ASVAB Arithmetic Reasoning Practice Test: Questions, Answers and Study Guide

ASVAB practice Arithmetic Reasoning tests your ability to solve math word problems.

It is one of the most important ASVAB practice sections because it counts toward your AFQT score, which helps determine basic enlistment eligibility.

Arithmetic Reasoning questions usually involve practical math situations. You may need to calculate distance, speed, time, averages, percentages, ratios, proportions, fractions, costs, quantities or rates.

This guide includes ASVAB Arithmetic Reasoning practice questions with answers and explanations, plus a study strategy to help you improve your score.

These are not official ASVAB questions. They are realistic practice questions designed for ethical preparation. Always verify current ASVAB rules, AFQT requirements and retest policies with OfficialASVAB.com, MEPS, Today’s Military or an official recruiter.

What Is ASVAB Arithmetic Reasoning?

ASVAB Arithmetic Reasoning, often abbreviated as AR, measures how well you solve arithmetic word problems.

Unlike Mathematics Knowledge, which tests more direct math concepts, Arithmetic Reasoning asks you to read a situation and decide what calculation is needed.

You may need to:

• identify relevant numbers;
• ignore extra information;
• choose the correct operation;
• solve a practical problem;
• estimate an answer;
• convert fractions, decimals and percentages;
• calculate rates and averages;
• work with distance, time and speed;
• solve basic proportions.

Arithmetic Reasoning is both a reading test and a math test.

Does Arithmetic Reasoning Count Toward the AFQT?

Yes. Arithmetic Reasoning counts toward the AFQT.

The AFQT is based on four ASVAB subtests:

AFQT Subtest	What It Measures
Arithmetic Reasoning	Math word problems
Mathematics Knowledge	High school math concepts
Word Knowledge	Vocabulary
Paragraph Comprehension	Reading comprehension

Because AR counts toward the AFQT, improving this section can help improve your basic enlistment eligibility score.

Related page:

• AFQT Practice Test

Arithmetic Reasoning vs Mathematics Knowledge

Arithmetic Reasoning and Mathematics Knowledge both test math, but they are different.

Section	Main Focus
Arithmetic Reasoning	Word problems and applied math
Mathematics Knowledge	Math concepts, formulas and direct calculations

Example:

• Arithmetic Reasoning: “A vehicle travels 180 miles in 3 hours. What is its average speed?”
• Mathematics Knowledge: “Solve for x: 2x + 6 = 18.”

You need both skills for a strong AFQT score.

Common ASVAB Arithmetic Reasoning Topics

Arithmetic Reasoning questions may include:

Topic	Example
Addition and subtraction	Total cost, remaining quantity
Multiplication and division	Items per box, miles per hour
Fractions	1/2, 2/3, 3/4 of a quantity
Decimals	Money, measurements, conversions
Percentages	Discounts, increases, proportions
Ratios	Comparing quantities
Rates	Miles per hour, items per minute
Averages	Mean of several numbers
Proportions	Scale maps, equal ratios
Time	Work schedules, elapsed time
Distance	Travel and speed problems
Measurement	Length, area, volume and units
Word equations	Translating words into math

Most AR questions are not advanced, but they require careful reading.

ASVAB Arithmetic Reasoning Formula Sheet

Use these formulas often.

Concept	Formula
Average	sum ÷ number of values
Speed	distance ÷ time
Distance	speed × time
Time	distance ÷ speed
Percent of a number	percent × number
Percent change	change ÷ original × 100
Ratio	part : part or part ÷ total
Area of rectangle	length × width
Perimeter of rectangle	2(length + width)
Unit rate	total ÷ number of units

Memorize the formulas, but practice applying them in word problems.

How to Solve ASVAB Arithmetic Reasoning Questions

Use this process:

1. Read the question carefully.
2. Identify what the question asks.
3. Write down the relevant numbers.
4. Ignore extra information.
5. Choose the correct operation.
6. Estimate the answer.
7. Calculate carefully.
8. Check units.
9. Make sure the answer makes sense.
10. Select the closest correct choice.

Do not start calculating before you know what the question is asking.

Arithmetic Reasoning Practice Test

Answer the questions before reading the explanations.

This practice test includes 30 ASVAB Arithmetic Reasoning-style questions.

Question 1: Basic Multiplication

A supply room has 12 boxes. Each box contains 8 batteries. How many batteries are there in total?

• A. 20
• B. 48
• C. 72
• D. 96

Answer and Explanation

Correct answer: D. 96

Multiply boxes by batteries per box:

12 × 8 = 96

There are 96 batteries.

Question 2: Division

A team of 6 people shares 54 meal packs equally. How many meal packs does each person receive?

• A. 6
• B. 8
• C. 9
• D. 12

Answer and Explanation

Correct answer: C. 9

Divide meal packs by people:

54 ÷ 6 = 9

Each person receives 9 meal packs.

Question 3: Average Speed

A vehicle travels 240 miles in 4 hours. What is its average speed?

• A. 40 miles per hour
• B. 50 miles per hour
• C. 60 miles per hour
• D. 80 miles per hour

Answer and Explanation

Correct answer: C. 60 miles per hour

Average speed equals distance divided by time:

240 ÷ 4 = 60

The vehicle travels 60 miles per hour.

Question 4: Distance

A truck travels at 55 miles per hour for 3 hours. How far does it travel?

• A. 110 miles
• B. 150 miles
• C. 165 miles
• D. 180 miles

Answer and Explanation

Correct answer: C. 165 miles

Distance equals speed multiplied by time:

55 × 3 = 165

The truck travels 165 miles.

Question 5: Time

A vehicle travels 180 miles at an average speed of 60 miles per hour. How long does the trip take?

• A. 2 hours
• B. 3 hours
• C. 4 hours
• D. 6 hours

Answer and Explanation

Correct answer: B. 3 hours

Time equals distance divided by speed:

180 ÷ 60 = 3

The trip takes 3 hours.

Question 6: Fractions

A fuel tank holds 120 gallons when full. If it is 3/4 full, how many gallons are in the tank?

• A. 30
• B. 60
• C. 90
• D. 100

Answer and Explanation

Correct answer: C. 90

Find 3/4 of 120:

120 × 3/4 = 90

The tank contains 90 gallons.

Question 7: Percent of a Number

A warehouse has 240 parts. If 15% of the parts are used, how many parts are used?

• A. 24
• B. 30
• C. 36
• D. 48

Answer and Explanation

Correct answer: C. 36

Convert 15% to a decimal:

0.15 × 240 = 36

So 36 parts are used.

Question 8: Discount

A jacket costs $80. It is discounted by 25%. What is the sale price?

• A. $20
• B. $40
• C. $60
• D. $75

Answer and Explanation

Correct answer: C. $60

Find 25% of $80:

0.25 × 80 = 20

Subtract the discount:

80 - 20 = 60

The sale price is $60.

Question 9: Average

A recruit completes 42 push-ups on Monday, 48 on Wednesday and 60 on Friday. What is the average number of push-ups?

• A. 48
• B. 50
• C. 54
• D. 60

Answer and Explanation

Correct answer: B. 50

Add the values:

42 + 48 + 60 = 150

Divide by 3:

150 ÷ 3 = 50

Question 10: Ratio

A mixture contains 3 parts water and 2 parts cleaner. If the mixture has 15 total parts, how many parts are cleaner?

• A. 3
• B. 5
• C. 6
• D. 9

Answer and Explanation

Correct answer: C. 6

The ratio is 3:2, so there are 5 total ratio parts.

Cleaner is 2 of the 5 parts.

15 ÷ 5 = 3

2 × 3 = 6

There are 6 parts cleaner.

Question 11: Proportion

If 4 notebooks cost $12, how much do 10 notebooks cost at the same price per notebook?

• A. $24
• B. $30
• C. $36
• D. $40

Answer and Explanation

Correct answer: B. $30

First, find the cost per notebook:

12 ÷ 4 = 3

Then multiply by 10:

10 × 3 = 30

The cost is $30.

Question 12: Map Scale

A map uses a scale of 1 inch = 15 miles. If two locations are 4 inches apart on the map, how far apart are they?

• A. 19 miles
• B. 30 miles
• C. 45 miles
• D. 60 miles

Answer and Explanation

Correct answer: D. 60 miles

Each inch represents 15 miles.

4 × 15 = 60

The locations are 60 miles apart.

Question 13: Elapsed Time

A training session begins at 8:15 a.m. and ends at 10:45 a.m. How long is the session?

• A. 1 hour 30 minutes
• B. 2 hours
• C. 2 hours 30 minutes
• D. 3 hours

Answer and Explanation

Correct answer: C. 2 hours 30 minutes

From 8:15 to 10:15 is 2 hours.

From 10:15 to 10:45 is 30 minutes.

Total time: 2 hours 30 minutes.

Question 14: Unit Rate

A machine fills 300 bottles in 5 minutes. How many bottles does it fill per minute?

• A. 50
• B. 60
• C. 75
• D. 150

Answer and Explanation

Correct answer: B. 60

Divide bottles by minutes:

300 ÷ 5 = 60

The machine fills 60 bottles per minute.

Question 15: Remaining Quantity

A crate contains 150 items. If 38 items are removed, how many items remain?

• A. 102
• B. 112
• C. 118
• D. 122

Answer and Explanation

Correct answer: B. 112

Subtract removed items from the total:

150 - 38 = 112

Question 16: Multi-Step Word Problem

A unit orders 6 boxes of supplies. Each box contains 24 items. If 30 items are used on the first day, how many items remain?

• A. 94
• B. 104
• C. 114
• D. 124

Answer and Explanation

Correct answer: C. 114

First, find total items:

6 × 24 = 144

Then subtract items used:

144 - 30 = 114

Question 17: Percentage Increase

A score increases from 40 to 50. What is the percent increase?

• A. 10%
• B. 20%
• C. 25%
• D. 50%

Answer and Explanation

Correct answer: C. 25%

Find the increase:

50 - 40 = 10

Divide by the original value:

10 ÷ 40 = 0.25

Convert to percent:

0.25 = 25%

Question 18: Percentage Decrease

A price decreases from $120 to $90. What is the percent decrease?

• A. 20%
• B. 25%
• C. 30%
• D. 40%

Answer and Explanation

Correct answer: B. 25%

Find the decrease:

120 - 90 = 30

Divide by the original price:

30 ÷ 120 = 0.25

Convert to percent:

0.25 = 25%

Question 19: Fractions and Subtraction

A container is 5/6 full. After some liquid is removed, it is 1/2 full. What fraction of the container was removed?

• A. 1/6
• B. 1/3
• C. 1/2
• D. 2/3

Answer and Explanation

Correct answer: B. 1/3

Subtract:

5/6 - 1/2

Convert 1/2 to sixths:

1/2 = 3/6

5/6 - 3/6 = 2/6 = 1/3

Question 20: Work Rate

A team can load 18 crates in 3 hours. At the same rate, how many crates can the team load in 8 hours?

• A. 36
• B. 42
• C. 48
• D. 54

Answer and Explanation

Correct answer: C. 48

First, find crates per hour:

18 ÷ 3 = 6

Then multiply by 8:

6 × 8 = 48

Question 21: Comparing Costs

Store A sells 5 batteries for $15. Store B sells 8 batteries for $28. Which store has the lower price per battery?

• A. Store A
• B. Store B
• C. Both are the same
• D. Cannot be determined

Answer and Explanation

Correct answer: A. Store A

Store A:

15 ÷ 5 = $3 per battery

Store B:

28 ÷ 8 = $3.50 per battery

Store A is cheaper.

Question 22: Simple Equation Word Problem

A number increased by 12 equals 35. What is the number?

• A. 12
• B. 23
• C. 35
• D. 47

Answer and Explanation

Correct answer: B. 23

Let the number be x.

x + 12 = 35

x = 35 - 12 = 23

Question 23: Area

A rectangular training field is 40 yards long and 25 yards wide. What is its area?

• A. 65 square yards
• B. 130 square yards
• C. 1,000 square yards
• D. 1,250 square yards

Answer and Explanation

Correct answer: C. 1,000 square yards

Area equals length × width:

40 × 25 = 1,000

Question 24: Perimeter

A rectangular room is 12 feet long and 9 feet wide. What is its perimeter?

• A. 21 feet
• B. 36 feet
• C. 42 feet
• D. 108 feet

Answer and Explanation

Correct answer: C. 42 feet

Perimeter:

2(length + width) = 2(12 + 9) = 2(21) = 42

Question 25: Mixed Units

A rope is 6 yards long. How many feet long is the rope?

• A. 12 feet
• B. 18 feet
• C. 24 feet
• D. 36 feet

Answer and Explanation

Correct answer: B. 18 feet

1 yard = 3 feet.

6 × 3 = 18 feet

Question 26: Decimal Money Problem

A meal costs $8.75. If you buy 4 meals, what is the total cost?

• A. $26.25
• B. $30.00
• C. $35.00
• D. $37.50

Answer and Explanation

Correct answer: C. $35.00

Multiply:

8.75 × 4 = 35.00

Question 27: Fraction of a Group

There are 84 people in a group. If 2/7 of the group is assigned to maintenance, how many people are assigned to maintenance?

• A. 12
• B. 18
• C. 24
• D. 28

Answer and Explanation

Correct answer: C. 24

Find 2/7 of 84:

84 ÷ 7 = 12

12 × 2 = 24

Question 28: Rate Problem

A printer prints 45 pages in 3 minutes. At the same rate, how many pages will it print in 10 minutes?

• A. 120
• B. 135
• C. 150
• D. 180

Answer and Explanation

Correct answer: C. 150

First, find pages per minute:

45 ÷ 3 = 15

Then multiply by 10:

15 × 10 = 150

Question 29: Choosing the Correct Operation

A supply depot has 320 uniforms. It ships 75 uniforms to one location and 90 to another. How many uniforms remain?

• A. 145
• B. 155
• C. 165
• D. 175

Answer and Explanation

Correct answer: B. 155

First, add shipped uniforms:

75 + 90 = 165

Then subtract:

320 - 165 = 155

Question 30: Challenging Multi-Step Problem

A truck uses 8 gallons of fuel to travel 96 miles. How many gallons will it use to travel 240 miles at the same rate?

• A. 16
• B. 18
• C. 20
• D. 24

Answer and Explanation

Correct answer: C. 20

First, find miles per gallon:

96 ÷ 8 = 12 miles per gallon

Then divide total miles by miles per gallon:

240 ÷ 12 = 20

The truck will use 20 gallons.

Arithmetic Reasoning Practice Score Guide

Use your score as a diagnostic only.

| Score | What It May Suggest | Next Step | |—|—| | 0-10 correct | You need basic arithmetic review | Study fractions, percentages, rates and word problems | | 11-18 correct | You understand some topics but need more consistency | Review missed question types | | 19-25 correct | Strong starting point | Add timed AR drills | | 26-30 correct | Very strong start | Practice harder multi-step word problems |

This practice set cannot predict your official ASVAB Arithmetic Reasoning score.

How to Study for ASVAB Arithmetic Reasoning

Use this study plan:

1. Review basic operations.
2. Practice fractions and decimals.
3. Practice percentages.
4. Practice ratios and proportions.
5. Practice average problems.
6. Practice distance-rate-time problems.
7. Practice money problems.
8. Practice measurement conversions.
9. Practice multi-step word problems.
10. Review every explanation.

Arithmetic Reasoning improves fastest when you practice the same problem types repeatedly.

One-Week Arithmetic Reasoning Study Plan

Day	Study Focus
Day 1	Basic operations, fractions and decimals
Day 2	Percentages and discounts
Day 3	Ratios, proportions and scale problems
Day 4	Averages, rates and unit rates
Day 5	Distance, speed and time
Day 6	Multi-step word problems
Day 7	Timed mixed practice and review

If math is your weakest AFQT area, repeat the plan for a second week.

Common Arithmetic Reasoning Mistakes

Avoid these mistakes:

• calculating before understanding the question;
• using the wrong operation;
• ignoring units;
• confusing percent with decimal;
• forgetting to divide for averages;
• mixing up distance, rate and time;
• rounding too early;
• choosing an answer that is unreasonable;
• skipping multi-step problems;
• not reviewing explanations;
• practicing only untimed questions.

Many AR mistakes are reading mistakes, not math mistakes.

How to Improve Speed

To improve speed:

• memorize common percent conversions;
• memorize fraction-decimal equivalents;
• practice multiplication and division facts;
• estimate before calculating;
• write down key numbers;
• skip unnecessary wording;
• recognize common problem types;
• practice timed sets.

Speed should come after accuracy.

Common Percent Conversions

Memorize these:

Percent	Fraction	Decimal
10%	1/10	0.10
20%	1/5	0.20
25%	1/4	0.25
33⅓%	1/3	0.333…
50%	1/2	0.50
75%	3/4	0.75

These conversions can save time on the ASVAB.

Common Fraction and Decimal Conversions

Fraction	Decimal
1/2	0.5
1/3	0.333…
1/4	0.25
1/5	0.2
1/8	0.125
3/4	0.75

Use these to solve faster without a calculator.

CAT-ASVAB Strategy for Arithmetic Reasoning

On the CAT-ASVAB:

• each section is timed;
• you cannot go back after submitting an answer;
• the test is adaptive;
• pacing matters;
• random guessing near the end can hurt your score.

For AR:

• read carefully before calculating;
• eliminate obviously wrong answers;
• estimate before choosing;
• do not submit until you are confident enough to move on.

Paper ASVAB Strategy for Arithmetic Reasoning

On the paper ASVAB:

• you can usually review within the current section if time remains;
• there is no penalty for guessing;
• do not leave blanks;
• mark difficult questions and return if allowed;
• use estimation to eliminate wrong answers.

Follow the instructions given by the test administrator.

Free vs Paid ASVAB Arithmetic Reasoning Prep

Free practice is useful when you are starting.

It can help you:

• understand AR question types;
• identify weak math topics;
• practice word problems;
• build confidence;
• decide whether you need structured prep.

Paid prep may help if:

• your AFQT score needs improvement;
• math is your weakest area;
• your test date is close;
• you need timed drills;
• you want detailed explanations;
• you need a full ASVAB study plan.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, AFQT practice test can help you rehearse timed sections and build answer consistency.

ASVAB practice test can help candidates become familiar with common question formats before the live assessment.

When your hiring step includes mixed sections, pre-employment assessment practice can support broader review before test day.

Yes. AFQT practice test can offer practice materials for similar assessment formats.

ASVAB practice test can support extra practice with explanations when you want more timed drills.

For additional preparation, pre-employment assessment practice may be useful when your invitation includes similar question types.

Before test day, AFQT practice test can help you rehearse timed sections and build answer consistency.

ASVAB practice test can help candidates become familiar with common question formats before the live assessment.

Related ASVAB Guides

Use these related pages to continue preparing:

Guide	Best For
ASVAB Practice Test	Full ASVAB practice
AFQT Practice Test	AFQT-focused prep
ASVAB Score Chart	Score interpretation
ASVAB Word Knowledge	Vocabulary
ASVAB Paragraph Comprehension	Reading
Army ASVAB Practice Test	Army-focused prep
Air Force ASVAB Practice Test	Air Force-focused prep
Navy ASVAB Practice Test	Navy-focused prep

Sources / Information to Verify Before Publication

Before publication, verify all Arithmetic Reasoning details with official sources.

Use official sources such as:

• OfficialASVAB.com;
• ASVAB Fact Sheet;
• OfficialASVAB Arithmetic Reasoning page;
• Official ASVAB sample questions;
• ASVAB Career Exploration Program;
• Today’s Military;
• official CAT-ASVAB information;
• official ASVAB retest policy;
• MEPS / USMEPCOM resources;
• official branch recruiting pages.

For this topic, useful official materials may include:

• OfficialASVAB Arithmetic Reasoning;
• OfficialASVAB sample questions;
• ASVAB Fact Sheet;
• OfficialASVAB CAT-ASVAB page;
• OfficialASVAB retest policy;
• ASVAB Career Exploration Program AFQT explanation;
• Today’s Military ASVAB sample questions.

Verify:

• whether Arithmetic Reasoning counts toward AFQT;
• current CAT-ASVAB question count and timing;
• current paper ASVAB question count and timing;
• current AFQT formula explanation;
• score validity period;
• retest waiting periods;
• branch minimum AFQT requirements;
• calculator rules if stated by testing instructions;
• current JobTestPrep ASVAB product page;
• current affiliate offer;
• product price if mentioned.

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