About Arithmetic Reasoning

Arithmetic Reasoning is one of the most important ASVAB sections because it directly contributes to your AFQT score, which determines enlistment eligibility. This section presents mathematical word problems that require you to apply arithmetic operations (addition, subtraction, multiplication, division) along with concepts like ratios, proportions, percentages, and basic algebra. On the CAT-ASVAB, you will have approximately 55 minutes for 15 questions. The key challenge is translating word problems into mathematical equations. Strong performance on AR, combined with MK, WK, and PC, will maximize your AFQT percentile.

Topics Covered

Basic Arithmetic Operations
Fractions & Decimals
Percentages & Ratios
Proportions
Rate Problems (Distance, Work, Time)
Simple Interest & Finance
Measurement & Unit Conversion
Basic Algebra Word Problems
Averages & Statistics
Number Series & Patterns

Sample Questions

Sample Question 1
If the ratio of boys to girls in a class is 3:2, and there are 30 students total, how many are girls?
  • 10
  • 12
  • 15
  • 18
Total parts = 3 + 2 = 5. One part = 30 ÷ 5 = 6. Girls = 2 × 6 = 12.
Sample Question 2
A cylindrical tank has a radius of 3 feet and height of 10 feet. What is its volume? (Use π ≈ 3.14)
  • 28.26 cubic feet
  • 94.2 cubic feet
  • 282.6 cubic feet
  • 942 cubic feet
Volume = πr²h = 3.14 × 9 × 10 = 282.6 cubic feet.
Sample Question 3
A train travels at 60 mph. How long will it take to travel 210 miles?
  • 3 hours
  • 3.5 hours
  • 4 hours
  • 4.5 hours
Time = Distance ÷ Speed = 210 ÷ 60 = 3.5 hours.

Study Tips for Arithmetic Reasoning

Master Word Problem Translation

The biggest challenge is converting English sentences into math equations. Practice identifying key words: 'of' means multiply, 'per' means divide, 'total' means add.

Practice Mental Math

You cannot use a calculator on the ASVAB. Practice doing arithmetic in your head or on scratch paper to build speed and accuracy.

Focus on AFQT Impact

AR is one of four AFQT subtests. Improving your AR score has a direct and significant impact on your overall AFQT percentile and enlistment eligibility.