Free ASVAB Arithmetic Reasoning Practice Test
Take this free ASVAB Arithmetic Reasoning practice test to see how you handle math word problems under pressure. Every question is scored instantly and comes with a full worked solution, not just the right letter.
One of the four subtests that make up your AFQT score. No sign-up, no payment, unlimited retakes.
ASVAB Arithmetic Reasoning Practice Test
Arithmetic Reasoning (AR) is one of the most important subtests on the ASVAB. It measures your ability to
solve math word problems real-life situations where you must figure out which mathematical
operation to apply.
Basic Operations & Money
At a used book store, Valentina bought three books for $2.65 each and paid with a $20 bill. How much change did she get?
Three books cost 3 × $2.65 = $7.95. Change from $20 is $20.00 − $7.95 = $12.05.
Basic Operations & Money
A radar system beeps once every second. How many times will it beep in 3 days?
One day has 24 × 60 × 60 = 86,400 seconds. Three days is 3 × 86,400 = 259,200 beeps.
Basic Operations & Money
A car's tire rotates 552 times per minute at a constant speed. How many times does it rotate in half an hour?
Half an hour is 30 minutes. 552 × 30 = 16,560 rotations.
Basic Operations & Money
A theater sells 340 tickets at $12 each for an evening show. What is the total revenue?
Multiply price by quantity: 340 × $12 = $4,080.
Basic Operations & Money
A worker is paid $18 per hour and works 37 hours in a week. What are the gross weekly earnings?
Multiply the hourly rate by the hours: $18 × 37 = $666.
Basic Operations & Money
A case holds 24 cans. A store receives 15 cases. How many cans is that in total?
Multiply cans per case by number of cases: 24 × 15 = 360 cans.
Percentages
Kayla left a $10.47 tip on a breakfast that cost $87.25. What percentage was the tip?
Divide the tip by the bill: 10.47 ÷ 87.25 = 0.12, which is 12%.
Percentages
Oscar bought a hat on sale for $5.06. The original price was $9.20. What was the percentage discount?
The discount is $9.20 − $5.06 = $4.14. As a percent of the original: 4.14 ÷ 9.20 = 0.45, or 45%.
Percentages
A waiter averages a 15% tip on the food he serves. If he serves $435 of food in one night, how much does he make in tips?
Multiply by the decimal: 0.15 × $435 = $65.25.
Percentages
Maya bought a boat for $18,340. It depreciated 15% in the first year. What was it worth at the end of that year?
It keeps 100% − 15% = 85% of its value. 0.85 × $18,340 = $15,589.
Percentages
A motorcycle costs $7,250 and depreciates 12% in its first year. What is it worth after one year?
It retains 88% of its value: 0.88 × $7,250 = $6,380.
Percentages
Tom needs 80% of the 20 questions on a test correct to pass. How many questions must he get right?
To find a percentage of a number, multiply by its decimal form: 0.80 × 20 = 16 questions.
Percentages
A $45 shirt is marked up so the store sells it for $54. What is the percent increase?
The increase is $54 − $45 = $9. As a percent of the original: 9 ÷ 45 = 0.20, or 20%.
Percentages
A laptop costs $600 before tax. If sales tax is 7%, what is the total price?
Tax is 0.07 × $600 = $42. Total is $600 + $42 = $642.
Percentages
In a class of 25 students, 15 are boys. What percentage of the class is boys?
To turn a part into a percentage, divide the part by the whole: 15 ÷ 25 = 0.60, which is 60%.
Interest
A savings account holds $2,000 and earns 4% simple interest per year. How much interest is earned in one year?
Simple interest = principal × rate × time = $2,000 × 0.04 × 1 = $80.
Interest
How much simple interest does $1,500 earn at 6% per year over 3 years?
Simple interest = $1,500 × 0.06 × 3 = $270.
Interest
$1,000 is invested at 5% interest compounded annually. What is the balance after 2 years?
After year 1: $1,000 × 1.05 = $1,050. After year 2: $1,050 × 1.05 = $1,102.50.
Rates & Speed
A phone company charges $2 for the first five minutes of a call and 30 cents per minute after that. What does a 25-minute call cost?
The first 5 minutes cost $2. The remaining 20 minutes cost 20 × $0.30 = $6.00. Total: $2 + $6 = $8.00.
Rates & Speed
It takes 5 seconds for 20 gallons of water to come out of a faucet. At this rate, how many gallons come out in 7 seconds?
The rate is 20 ÷ 5 = 4 gallons per second. In 7 seconds: 4 × 7 = 28 gallons.
Rates & Speed
A car travels 360 kilometers in 5 hours. At the same speed, how far will it travel in 9 hours?
The speed is 360 ÷ 5 = 72 km/h. In 9 hours: 72 × 9 = 648 km.
Rates & Speed
Mia earns $8.10 per hour and works 40 hours. Charlotte earns $10.80 per hour. How many hours must Charlotte work to match Mia's earnings?
Mia earns 40 × $8.10 = $324. Charlotte needs $324 ÷ $10.80 = 30 hours.
Rates & Speed
A printer prints 18 pages per minute. How long does it take to print 270 pages?
Divide the pages by the rate: 270 ÷ 18 = 15 minutes.
Rates & Speed
A train leaves at 9:00 a.m. traveling 60 mph. How far has it gone by 11:30 a.m.?
The time is 2.5 hours. Distance = rate × time = 60 × 2.5 = 150 miles.
Rates & Speed
A grocery store sells 3 pounds of apples for $4.50. At that rate, what do 7 pounds cost?
The unit price is $4.50 ÷ 3 = $1.50 per pound. Seven pounds cost 7 × $1.50 = $10.50.
Rates & Speed
A machine fills 480 bottles in 8 hours. How many bottles does it fill in 5 hours at the same rate?
The rate is 480 ÷ 8 = 60 bottles per hour. In 5 hours: 60 × 5 = 300 bottles.
Ratios & Proportions
On a map, 10 inches represents 100 feet. What actual distance does 25 inches represent?
The scale is 100 ÷ 10 = 10 feet per inch. So 25 inches is 25 × 10 = 250 feet.
Ratios & Proportions
One in every 9 people in a town votes for party A and the rest vote for party B. In a town of 810 people, how many vote for party B?
Party A gets 810 ÷ 9 = 90 votes. Party B gets the rest: 810 − 90 = 720.
Ratios & Proportions
A recipe that serves 4 needs 6 cups of flour. How many cups are needed to serve 10?
Flour per serving is 6 ÷ 4 = 1.5 cups. For 10 servings: 10 × 1.5 = 15 cups.
Ratios & Proportions
The ratio of dogs to cats at a shelter is 3 to 5. If there are 24 dogs, how many cats are there?
Each 'part' is 24 ÷ 3 = 8 animals. Cats are 5 parts: 5 × 8 = 40.
Ratios & Proportions
Two pizza ovens burn pizzas. Oven #1 burns three times as many as Oven #2. If 12 pizzas were burnt in total, how many did Oven #2 burn?
Let Oven #2 burn x. Then Oven #1 burns 3x, so x + 3x = 12, meaning 4x = 12 and x = 3.
Ratios & Proportions
A photo 4 inches wide and 6 inches tall is enlarged so its width becomes 10 inches. What is the new height?
The scale factor is 10 ÷ 4 = 2.5. New height is 6 × 2.5 = 15 inches.
Ratios & Proportions
A blueprint uses a scale of 1 inch to 4 feet. A wall measures 7 inches on the blueprint. How long is the real wall?
Each inch on the blueprint stands for 4 feet, so multiply by the scale: 7 × 4 = 28 feet.
Averages
Sofia drives at 70 km/h for 2 hours, then 63 km/h for 5 hours. What was her average speed over the 7 hours?
Total distance is (70×2) + (63×5) = 140 + 315 = 455 km. Average speed is 455 ÷ 7 = 65 km/h.
Averages
A student scored 78, 85, and 92 on three tests. What is the average score?
Add the scores: 78 + 85 + 92 = 255. Divide by 3: 255 ÷ 3 = 85.
Averages
The average of four numbers is 20. Three of them are 15, 22 and 18. What is the fourth number?
The four numbers total 4 × 20 = 80. The known three sum to 55, so the fourth is 80 − 55 = 25.
Averages
On five quizzes a student averaged 88. To raise the average to 90 over six quizzes, what must the sixth score be?
Five quizzes total 5 × 88 = 440. Six quizzes must total 6 × 90 = 540. The sixth score is 540 − 440 = 100.
Probability
A box has 5 blue, 4 red and 3 yellow marbles. If one marble is drawn at random, what is the probability it is red or yellow?
There are 4 + 3 = 7 favorable marbles out of 12 total, so the probability is 7/12.
Probability
A box has 4 red and 8 green marbles. What is the probability of drawing a red marble at random?
There are 4 red out of 12 total, which is 4/12 = 1/3.
Probability
A standard six-sided die is rolled once. What is the probability of rolling a number greater than 4?
The numbers greater than 4 are 5 and 6, so 2 out of 6, which is 1/3.
Probability
A bag holds 10 tickets numbered 1 to 10. What is the probability of drawing an even number?
There are 5 even numbers (2, 4, 6, 8, 10) out of 10, which is 5/10 = 1/2.
Unit Conversion
Stephen has a 5-gallon bucket with 3.5 gallons of lemonade in it. How many pints must he add to fill it to 5 gallons? (1 gallon = 8 pints)
He needs 5 − 3.5 = 1.5 more gallons. At 8 pints per gallon, that is 1.5 × 8 = 12 pints.
Unit Conversion
How many minutes are there in 3.5 hours?
There are 60 minutes in an hour, so multiply by 60: 3.5 × 60 = 210 minutes.
Unit Conversion
A recipe calls for 2 quarts of milk. How many cups is that? (1 quart = 4 cups)
There are 4 cups in a quart, so multiply by 4: 2 × 4 = 8 cups.
Unit Conversion
A runner completes a 5-kilometer race. About how many meters is that?
One kilometer is 1,000 meters, so 5 km is 5 × 1,000 = 5,000 meters.
Unit Conversion
A package weighs 48 ounces. How many pounds is that? (1 pound = 16 ounces)
There are 16 ounces in a pound, so divide by 16: 48 ÷ 16 = 3 pounds.
Unit Conversion
How many seconds are there in 4 hours?
One hour has 3,600 seconds, so 4 hours is 4 × 3,600 = 14,400 seconds.
Area & Geometry
A room floor is 15 feet long and 10 feet wide. How much flooring is needed to cover it?
Area of a rectangle is length × width: 15 × 10 = 150 square feet.
Area & Geometry
Aisha paints a room with four walls each 10 feet high. Two walls are 10 feet wide and two are 15 feet wide. A half gallon covers 55 sq ft. Paint comes in 1-gallon cans. How many cans does she need?
Wall area is 2×(10×10) + 2×(15×10) = 200 + 300 = 500 sq ft. One gallon covers 110 sq ft, so she needs 500 ÷ 110 ≈ 4.5, which rounds up to 5 cans.
Area & Geometry
A rectangular garden is 12 feet by 8 feet. What is its perimeter?
Perimeter is 2 × (length + width) = 2 × (12 + 8) = 2 × 20 = 40 feet.
Area & Geometry
A square tile has a side of 9 inches. What is its area?
Area of a square is side × side: 9 × 9 = 81 square inches.
Word Problems & Number Sense
Five years ago, Amy was three times as old as Mike. Mike is 10 now. How old is Amy?
Five years ago Mike was 5, so Amy was 3 × 5 = 15. That was five years ago, so Amy is now 15 + 5 = 20.
Word Problems & Number Sense
A tank is 3/4 full and holds 60 gallons when full. How many gallons are in it now?
Three-quarters of 60 is (3/4) × 60 = 45 gallons.
Word Problems & Number Sense
One painter can paint a fence in 6 hours. Working together with a second painter of equal speed, how long does it take?
Two equal painters work twice as fast, so the job takes half the time: 6 ÷ 2 = 3 hours.
Word Problems & Number Sense
A jacket normally $80 is 25% off, and then $5 more is taken at the register. What is the final price?
25% off $80 removes $20, leaving $60. Taking $5 more gives $60 − $5 = $55.
Word Problems & Number Sense
John is twice as old as his sister. The sum of their ages is 27. How old is John?
Let the sister be x. Then John is 2x, so x + 2x = 27, giving 3x = 27 and x = 9. John is 2 × 9 = 18.
Word Problems & Number Sense
Which of the following is a whole number?
Whole numbers are the non-negative counting numbers 0, 1, 2, 3 and so on. Of the choices, only 7 qualifies. The others are negative, a fraction and a decimal.
WHAT TO EXPECT
What Is on the ASVAB Arithmetic Reasoning Test?
Arithmetic Reasoning, listed as AR on your score report, is the word problem section.
It does not test whether you can do the math. It tests whether you can work out which math to do.
Every question is a short story with numbers in it. Your job is to pull out what matters, ignore
what does not, set up the calculation and solve it. The arithmetic itself rarely goes past what you
learned by ninth grade. These are the most common problem types:
Rates and Speed: distance, time and how fast something travels
Percentages: discounts, tips, sales tax, interest and percent change
Ratios and Proportions: map scales, recipes, mixing and unit conversion
Averages: finding a mean, or working backwards from one
Money: wages, total cost, change, profit and simple budgeting
Work and Time: how long a job takes with one or more people
Basic Probability: simple chances, usually with marbles, cards or coins
TEST FORMAT
ASVAB Arithmetic Reasoning Test Format
| CAT-ASVAB (computer) | Paper ASVAB | |
|---|---|---|
| Questions | CAT-ASVAB15 | Paper ASVAB30 |
| Time limit | CAT-ASVAB55 minutes | Paper ASVAB36 minutes |
| Time per question | CAT-ASVABAbout 3 min 40 sec | Paper ASVABAbout 1 min 12 sec |
| Change an answer | CAT-ASVABNot allowed | Paper ASVABAllowed |
| Penalty for guessing | CAT-ASVABYes | Paper ASVABNo |
These figures come from the official ASVAB Fact Sheet. You will still find sites publishing 16 questions in 39 minutes, which is from an older version of the computer test.
The time difference is the part worth noticing. Arithmetic Reasoning gets by far the most generous clock on the whole computer test, roughly three and a half minutes per question. Nobody rushes out of this section. If you are running out of time on AR, the problem is not speed, it is that you are stuck on how to set the problem up.
WHY IT MATTERS
Does Arithmetic Reasoning Count Toward Your AFQT Score?
Yes, and it is one of only four subtests that do. Your AFQT raw score is calculated as 2VE + AR + MK, where VE combines Word Knowledge and Paragraph Comprehension.
That formula matters. Arithmetic Reasoning is one of just two math scores in it, so a weak AR score pulls your AFQT down directly, and the AFQT is what decides whether you can enlist at all. Most branches want a minimum AFQT of 31 with a high school diploma, and 50 with a GED.
If you only have time to prepare for four subtests, this is one of them.
TEST-DAY RULE
No Calculator Is Allowed
You cannot use a calculator anywhere on the ASVAB, including Arithmetic Reasoning. You get scratch paper and a pencil.
Practice the arithmetic by hand while you prepare. Long multiplication, long division, fractions and percentages all need to be automatic, because doing them slowly on test day eats the time you need for thinking.
QUICK REFERENCE
Formulas Worth Knowing Before Test Day
You do not need many, but these come up constantly:
Distance = rate × time: rearranged, rate = distance ÷ time
Percent of a number: multiply by the decimal (15% of 80 = 0.15 × 80)
Percent change: difference ÷ original, then × 100
Average (mean): total ÷ how many
Simple interest: interest = principal × rate × time
Total cost: price × quantity, then add tax or subtract discount
KEEP PRACTICING
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