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ASVAB practice questions and answers
20 free questions from our 300-question ASVAB bank, each with the correct answer, explanation, and source note. Official format: CAT-ASVAB (adaptive) or paper form · AFQT reported as a 1–99 percentile · no universal passing score.
Percentages
1. A military base receives 200 cases of MREs. If 15% are vegetarian meals, how many vegetarian MREs are there?
Answer: B. To find 15% of 200, convert the percentage to a decimal (0.15) and multiply by the total: 0.15 × 200 = 30. The other choices come from misidentifying the percentage (25 is roughly 12.5%, 35 is 17.5%, 40 is 20%). Always convert the percent to a decimal before multiplying.
Source: ASVAB — Arithmetic Reasoning: Percentages
Rate time distance
2. A convoy travels at a constant speed of 45 mph. How many miles does the convoy cover in 3 hours?
Answer: B. Distance equals speed multiplied by time: 45 mph × 3 hours = 135 miles. The other answers result from arithmetic errors — for example, 45 × 4 = 180 or incorrectly adding the numbers. The distance formula D = R × T is fundamental to these problems.
Source: ASVAB — Arithmetic Reasoning: Rate, Time, and Distance
Ratios proportions
3. A mess hall serves meals with a main-dish-to-side-dish ratio of 2:3. If 180 side dishes are served, how many main dishes are served?
Answer: C. The ratio of main to side dishes is 2:3, meaning main/side = 2/3. Multiply 180 by 2/3 to get 120 main dishes. A common mistake is reversing the ratio and multiplying by 3/2, which would give 270 — not an option here but a frequent error on timed tests.
Source: ASVAB — Arithmetic Reasoning: Ratios and Proportions
Word problems
4. A platoon of 48 soldiers is organized into fire teams of 8 soldiers each. If 16 soldiers are reassigned, how many full fire teams remain?
Answer: B. After 16 soldiers leave, 48 − 16 = 32 soldiers remain. Dividing by the fire team size: 32 ÷ 8 = 4 full fire teams. Choosing 6 ignores the reassignment entirely (48 ÷ 8 = 6). Always read carefully whether the problem asks for a before or after scenario.
Source: ASVAB — Arithmetic Reasoning: Basic Word Problems
Financial math
5. A soldier deposits $500 in a savings account that earns 4% simple interest per year. How much interest is earned after 3 years?
Answer: C. Simple interest uses the formula I = P × r × t. Here P = 500, r = 0.04, and t = 3, so I = 500 × 0.04 × 3 = $60. The choice $40 reflects calculating interest for only 2 years, while $50 confuses simple with a miscalculation. Remember simple interest does not compound.
Source: ASVAB — Arithmetic Reasoning: Simple Interest and Financial Math
Algebra
6. Solve for x: 3x + 7 = 22
Answer: C. Subtract 7 from both sides to get 3x = 15, then divide both sides by 3 to find x = 5. Check by substituting: 3(5) + 7 = 15 + 7 = 22, which confirms the solution. A common error is dividing 22 by 3 without first subtracting the constant term.
Source: ASVAB — Mathematics Knowledge: Solving Linear Equations
Geometry
7. What is the perimeter of a rectangular training area that is 50 yards long and 30 yards wide?
Answer: C. Perimeter is the total distance around a shape. For a rectangle, P = 2(L + W) = 2(50 + 30) = 2(80) = 160 yards. The choice 150 is half the perimeter, and 300 is the area (50 × 30). Distinguishing perimeter from area is a key skill on the ASVAB.
Source: ASVAB — Mathematics Knowledge: Geometry — Perimeter
Fractions decimals
8. What is the sum of 3/4 and 2/3?
Answer: C. Find the least common denominator, which is 12. Convert: 3/4 = 9/12 and 2/3 = 8/12. Add the numerators: 9 + 8 = 17, giving 17/12, which simplifies to 1 5/12. The choice 5/7 comes from incorrectly adding numerators and denominators separately, a very common mistake.
Source: ASVAB — Mathematics Knowledge: Fractions and Decimals
Number properties
9. What is the greatest common factor of 24 and 36?
Answer: C. List the factors: 24 has factors 1, 2, 3, 4, 6, 8, 12, 24. The factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36. The largest factor both numbers share is 12. Choosing 6 is a common error because 6 is a common factor but not the greatest one.
Source: ASVAB — Mathematics Knowledge: Number Properties
Basic statistics
10. What is the mean of the numbers 12, 15, 18, 21, and 24?
Answer: C. The mean is the sum divided by the count: (12 + 15 + 18 + 21 + 24) ÷ 5 = 90 ÷ 5 = 18. The median also happens to be 18 here, but in general the mean and median can differ. The choice 17 results from dividing by 6 instead of 5.
Source: ASVAB — Mathematics Knowledge: Basic Statistics
Percentages
11. A unit's equipment budget increased from $50,000 to $62,500. What was the percent increase?
Answer: C. The increase is $62,500 − $50,000 = $12,500. Percent increase equals the change divided by the original amount: ($12,500 ÷ $50,000) × 100 = 25%. Dividing by the new amount ($12,500 ÷ $62,500 = 20%) is a frequent mistake that yields the wrong answer.
Source: ASVAB — Arithmetic Reasoning: Percentages
Percentages
12. A soldier earns $3,200 per month. After receiving a 5% raise, what is the soldier's new monthly pay?
Answer: B. First calculate 5% of $3,200: 0.05 × 3,200 = $160. Then add the raise to the original salary: $3,200 + $160 = $3,360. The choice $3,250 reflects a miscalculation of 5%, while $3,520 would be a 10% raise. Always find the dollar amount of the percentage first.
Source: ASVAB — Arithmetic Reasoning: Percentages
Rate time distance
13. Two Humvees leave the same base at the same time, traveling in opposite directions at 50 mph and 65 mph. How far apart are they after 4 hours?
Answer: B. When two objects travel in opposite directions, their speeds add: 50 + 65 = 115 mph. Multiply by the time: 115 × 4 = 460 miles. Students often calculate each vehicle's distance separately (200 and 260 miles) and then must remember to add them — the final answer is the same either way.
Source: ASVAB — Arithmetic Reasoning: Rate, Time, and Distance
Rate time distance
14. A patrol car must travel 300 miles to reach a checkpoint in 5 hours. What minimum average speed is required?
Answer: B. Speed equals distance divided by time: 300 ÷ 5 = 60 mph. This is the minimum average speed needed to cover the distance in exactly 5 hours. Driving slower means arriving late. The other choices represent common rounding or misreading errors.
Source: ASVAB — Arithmetic Reasoning: Rate, Time, and Distance
Ratios proportions
15. A scale drawing of a tank uses a ratio of 1:72. If the drawing measures 8 inches long, what is the actual tank length in inches?
Answer: C. A 1:72 scale means every 1 inch on the drawing represents 72 inches in reality. Multiply: 8 × 72 = 576 inches. Dividing instead of multiplying (8 ÷ 72 ≈ 0.11) would give a nonsensical result. Always remember the scale goes from model to real by multiplication.
Source: ASVAB — Arithmetic Reasoning: Ratios and Proportions
Ratios proportions
16. Three units share a 1,500-gallon water supply in the ratio 2:3:5. How many gallons does the largest unit receive?
Answer: D. Add the ratio parts: 2 + 3 + 5 = 10 total parts. The largest unit gets 5 out of 10 parts. Multiply: (5/10) × 1,500 = 750 gallons. A common error is dividing by the number of units (1,500 ÷ 3 = 500) instead of using the ratio weights.
Source: ASVAB — Arithmetic Reasoning: Ratios and Proportions
Word problems
17. A shipping container holds 200 crates. Crates are loaded at a rate of 5 per minute and unloaded at 8 per minute. How many minutes does it take to completely fill and then empty one container?
Answer: D. Loading time: 200 ÷ 5 = 40 minutes. Unloading time: 200 ÷ 8 = 25 minutes. Total time: 40 + 25 = 65 minutes. Students sometimes try to combine the rates by subtraction or averaging, which gives an incorrect answer. Treat each operation separately.
Source: ASVAB — Arithmetic Reasoning: Basic Word Problems
Word problems
18. A radio transmits for 15 minutes, rests for 5 minutes, then repeats this cycle. How many full cycles are completed in 2 hours?
Answer: D. One full cycle takes 15 + 5 = 20 minutes. Two hours is 120 minutes. Divide: 120 ÷ 20 = 6 full cycles. If you ignore the rest period and divide 120 by 15, you get 8 — but the radio is not transmitting the entire time. Always account for all parts of a cycle.
Source: ASVAB — Arithmetic Reasoning: Basic Word Problems
Financial math
19. A service member borrows $3,000 at 6% simple interest for 2 years. What is the total amount that must be repaid?
Answer: C. Interest owed: $3,000 × 0.06 × 2 = $360. Total repayment: $3,000 + $360 = $3,360. The choice $3,600 would result from compound interest, while $3,180 represents interest for only 1 year. Simple interest means the principal does not change each year.
Source: ASVAB — Arithmetic Reasoning: Simple Interest and Financial Math
Algebra
20. If 2y − 8 = 14, what is the value of y?
Answer: D. Add 8 to both sides: 2y = 22. Divide both sides by 2: y = 11. Verify: 2(11) − 8 = 22 − 8 = 14. A common mistake is subtracting 8 instead of adding, which gives y = 3. Always perform the inverse operation to isolate the variable.
Source: ASVAB — Mathematics Knowledge: Solving Linear Equations
That’s the free set. The full bank has 300.
More original practice questions across the listed topics, a 50-question timed benchmark, and saved mistake review. Internal QuizCram practice target. The ASVAB has no passing score — the AFQT is reported as a percentile from 1 to 99 and each service branch sets its own minimum. One payment of $14.99, yours forever.