Chapter 6

Arithmetic Reasoning

Know What to Expect

For the Arithmetic Reasoning (AR) section of the paper-and-pencil ASVAB, you will have 36 minutes to complete 30 arithmetic word problems. For the CAT-ASVAB, you will have 39 minutes to complete 16 problems. This chapter will review the concepts you need to understand in order to succeed on the Arithmetic Reasoning test. As you work through this chapter, don’t forget that many problems are best solved by using the strategies you read about in chapter 5.

The principles covered in this chapter will also serve you well as the building blocks for Mathematics Knowledge (MK), which will be the focus of chapter 7. Both the AR and MK subtests are particularly important because they are part of the AFQT score. Additionally, high AR and MK scores are required for you to be eligible to enter many of the specialized occupations in the military.

This chapter will take you through a review of arithmetic concepts including:

• key arithmetic definitions
• number properties
• absolute value
• primes, factors, multiples, and remainders
• divisibility rules
• fractions, decimals, and scientific notation
• exponents and radicals
• factorials

The chapter will then review applied arithmetic concepts, such as:

• order of operations and calculation rules
• ratios, proportions, and rates
• combined work
• percentages
• averages, means, medians, and modes
• sequences and probability

The chapter will also discuss Arithmetic word problems including:

• translation
• word problems with formulas

The chapter concludes with a practice set.