How the Arithmetic Reasoning subtest works
Arithmetic Reasoning is the second ASVAB subtest. On the CAT-ASVAB it has 15 scored questions and a 55-minute limit, which is 3 minutes 40 seconds a question. Each is a short word problem about everyday things such as fuel, pay, distances or discounts, in US units and dollars, with four answers to choose from.
The official topic list covers one-step and multi-step problems with whole numbers and rational numbers, ratio and proportion, interest and percentage, and measurement. Many questions turn on doing the right operations in the right order rather than on hard arithmetic.
It is adaptive, so the difficulty follows your answers, and you cannot return to a question. Arithmetic Reasoning counts towards your AFQT, and it is one of the two parts of the Army General Technical (GT) score, which adds it to your verbal score.
How to solve an Arithmetic Reasoning problem
Use the same five steps on every question:
- Read the last sentence first, so you know exactly what you are finding: a total, a difference, a rate or what is left.
- Write down the numbers with their units, and convert to one unit before you calculate: 12 inches to a foot, 3 feet to a yard, 16 ounces to a pound.
- Decide the steps in order, then work them on scratch paper, one line each.
- Estimate roughly, so a slipped decimal point stands out.
- Check that your answer is what the question asked for, not a number from halfway through the working.
Worked example
“A hardware store sells a drill for $120. This week it is 25% off, and members get a further 10% off the sale price. What does a member pay?” A. $78, B. $81, C. $90, D. $93.
The question asks for the final price after both discounts, so take them in order. 25% of $120 is $30, so the sale price is $90. Then 10% of $90 is $9, so a member pays $81, option B.
Option C, $90, is the halfway answer: the sale price before the member discount. Option A, $78, comes from adding the discounts to make 35% off $120, which is wrong because the second discount applies to the lower price.
Tips for the real Arithmetic Reasoning subtest
- Use the time. 55 minutes is the longest limit of any ASVAB subtest, so write out every step rather than working in your head.
- Practise without a calculator now. Long multiplication, long division and turning fractions into decimals need to be quick and reliable on paper.
- Learn the conversions that come up in US word problems: 5,280 feet in a mile, 4 quarts in a gallon, 60 minutes in an hour.
- Know simple interest (interest = principal × rate × time) and percentage change (change ÷ original).
- If time runs short, keep answering properly. The CAT-ASVAB applies a large penalty when several answers at the end of a subtest are wrong, so rushed guesses do more harm than good.
Practise Arithmetic Reasoning on CogniPrep
Our Arithmetic Reasoning game gives you 15 adaptive word problems with the real 55-minute clock, US units and no calculator. It starts at medium difficulty and adapts to each answer, and questions left when time runs out are scored as if you had guessed at random. You get a standard score on the ASVAB scale, where 50 is the average for US 18 to 23 year olds, and the AFQT percentile you would get if your other three AFQT subtests matched it. The questions and their difficulty ratings are ours, so treat the result as a guide.