ASVABStudy Topic
ASVAB Arithmetic Reasoning Foundations Study Guide
Practice rates, work, mixtures, proportions, fractions, percentages, measurement, and multi-step word problems.
Topic Overview
Translate the story into units
Identify what is given and what is requested before choosing an operation. Distance divided by time produces speed; distance divided by miles per gallon produces gallons. For a mixture, keep the amount of concentrate separate from total volume. Adding water changes the denominator of the concentration fraction without changing the amount of concentrate.
Combine rates instead of times
If one pump fills a tank in six hours, its rate is one-sixth of a tank per hour. A three-hour pump fills one-third per hour. Together they fill one-half per hour and require two hours for one tank, assuming the rates stay constant. Similar care is needed for average speed: add segment distances and times separately, then divide the totals.
Check practical constraints
A mathematical quotient may not be the requested count. Cutting 2.5-foot pieces from 19 feet gives 7.6 mathematically, but only seven complete pieces fit. Sequential percentages apply to the current amount at each step. A 20% increase followed by a 20% decrease takes 100 to 120 to 96. Estimate before calculation, keep units throughout, and check whether rounding or whole-number constraints change the final selection.
- Adding completion times instead of rates in combined-work problems.
- Averaging speeds without computing total time.
- Ignoring the difference between complete pieces and a fractional quotient.
- Assuming equal percentage increases and decreases cancel.
Checkpoint Quiz
Test your understanding of ASVAB Arithmetic Reasoning Foundations
These questions are for study practice only and are not official exam questions.
1. A truck travels 210 miles in 3.5 hours at a constant speed. What is its speed?
2. A vehicle uses 8 gallons for 224 miles. How many gallons are needed for 350 miles at the same rate?
3. A worker must arrive at 8:15 a.m. The trip takes 45 minutes. What is the latest departure time if no extra time is allowed?
4. A vehicle travels 120 miles at 40 mph and 120 miles at 60 mph. What is its average speed for the complete trip?
5. A $240 tool is discounted by 15%. What is the sale price before tax?
6. A tank fills at 7 gallons per minute. If it already contains 18 gallons, how much will it contain after 6 more minutes, assuming no overflow or loss?
7. A crew completes 3/5 of a job on Monday and 1/4 on Tuesday. What fraction of the job remains?
8. A rope is cut into pieces 2.5 feet long. How many complete pieces can be cut from 19 feet, ignoring cutting loss?
9. A team needs 18 workers for a job. If 2/3 of the positions are filled, how many more workers are needed?
10. A scale drawing shows a 12-foot wall as 3 inches long. How long should a 20-foot wall be in the drawing at the same scale?
Frequently asked questions
How do I solve a combined-work problem?
Express each worker or machine as a fraction of the job per time unit, add rates, then find the time for one job.
What stays constant when water is added to a mixture?
The amount of the original concentrate stays constant if none is removed or reacts, while total volume increases.
When should I round down?
When the question asks for complete items that must fit within a fixed resource, a leftover fraction cannot form another complete item.
How do I avoid unit errors?
Write units beside quantities and check that the operations leave the units requested by the question.
