ASVAB · AFQT
Arithmetic Reasoning
Arithmetic Reasoning is the ASVAB subtest in which you solve arithmetic word problems and pick the answer among four.
- Items
- 15
- Time
- 55 minutes
- Format
- Computer-adaptive
- Answer options
- 4
- Calculator
- Not allowed
- Counts toward
- AFQT
Screens of the trainer
The subtest
Measures
The subtest measures your ability to solve arithmetic word problems.
Its score counts toward the AFQT, with Word Knowledge, Paragraph Comprehension and Mathematics Knowledge. The AFQT decides eligibility to enlist.
Format
The subtest is computer-adaptive: each item is chosen from your earlier answers, and an answer cannot be changed once submitted.
The 15 items run in 55 minutes, the longest time limit of the ASVAB. Each item offers four answer options, and no calculator is allowed.
On paper, the subtest has 30 items in 36 minutes.
Scoring
The subtest is reported as a standard score. The items are scaled for difficulty, so the score is comparable between test-takers who saw different items.
That standard score is combined with the three other AFQT subtests into the AFQT, a percentile from 1 to 99.
Item types
Word problems
Each item is a short word problem in plain text with four numbers as choices. The problems are one-step and multi-step, and a multi-step problem asks you to choose which operations to do and in what order before you compute.
They deal with whole numbers and fractions, ratio and proportion, interest and percentages, and measurement.
Free practice test
Item 1 of 5
A parking lot has 240 spaces, and 75% of them are filled. How many spaces are filled?
Show the answer
Answer: 180
75% of the 240 spaces is 240 × 0.75 = 180 spaces.
Item 2 of 5
A crate holds 12 packages that each weigh 8 ounces. How many pounds does the crate of packages weigh?
Show the answer
Answer: 6
Total ounces: 12 × 8 = 96 ounces, then convert to pounds: 96 ÷ 16 = 6 pounds.
Item 3 of 5
A truck travels for 2 hours at 50 mph, then for 3 hours at 40 mph. What is the total distance covered, in miles?
Show the answer
Answer: 220
The first leg covers 50 × 2 = 100 miles and the second leg covers 40 × 3 = 120 miles. Total distance = 100 + 120 = 220 miles.
Item 4 of 5
A student needs an average of 85 across 4 quizzes. The first three quizzes scored 80, 88, and 90. What is the minimum score needed on the fourth quiz to reach that average?
Show the answer
Answer: 82
Total needed: 85 × 4 = 340. The three known quizzes sum to 80 + 88 + 90 = 258, so the fourth needs 340 − 258 = 82.
Item 5 of 5
Two painters start a wall together. Painter A alone would need 10 hours and Painter B alone would need 15 hours, but after 3 hours Painter B is called away and Painter A finishes the wall alone. How many hours does the wall take from start to finish?
Show the answer
Answer: 8
Combined rate = 1/10 + 1/15 = 1/6 of the wall per hour, so in 3 hours the pair finishes 1/2 of the wall.
Painter A alone needs (1/2) ÷ (1/10) = 5 hours for the rest, for a total of 3 + 5 = 8 hours.
The Frontline Forge trainer
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Feedback after each answer
Training mode shows the correct answer and its calculation, and the clock pauses while you read.
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15 items in 55 minutes, ranked
Test mode runs 15 items with four options in 55 minutes, the count and time of the real subtest. Each score is ranked against the scores of other test-takers, and the Statistics page plots the ranking of every attempt.
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600 word problems, worked by hand
Each attempt draws its 15 items from a bank of 600 word problems: percentages; fractions and ratios; travel and work rates; prices and wages; unit conversions, areas and volumes; and averages. Every explanation works the arithmetic without a calculator.