ASVAB Arithmetic Reasoning Practice Questions
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Arithmetic Reasoning is one of the four AFQT sections, so it counts twice over: toward whether you can enlist, and toward several line scores. It is word problems, no calculator, and the numbers are deliberately awkward so you cannot do them by pattern.
Practice questions
A tire rotates 552 times in one minute. How many times does it rotate in half an hour?
- A16,560
- B3,312
- C27,600
- D33,120
Explanation
Half an hour is 30 minutes, so multiply: 552 × 30. Break it up — 552 × 3 = 1,656, then add the zero for the ten: 16,560. A sanity check helps here, since 552 × 30 must be a bit over 500 × 30 = 15,000.
A motorcycle costs $7,250 and loses 12 percent of its value in the first year. What is it worth after one year?
- A$6,380
- B$6,470
- C$6,820
- D$7,130
Explanation
Ten percent of 7,250 is 725, and two percent is 145. Together that is 870 of value lost. 7,250 − 870 = 6,380. Splitting a percentage into ten percent plus the remainder is the fastest way to do these by hand.
A pump moves 20 gallons in 5 seconds. At the same rate, how many gallons does it move in 7 seconds?
- A25
- B28
- C30
- D35
Explanation
First find the rate: 20 ÷ 5 = 4 gallons per second. Then 4 × 7 = 28. Rate problems are almost always two steps like this, and the mistake people make is trying to do it in one.
One in every 9 people in a town of 810 volunteers with the fire service. How many volunteers are there?
- A81
- B90
- C99
- D72
Explanation
810 ÷ 9 = 90. Watch the wording: 'one in every nine' is a division, not a subtraction. Reading it as 'nine out of 810' would give you a completely different number.
Two crews clear a road. The first clears 3 miles per hour, the second 2 miles per hour. Working from opposite ends of a 20 mile road, how long until they meet?
- A3 hours
- B4 hours
- C5 hours
- D6 hours
Explanation
Working toward each other their rates add: 3 + 2 = 5 miles per hour combined. Then 20 ÷ 5 = 4 hours. The trick with combined work problems is recognising that you add the rates, never the times.
Estimate before you calculate
Look at the four options first. Often two are obviously too large or too small, and a rough estimate rules them out in seconds. On a section that gives you well under a minute a question, that is the difference between finishing and not.