ASVAB Practice: Arithmetic Reasoning Sample Questions

By Rod Powers

You should practice before taking the ASVAB. You can start with practice exams and questions to see where you stand. The following questions give you a good idea of what to expect.

Sample questions

Arithmetic Reasoning

Time: 36 minutes for 30 questions

Directions: Arithmetic Reasoning is the second subtest of the ASVAB. These questions are designed to test your ability to use mathematics to solve various problems that may be found in real life — in other words, math word problems.

  1. Delia has been walking at a constant speed of 2.5 miles per hour for 12 minutes. How many miles has she walked?

    • (A)0.2 miles

    • (B)0.5 miles

    • (C)2 miles

    • (D)4.8 miles

  2. A rectangular deck is 6 meters long and 8 meters wide. What is the distance from one corner of the deck to the opposite corner?

    [Credit: Illustration by Thomson Digital]

    Credit: Illustration by Thomson Digital
    • (A)10 m

    • (B)12 m

    • (C)14 m

    • (D)15 m

  3. Tom is going to hang three framed pictures side by side on a wall. How many different ways can he arrange the pictures?

    • (A)9

    • (B)5

    • (C)6

    • (D)27

  4. A cleaning company charges by the square foot. The company charged $600 to clean 4,800 square feet of space. How much would the company charge to clean 12,000 square feet of space?

    • (A)$950

    • (B)$1,200

    • (C)$1,400

    • (D)$1,500

  5. Kendra earns $12 an hour. Her employer pays 1.5 times her normal pay rate for overtime. Last week, she worked 40 hours plus 4 hours overtime. How much did she earn last week?

    • (A)$552

    • (B)$528

    • (C)$1,400

    • (D)$480

  6. A hot tub is 75 percent full with 600 gallons of water. How many gallons of water are in the hot tub when it’s half full?

    • (A)200 gallons

    • (B)400 gallons

    • (C)800 gallons

    • (D)300 gallons

  7. Angela has 15 quarters and dimes in the cash register. The total value of the quarters and dimes is $2.55. How many dimes are in the cash register?

    • (A)8 dimes

    • (B)7 dimes

    • (C)3 dimes

    • (D)10 dimes

  8. A rectangular table top measures 48 inches long by 36 inches wide. A square game board that is 18 inches on each side is on the table top. Which amount of the table top’s area is not covered by the game board?

    • (A)1,710 in2

    • (B)1,404 in2

    • (C)1,656 in2

    • (D)96 in2

  9. A map of Texas has a scale of 1 cm = 11 km. The actual distance between Dallas and San Antonio is about 440 km. How far apart are the cities on the map?

    • (A)11 cm

    • (B)44 cm

    • (C)40 cm

    • (D)22 cm

  10. Jake is four years older than Kenneth. Alicia is two years younger than Kenneth. The sum of Jake, Kenneth, and Alicia’s ages is 38. What is Kenneth’s age?

    • (A)9

    • (B)15

    • (C)12

    • (D)10

Answers and explanations

  1. B. 0.5 miles

    Convert the minutes to hours by dividing 12 by 60: 12 ÷ 60 = 0.2 hours. Use the distance formula, d = rt, to find the distance in miles that she walked: d = 2.5(0.2) = 0.5 miles.

  2. A. 10 m

    Use the Pythagorean theorem, a2 + b2 = c2:


    Length is always positive.

  3. C. 6

    For the first picture to be hung on the wall, there are three choices. After he hangs the first picture, there are two choices left for the second picture, and then one choice left for the last picture. Multiply to find the number of different ways he can arrange the three pictures: (3)(2)(1) = 6 ways.

  4. D. $1,500

    First, determine how much it charges per square foot. Divide $600 by 4,800 to find that out: $600 ÷4,800 = $0.125 per square foot. You want the company to clean 12,000 square feet, so multiply that number by the per-square-foot rate: 12,000 × $0.125 = $1,500.

  5. A. $552

    Kendra earned $12(40) = $480 for the 40 hours she worked. Her overtime pay rate is 1.5($12) = $18 per hour. She earned an additional $18(4) = $72 in overtime pay. Her total pay last week was $480 + $72 = $552.

  6. B. 400 gallons

    Seventy-five percent of the total amount of water the tub will hold, x, is equal to 600 gallons. You can represent this fact with the equation 0.75x = 600.


    The full hot tub holds 800 gallons of water. Half of 800 gallons is 400 gallons.

  7. A. 8 dimes

    The value of the quarters is 25q, and the value of the dimes is 10d. So the value of dimes and quarters is 25q + 10d = 255.

    You also know that the total number of coins is 15, so q + d = 15. You can rearrange this equation to isolate q: q = 15 – d. Now you can substitute that for the q in the first equation and solve for d:


  8. B. 1,404 in2

    Use the formula for a rectangle, a = lw, to find the area of the table top: a = 48(36) = 1,728 in2. The formula for the area of a square is a = s2, where s is the length of one side. Use it to find the area of the game board: a = 182 = 324 in2.

    Then you can find the amount of area not covered by the game board by subtracting the area of the game board from the area of the table top: 1,728 in2 – 324 in2 = 1,404 in2.

  9. C. 40 cm

    Let x represent the distance between the cities on the map:


  10. C. 12

    Let x represent Kenneth’s age. You can then write Jake’s age as x + 4 and Alicia’s age as x – 2. The sum of their ages is 38. Write and solve an equation to find x: