ASVAB Arithmetic Reasoning: How to Solve Word Problems

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Translate the question before calculating

ASVAB Arithmetic Reasoning word problems become easier when you separate the story from the mathematical relationship. Begin by naming the unknown and its unit. Then identify the quantities that determine it, write an equation, calculate, and check whether the result answers the actual question. Finding a number is only half the job; finding the right quantity is the other half.

Use five steps on scratch paper: target, facts, relationship, calculation, check. For “How long will the trip take?” the target is time, not distance or speed. A fuel capacity mentioned in the same story might be irrelevant. Crossing out information you do not need can be more useful than underlining every number.

The examples below are original teaching problems. They show different relationships so you can practice choosing a method rather than memorizing a particular answer. Review the Arithmetic Reasoning subject guide if you need a map of the broader topic.

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Rates: keep the units attached

A truck travels 168 miles in 3 hours. Its average speed is distance divided by time: 168 ÷ 3 = 56 miles per hour. If it continues at that average speed for another 2 hours, the additional distance is 56 × 2 = 112 miles. Notice that the second question asks for additional distance, not total distance.

Now change the problem: a vehicle travels at 48 miles per hour for 45 minutes. Convert the time to hours before multiplying: 45/60 = 3/4 hour. Distance = 48 × 3/4 = 36 miles. Multiplying 48 by 45 without converting the units creates a result that does not describe miles.

Keep a short unit label beside each value. Miles per hour multiplied by hours produces miles. Miles divided by miles per hour produces hours. This check often reveals a reversed division before you finish the calculation.

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Ratios: count parts before people or objects

A supply box contains red and blue markers in a ratio of 2:3. There are 35 markers altogether. The ratio contains five total parts, so one part is 35 ÷ 5 = 7 markers. Red markers occupy two parts: 2 × 7 = 14. Blue markers occupy three parts: 3 × 7 = 21. The counts add back to 35 and retain the original ratio.

A common mistake is treating 2:3 as “two out of three.” It actually means two red for every three blue, or two red out of five total. Ask whether the question gives a part-to-part ratio or a part-to-whole fraction before you set up your calculation.

If the question instead supplies 18 blue markers, three parts equal 18, so each part is six and there are 12 red markers. The same relationship works even when the total is not given.

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Averages and combined work

Four practice sessions lasted 20, 25, 30, and 45 minutes. The mean is their total divided by their count: 120 ÷ 4 = 30 minutes. To average 32 minutes across five sessions, the total must be 5 × 32 = 160 minutes. The fifth session therefore needs to last 160 − 120 = 40 minutes. Work backward from the required total when an average includes an unknown value.

For work problems, add rates rather than completion times. Suppose one pump fills a tank in 6 hours and another fills the same tank in 3 hours. Their rates are 1/6 and 1/3 tank per hour. Together they fill 1/2 tank per hour, so one tank takes 2 hours, assuming constant rates and simultaneous operation. Adding 6 + 3 would not describe the combined process.

The reasonableness check matters: two working pumps should finish sooner than either pump alone. An answer greater than 3 hours signals a setup problem in this example.

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Practice recognizing the relationship

Build a small review sheet with one solved example each for rates, ratios, percentages, averages, and combined work. On your next session, cover the calculations and identify the relationship first. If you cannot name it, reread the target rather than immediately trying random operations.

After solving, explain why each number belongs in the equation. “I divided because it was a division question” is not enough; “I divided miles by hours to get miles per hour” demonstrates the relationship. When you miss an item, label the error as translation, units, arithmetic, or reading. That diagnosis determines what to practice next.