ASVAB Arithmetic Reasoning (Math Word Problems) Practice Questions

By Rod Powers

Arithmetic Reasoning questions are math problems expressed in a story format. Your goal is to determine what the question is asking by picking out the relevant factors needed to solve the problem, set up mathematical equations as needed, and arrive at the correct solution. Sounds easy, right?

Sample questions

Try your hand at the following questions.

  1. If apples are on sale at 15 for $3, what’s the cost of each apple?
    • A. 50 cents
    • B. 25 cents
    • C. 20 cents
    • D. 30 cents
  2. A noncommissioned officer challenged her platoon of 11 enlisted women to beat her record of performing a 26-mile training run in 4 hours. If all the enlisted women match her record, how many miles will they have run?
    • A. 71.5 miles
    • B. 6.5 miles
    • C. 286 miles
    • D. 312 miles
  3. Diane gets her hair cut and colored at an expensive salon in town. She’s expected to leave a 15% tip for services. If a haircut is $45 and a color treatment is $150, how much of a tip should Diane leave?
    • A. $22.50
    • B. $29.25
    • C. $20.00
    • D. $224.25
  4. A bag of sand holds 1 cubic foot of sand. How many bags of sand are needed to fill a square sandbox measuring 5 feet long and 1 foot high?

    • A. 25 bags
    • B. 5 bags
    • C. 10 bags
    • D. 15 bags
  5. The day Samantha arrived at boot camp, the temperature reached a high of 90 degrees in the shade and a low of –20 degrees at night in the barracks. What was the average temperature for the day?

    • A. 35 degrees
    • B. 45 degrees
    • C. 55 degrees
    • D. 62 degrees

Answers and explanations

Use this answer key to score the Arithmetic Reasoning practice questions.

  1. C. Divide $3 by 15. The answer is $0.20, so the correct answer is Choice (C).
  2. C. Multiply 26 × 11. The other information in the question is irrelevant — it’s there to throw you off. The correct answer is Choice (C). You can immediately eliminate Choice (B) because it isn’t a reasonable answer. Identifying unreasonable answers (through the process of elimination) can help you choose the correct answer choice faster.
  3. B. Add 45 and 150 to get the cost of the services ($45 + $150 = $195); then multiply the answer by 0.15 (15%) to find the tip. The question asks for the amount of the tip, so the correct answer is Choice (B), $29.25. You can immediately eliminate Choice (D), because the amount is far too high to make sense.
  4. A. To find the volume of the sandbox, you take length times width times height (V=lwh). Don’t forget that the measurements are for a square sandbox, so you can assume that if the box is 5 feet long, then it’s also 5 feet wide. So 5 × 5 ×1 is 25 cubic feet. Each bag holds 1 cubic foot of sand, and 25 ÷ 1 = 25. Choice (A) is the correct answer. If you were thinking answer Choice (B) sounded good, remember that the answer should make sense. Five cubic feet of sand would not fill a very large sandbox, would it?
  5. A. Add the two temperatures: 90 + (–20) = 70). Divide 70 by 2 to reach the average temperature, 35. Choice (A) is the correct answer.