The trick with Arithmetic Reasoning is reading slowly and setting up carefully, then doing the arithmetic fast. Try each problem yourself first - pick an answer - and only then open the solution. That's how practice actually moves your score.
Q1Ratios
- A. 20
- B. 40
- C. 44
- D. 180
Show the solution
A ratio splits the total into "parts." Add the ratio numbers to find how many parts there are in total:
2 + 9 = 11 parts
Now find how many people are in one part by dividing the total by the number of parts:
220 ÷ 11 = 20 people per part
Officers are 2 parts, so:
2 × 20 = 40 officers
Answer: B. 40
Common trap: choice A (20) is the value of one part, not the officer count. The test loves to offer the number you'd get if you stopped one step early.
Q2Rate and time
- A. 32 minutes
- B. 36 minutes
- C. 40 minutes
- D. 45 minutes
Show the solution
"Steady pace" means you can find the time for one mile, then scale up. Find the per-mile time:
24 ÷ 3 = 8 minutes per mile
Multiply by the new distance:
5 × 8 = 40 minutes
Answer: C. 40 minutes
Almost every rate problem on the ASVAB is solved this way: get the "per one" value first, then multiply.
Q3Percent
- A. 80%
- B. 82%
- C. 85%
- D. 88%
Show the solution
Percent means "out of 100." Divide the part by the whole, then multiply by 100:
68 ÷ 80 = 0.85
0.85 × 100 = 85%
Answer: C. 85%
If division feels slow, estimate first: 68 out of 80 is clearly more than 80% and less than 90%, which already rules out two answers.
Q4Unit cost
- A. $144.00
- B. $152.00
- C. $162.00
- D. $171.00
Show the solution
Total cost is the price per item times the number of items:
36 × $4.50
Break it apart to do it in your head: 36 × 4 = 144, and 36 × 0.50 = 18. Add them:
144 + 18 = $162.00
Answer: C. $162.00
Splitting a price into a whole-dollar part and a cents part is faster and less error-prone than long multiplication under time pressure.
Q5Two-step word problem
- A. 8 gallons
- B. 12 gallons
- C. 16 gallons
- D. 24 gallons
Show the solution
First find how many 15-mile segments are in the trip:
120 ÷ 15 = 8 segments
Each segment burns 2 gallons, so multiply:
8 × 2 = 16 gallons
Answer: C. 16 gallons
Two-step problems are where most points are lost - not because the math is hard, but because people answer after the first step (choice A, 8) and move on.
The pattern behind every one of these
Notice what all five had in common: the hard part was never the arithmetic. It was reading the problem, deciding what to calculate, and not stopping a step early. That's exactly the skill the ASVAB rewards - and the only way to build it is reps on questions written the way the real test writes them.
Ready for a full-length practice set?
These five are a taste. Our downloadable ASVAB practice pack gives you a full timed exam with worked explanations for every question - start with the free sample, then grab the complete pack when you're ready.
Want the complete set? The full ASVAB practice tests covering all nine subtests are on Udemy with 300 practice questions and visuals.