ASVAB Arithmetic Reasoning Practice Test 2020 Sample Questions Answers (PDF)

ASVAB Arithmetic Reasoning Practice Test 2020 Sample Questions Answers (PDF). Free download for Armed Services Vocational Aptitude Battery exam and Armed Forces Qualification Test (AFQT) exam preparation online.

Arithmetic Reasoning (AR) tests the ability to solve basic arithmetic problems one encounters in everyday life. One-step and multi-step word problems require addition, subtraction, multiplication, and division, and choosing the correct order of operations when more than one step is necessary. The items include operations with whole numbers, operations with rational numbers, ratio and proportion, in terest and percentage, and measurement. Arithmetic Reasoning is one factor that helps characterize mathematics comprehension and it also assesses logical thinking.

Actual Exam Content in AR Part

Test Type

Number of Question

ASVAB Paper-and-Pencil 30-items
CAT-ASVAB Test 16-items

ASVAB Arithmetic Reasoning Practice Test 2020

The following ASVAB Arithmetic Reasoning Practice Test is only for reference purpose, it’s not an actual exam test questions. You can download our free ASVAB Arithmetic Reasoning PracticeQuestion in PDF (printable and editable), this will help you to make better ASVAB Test Prep offline. You can also use these files (PDF, DOC) as worksheets.

Name of the Test ASVAB Practice Test | AFQT Practice Test
ASVAB Stands for Armed Services Vocational Aptitude Battery
AFQT Stands for Armed Forces Qualification Test
Test Type Sample Multiple Choice Test
Total Questions 30 (thirty)
Answers and Explanation Available
Printable and Editable PDF Available
Subject Name Arithmetic Reasoning (AR)
Purpose Measures ability to solve basic arithmetic word problems

Q1. Lisa went to the grocery store and bought a package of hot dogs for $3.54, a package of buns for $1.79, a container of mustard for $2.10, a jar of relish for $2.16, and a bag of charcoal for $5.15. What was her total bill?

  • A. $12.64
  • B. $14.74
  • C. $16.15
  • D. $16.74
View Correct Answer
 Answer: B

This is a simple addition problem. Add the amounts to get the total of $14.74.

Q2. Kim bought a blouse for $17.16, a skirt for $38.19, and a purse for $35.14. If she hands the clerk a $100 bill, what is her change?

  • A. $1.53
  • B. $9.51
  • C. $10.67
  • D. $14.15
View Correct Answer
 Answer: B

This problem has two steps. First, you need to add the amount spent. Then you need to subtract that amount from the $100 bill. The total amount spent is $90.49, so, subtracting that from $100, the change is $9.51. 

Q3. Cassidy answered 38 questions correctly on a test with 45 items. To the nearest percent, what percent did she answer correctly?

  • A. 72%
  • B. 78%
  • C. 84%
  • D. 89%
View Correct Answer
 Answer: C

. In order to calculate the percent, you need to divide the total number of items into the number answered correctly. In this case, you would divide 45 into 38 and get 0.8444. To change that to a percent, move the decimal point two places to the right and add the percent sign to get 84.44%. Since the question asks for the nearest percent, the answer would be 84%.

Q4.Susan’s test scores for Social Studies are 81, 76, 91, 73, and 79. What is her average score? 

  • A. 80
  • B. 87
  • C. 91
  • D. 93
View Correct Answer
 Answer: A 

To find the average, add up the numbers and divide by the number of numbers. In this problem, the numbers add to 400. Dividing that by 5
gives the correct result of 80 as the average.

Q5. A box of chocolates has 45 pieces. If 9 pieces have nuts in them, what percentage are without nuts?

  • A. 20%
  • B. 45%
  • C. 79%
  • D. 80%
View Correct Answer
 Answer: D

This problem needs to be completed in two steps. First, you need to determine what percent of chocolates have nuts, then you subtract that from 100% to determine what percent do not have nuts. So, dividing 9 by 45 results in the percent that have nuts, which is 20%. Subtracting that number from 100% gives the correct answer: 80% of the chocolates do not have nuts. 

Q6. In the Metro Bicycle Club, 6 of 48 members are females. What is the ratio of females to all club members?

  • A. 3/16
  • B. 1/15
  • C. 1/4
  • D. 1/8
View Correct Answer
 Answer: D

To find the ratio of one number to another, create a fraction to show the relationship. In this problem, there are 6 female club members out of a total of 48 members. So the fraction that shows the relationship is 6/48 . This fraction needs to be simplified to 1/8 , the correct answer. You might see a ratio written as 1:8 on the ASVAB test. 1/88and 1:8 mean the same thing. 

Q7. A teacher has assigned 192 pages of reading. If Vanessa starts reading on Monday and reads 48 pages each day, on what day will she complete the assignment?

  • A. Wednesday
  • B. Thursday
  • C. Friday
  • D. Saturday
View Correct Answer
 Answer: B

If Vanessa has 192 pages of reading and reads 48 pages each day, on Monday she has read 48 pages, on Tuesday she has read 2(48) or 96 pages, on Wednesday she has ready 3(48) or 144 pages, and on Thursday she has read 4(48) or 192 pages. Thursday is the correct answer. Another way to do this is to divide 192 by 48 to get 4. If Monday is 1, Tuesday is 2, Wednesday is 3, and Thursday is 4. Again, Thursday is the correct answer. 

Q8. Samuel is saving coins in a jar so that he can purchase a software program. He has saved 94 nickels, 44 quarters, and 112 dimes. If he reaches into the jar to pick one coin at random, what is the probability that he will pick a dime?

  • A. 1/2
  • B. 2/3
  • C.  56/125
  • D. 112/138
View Correct Answer
 Answer: C

Probability = number of favorable outcomes/number of possible outcomes. In this problem, a favorable outcome would be selecting a dime.
There are 112 dimes or favorable outcomes. The number of possible outcomes is the sum of all the coins, or 94 + 44 + 112 = 250. So
Probability = 112/250 Simplified, this is 56/125

Q9. Rene deposits $4,000 in a savings account that earns 4% simple interest per year. How much interest will she earn after 3 years?

  • A. $112
  • B. $350
  • C. $380
  • D. $480
View Correct Answer
 Answer: D

Simple interest problems use the formula I = prt, where I is the amount of interest, p is the principal or the amount saved or invested, r is the rate of interest, and t is the amount of time that the interest is accruing. In this problem, you are asked to find the interest, given that the principal is $4,000, the rate of interest is 4%, and the amount of time is 3 years. Substituting this information into the formula, you get

I = 4,000(0.04)(3) = $480 of interest

Q10. Leah flies 5,200 miles in 11 hours. What is the average speed of her airplane?

  • A. 472.73 miles/hour
  • B. 499.17 miles/hour
  • C. 512.33 miles/hour
  • D. 587.43 miles/hour
View Correct Answer
 Answer: A

Q11. The Kent High School Booster’s Club has 250 members. In 90 days it hopes to have a membership of 376 by initiating a Web-based membership campaign. On average, how many new members does it need to sign up each day to reach that goal?

  • A. 1
  • B. 1.4
  • C. 1.5
  • D. 2.2
View Correct Answer
 Answer: B

The Booster’s Club has 250 members and wants to reach 376 members in 90 days. Subtracting 250 from 376, the club needs to attract 126 new members. To do this in 90 days, the club must attract 126 ÷ 90 = an average of 1.4 members each day

Q12. Max has a rectangular garden that is 3 feet by 7 feet. If he needs 2 ounces of fertilizer per square foot for the garden to flourish, how many ounces must he use?

  • A. 21 oz
  • B. 42 oz
  • C. 44 oz
  • D. 56 oz
View Correct Answer
 Answer: B

Here you need to calculate the number of square feet in the garden and then determine how many ounces of fertilizer are needed. The area of
a rectangular garden is calculated by multiplying the length × the width. So in this problem, the area is 21 ft². If you need 2 oz of fertilizer for
every square foot, then you need to multiply 2 by the number of square feet. 21 × 2 = 42 oz 

Q13. The local electronics store is holding a 20%-off sale on all its products. Marla selects 2 CDs at the original price of $16.99 each. What is the price of the two CDs after the 20% discount?

  • A. $15.99
  • B. $22.50
  • C. $25.78
  • D. $27.18
View Correct Answer
 Answer: D

Calculate the cost of the two CDs:
$16.99 × 2 = $33.98
Reduce that amount by 20% by multiplying the
total cost by 0.20:
0.20 × 33.98 = $6.80
Subtract $6.80 from the original cost:
$33.98 – $6.80 =  $27.18 

Q14. The Berkeley Department Store is running a special back-to-school sale on shoes in September. A pair of shoes costs $67.50. In October the price increases to $87.75. What percent increase is the price in October?

  • A. 15%
  • B. 20%
  • C. 24%
  • D. 30%
View Correct Answer
 Answer: D

Use the following formula: Percent of change = (amount of change / starting point) 

Q15. Two numbers together add to 300. One number is twice the size of the other. What are the two numbers?

  • A. 25; 50
  • B. 50; 100
  • C. 75; 150
  • D. 100; 200
View Correct Answer
 Answer: D

Set this up as an equation. A number plus 2
times that number is 300.
x + 2x = 300

Solve for x.
3x = 300
x = 100
So one number is 100 and the other is twice that, or 200. 

Q16. Hugo is making a picture frame for a photo of his family. The photo is 8 inches by 10 inches. If the wood for the frame costs 50 cents an inch, how much will the wood for the frame cost?
A. $9.00
B. $12.00
C. $15.00
D. $18.00

View Correct Answer
 Answer: D

To answer this question, you need to know the perimeter of the frame. For a rectangle, the perimeter is 2l + 2w. If w = 8 and l = 10, then
the perimeter = 2(8) 2(10) = 36 inches. At $0.50 per inch, multiply 36 × $0.50 to get the price of the wood. 36 × $0.50 = $18.00  /su_spoiler]

Q17. The distance across the circular mouth of a volcano running through its center is 75 yards. What is the distance around its mouth?

  • A. 145.5 yd
  • B. 215.5 yd
  • C. 235.5 yd
  • D. 315.5 yd
View Correct Answer
 Answer: C

. To find the circumference of a circle, use the formula C = 2r. In this problem, you are given the diameter. You need to use the radius, which is ½ d, or 37.5 yards. Substitute the information into the formula.

C= 2Π(37.5)
C= 2(3.14)(37.5) = 235.5 yd
Note that you can skip a step if you remember the formula C = Πd. Substitute the information you have. C = Π(75) = 235.5 yd

Q18. Sue spent one-third of her life in Kansas. If Sue is 39, how many years did she spend in Kansas?

  • A. 9
  • B. 12
  • C. 13
  • D. 15
View Correct Answer
 Answer: C

In this problem, you need to find 1/3 of 39. Dividing 39 by 3 gives you 13.

Q19. Brian shoots hoops with Dave, who is two years younger than Brian. If Brian is 17, how old is Dave?

  • A. 15
  • B. 17
  • C. 19
  • D. 21
View Correct Answer
 Answer: A

Create an equation to solve this problem.
Dave = Brian – 2.
You are told that Brian is 17. Substitute that information into the formula.
Dave = 17 – 2
Dave = 15 

Q20. Al has three times as much money as Bill. Bill has two times as much money as Charlie. If Charlie has $5.89, how much money does Al have?

  • A. $11.78
  • B. $19.79
  • C. $29.24
  • D. $35.34
View Correct Answer
 Answer: D

Create equations to solve this problem.
Al = 3(Bill)
Bill = 2(Charlie)
Charlie = $5.89
Solve for Al. Substitute what you know into the formulas.
Bill = 2($5.89)
Bill = $11.78
To find Al, substitute what you know about Bill.
Al = 3($11.78)
Al = $35.34

Q21. The car owned by Marisa gets an average of 16 miles per gallon of gas on the highway. If she recently took a trip of 1,344 miles, how many gallons of gas did she use?

  • A. 34 gallons
  • B. 57 gallons
  • C. 78 gallons
  • D. 84 gallons
View Correct Answer
 Answer: D

In this problem, you need to calculate the number of 16-mpg units there are in 1,344. Do this
by dividing 1,344 by 16.
1,344 ÷ 16 = 84 gallons 

Q22. A rectangular swimming pool is 6 feet deep, 28 feet long, and 12 feet wide. What is the volume of the pool?

  • A. 1,655 ft³
  • B. 1,799 ft³
  • C. 2,016 ft³
  • D. 2,546 ft³
View Correct Answer
 Answer: C

To solve this problem, use the formula V = Iwh. You have been given the dimensions of l = 28 ft, w = 12 ft, and h = 6 ft. Substitute that
information into the formula. V = (28)(12)(6), V = 2016 ft³ 

Q23. Josh wants to put a fence around his rectangular garden. The garden is 6 feet by 15 feet. How much fencing must he purchase?

  • A. 30 feet
  • B. 35 feet
  • C. 42 feet
  •  D. 47 feet
View Correct Answer
 Answer: C

You need to calculate the perimeter of the garden. The perimeter is the sum of all the sides, or use the formula P = 2l + 2w. You are given the
dimensions of 6 feet and 15 feet. Substitute that information into the formula.

P = 2(6) +  2(15)
P = 42 ft

Q24.In a recent election, Joe received 32% of the votes, Samantha received 14% of the votes, Sally received 42% of the votes, and Cal received 12% of the votes. If 5,000 votes were cast, how many votes did Samantha receive?

  • A. 300
  • B. 450
  • C. 535
  • D. 700
View Correct Answer
 Answer: D

To calculate 14% of 5,000, multiply 5,000 by 0.14.
5,000(0.14) = 700 votes 

Q25. A circular pool is 3.5 meters deep and has a radius of 9 meters. What is the volume?

  • A. 450.2 m³
  • B. 575.9 m³
  • C. 890.2 m³
  • D. 974.4 m³
View Correct Answer
 Answer: C

To calculate the volume of a cylinder, use the formula V = r²h. In this problem, the radius is 9 m. The height is given as 3.5 m. Substitute that information into the formula.

V = (3.14)(9²)(3.5)
V = (3.14)(81)(3.5)
V = 890.19 or 890.2 m³ 

Q26. The diameter of a planet is 8,000 miles. What is its circumference?

  • A. 19,412 miles
  • B. 20,889 miles
  • C. 25,120 miles
  • D. 28,475 miles
View Correct Answer
 Answer: C

Use the formula C = 2r or C = d. You are given a diameter of 8,000 miles. Substitute that into the formula.
C = (8,000)
C = 3.14(8,000)
C = 25,120 mi 

Q27. Will has $4,355.19 in his checking account. He writes checks for $1,204.90 and $890.99. How much is left in Will’s account?

  • A. $1,189.65
  • B. $2,259.30
  • C. $2,867.30
  • D. $2,989.50
View Correct Answer
 Answer: B

To calculate the answer to this question, add up the amount of the checks and subtract that from the current amount in the checking account.
$4,355.19 – ($1,204.90 + $890.99) = $2,259.30

Q28. A club collected $585.00. If 75% of that came from membership dues, how much money came from the dues?

  • A. $413.15
  • B. $438.75
  • C. $465.75
  • D. $525.05
View Correct Answer
 Answer: B

Multiply $585.00 by 0.75 to get $438.75.

Q29. Danny buys a computer originally priced at $750.00, software programs originally priced at $398.75, a printer originally priced at $149.98, and a case of paper originally priced at $24.99. All items are on sale for 20% off. How much will Danny save because of the sale?

  • A. $124.94
  • B. $196.74
  • C. $236.24
  • D. $264.74
View Correct Answer
 Answer: D

Calculate the total cost of the items and then multiply by 20% to determine how much Danny will save.
$750 + $398.75 + $149.98 + $24.99 = $1,323.72
$1,323.72 × 0.20 = $264.74 savings from the sale 

Q30. A ladder is placed against a building. If the ladder makes a 55° angle with the ground, what is the measure of the angle that the ladder makes with the building?

  • A. 35°
  • B. 40°
  • C. 55°
  • D. 90°
View Correct Answer
 Answer: A

In this problem, you know two of the three angles, one measuring 55° and the other measuring 90°. Together those two angles measure 145°. Since a triangle has a total of 180°, the third angle must measure 180° 145° 35°

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