 3 5 = 24 x \frac{3}{5} = \frac{24}{x} 5 3 = x 24 Cross multiply: 3 x = 5 × 24 = 120 3x = 5 \times 24 = 120 3 x = 5 × 24 = 120 x = 120 3 = 40 x = \frac{120}{3} = 40 x = 3 120 = 40 girls

Test Your Knowledge

A car travels at 65 mph for 4 hours. How many miles does it travel?

240 miles

250 miles

260 miles

270 miles Check Answer Need a hint? AI

Test Your Knowledge

Alice can complete a job in 8 hours. Bob can complete the same job in 12 hours. Working together, how long will it take them?

4 hours

4.8 hours

5 hours

6 hours Check Answer Need a hint? AI

Test Your Knowledge

A shirt priced at $45 is marked down 20%. What is the sale price?

$25

$36

$40 Check Answer Need a hint? AI

Test Your Knowledge

The ratio of cats to dogs at a shelter is 4:7. If there are 28 dogs, how many cats are there?

20 Check Answer Need a hint? AI

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