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ASVAB Practice Test · Arithmetic Reasoning

ASVAB Practice Test: Arithmetic Word Problems Concepts

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Overview

This chapter is about turning a short story into a math problem and solving it. The math itself is usually simple, such as adding, multiplying, or finding a percent. The hard part is reading carefully, picking out the numbers you need, and choosing the right formula.

Many problems use a few standard formulas. Distance equals rate times time. An average is the total divided by the number of items. Simple interest equals principal times rate times time. A percent means a number out of 100, so 25 percent is 0.25.

Ratio and proportion problems compare two amounts. If 3 cans cost 6 dollars, you can set up 3 over 6 equals 5 over x and cross-multiply to find the cost of 5 cans. For percent change, divide the amount of change by the original amount, not by the new amount.

A good habit is to write down what the question asks before you start. Watch the units, such as minutes versus hours or inches versus feet, and change them so they match. After you get an answer, check that it makes sense in the story.

Key concepts

  • Distance, rate, time

    Distance = rate x time. If you know two of the three, you can find the third: rate = distance / time, and time = distance / rate.

    Memory tipDriving 50 miles per hour for 3 hours covers 150 miles.

  • Average (mean)

    Add all the values, then divide by how many values there are.

    Memory tipAverage x count = total.

  • Percent

    A percent is a part out of 100. To find a percent of a number, change the percent to a decimal and multiply. For example, 20% of 50 = 0.20 x 50 = 10.

    Memory tipMove the decimal point two places left.

  • Percent change

    Percent change = (new amount - original amount) / original amount x 100. A rise from 40 to 50 is a change of 10, and 10 / 40 = 25%.

    Memory tipAlways divide by the starting amount.

  • Simple interest

    Interest = principal x rate x time (I = P x R x T). The rate is per year, so time must be in years.

    Memory tipSix months is 0.5 year.

  • Ratio and proportion

    A ratio compares two amounts, such as 2 to 3. A proportion says two ratios are equal. Cross-multiply to find the missing number.

    Memory tipKeep the same units on top and bottom.

Often tested

  • Distance = rate x time.
  • Average = total / number of items.
  • Percent change divides by the original amount.
  • Change units so they match before you calculate.
  • Check that your answer makes sense in the story.

3 sample questions

Verified practice questions from this unit.

Practice questionReviewedArithmetic Reasoning › Arithmetic Word Problems★★★★★

Question 1. A warehouse worker earns $18 per hour. How much does the worker earn for a 40-hour week?

  1. ① $760
  2. ② $720
  3. ③ $58
  4. ④ $680
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Answer: ② $720

Key point: Pay = hourly rate x hours

  1. Multiply the hourly pay by the hours worked.
  2. $18 x 40 = $720.

Check: $720 divided by 40 hours = $18 per hour.

Wrong choices

  • (A) $760: $760 is 40 hours at $19, not $18.
  • (C) $58: $58 comes from adding 18 and 40 instead of multiplying.
  • (D) $680: $680 is 40 hours at $17, not $18.
Practice questionReviewedArithmetic Reasoning › Arithmetic Word Problems★★★★★

Question 2. A truck drives at a steady 55 miles per hour for 4 hours. How far does it travel?

  1. ① 230 miles
  2. ② 220 miles
  3. ③ 59 miles
  4. ④ 200 miles
▼ Show answer and explanation▲ Hide answer and explanation

Answer: ② 220 miles

Key point: Distance = rate x time

  1. Distance = speed x time.
  2. 55 x 4 = 220 miles.

Check: 220 miles / 4 hours = 55 miles per hour.

Wrong choices

  • (A) 230 miles: 230 miles is 10 miles too many; 55 x 4 is 220.
  • (C) 59 miles: 59 comes from adding 55 and 4.
  • (D) 200 miles: 200 miles would be 50 miles per hour for 4 hours.
Practice questionReviewedArithmetic Reasoning › Arithmetic Word Problems★★★★★

Question 3. On four safety quizzes, a worker scored 82, 90, 76, and 88. What is the worker's average score?

  1. ① 86
  2. ② 84
  3. ③ 85
  4. ④ 82
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Answer: ② 84

Key point: Average = total / number of items

  1. Add the scores: 82 + 90 + 76 + 88 = 336.
  2. Divide by the number of quizzes: 336 / 4 = 84.

Check: 84 x 4 = 336.

Wrong choices

  • (A) 86: 86 is the middle of 82 and 90 only, ignoring the other scores.
  • (C) 85: 85 is not the average; 85 x 4 = 340, not 336.
  • (D) 82: 82 is just the first score, not the average.
Practice 5 questions from this unit →