How Arithmetic Reasoning works
Each question is a short real-world problem: fuel used over a distance, a distance on a map, the cost of equal numbers of two items, a percentage increase, the volume of a tank. Five numeric options follow, and only one is right.
It is the second subtest of the sitting and the longest of the ability subtests, at 29 minutes. No calculator is allowed; you work on the scratch paper you are given.
Arithmetic Reasoning and Math Knowledge together make the Quantitative composite. The minimum for any commission is the 10th percentile of Air Force applicants on that composite, and both subtests also count towards Academic Aptitude.
A method for word problems
Most mistakes on this subtest are set-up mistakes, not arithmetic ones:
- Write down what the question asks for in a word or two, with its unit: “minutes”, “dollars per pound”.
- Write the units next to every number you copy out. A rate in miles per hour multiplied by minutes is a warning.
- Estimate first. If you expect “about 60” and your working gives 600, you know to look again.
- Use the options. Five answers spread far apart tell you an estimate is enough; five close together tell you to work exactly.
- When a problem has several steps, check which step the question actually asks for. Wrong options are often a correct intermediate result.
Worked examples
“On a map, 1 inch represents 12 miles. Two towns are 3.5 inches apart. How many minutes does it take to drive between them at 42 miles per hour? (A) 42 (B) 54 (C) 60 (D) 66 (E) 72.” The distance is 3.5 × 12 = 42 miles, and 42 miles at 42 miles per hour takes one hour, so C, 60 minutes. Option A is the distance in miles, an answer to the wrong question.
“A jacket costs $80 after a 20% discount. What was the original price? (A) $64 (B) $96 (C) $100 (D) $104 (E) $120.” After the discount you pay 80% of the original, so the original is 80 ÷ 0.8 = $100, option C. Adding 20% to $80 gives $96, option B, which is the usual slip.
Tips for the real subtest
- Practise without a calculator from the start, including long division and decimals. Slow arithmetic is what uses up the 29 minutes.
- Learn the US conversions you will need without a table: 12 inches to a foot, 3 feet to a yard, 5,280 feet to a mile, 16 ounces to a pound, 4 quarts to a gallon.
- Skip a problem that stalls you, mark an answer, and come back if time allows. Every question carries the same weight.
- Never leave a blank. There is no penalty for a wrong answer.
Practise Arithmetic Reasoning on CogniPrep
Our Arithmetic Reasoning game is free. It gives you 25 word problems in 29 minutes, five options each with numeric answers in order from smallest to largest, in US units and dollars, and no calculator. You can move back and change answers until time runs out. Your result is the number right, with the topics you missed and a comparison with other CogniPrep users. It is not an AFOQT percentile.