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
A contractor needs 3/4 of a pound of nails for each section of fence. How many pounds are needed for 12 sections?
  • 6 pounds
  • 9 pounds
  • 12 pounds
  • 16 pounds
Each fence section uses 3/4 pound of nails. For 12 sections, multiply 12 × 3/4 = 36/4 = 9. Therefore the contractor needs 9 pounds total. This is a unit-rate scaling problem.
Sample Question 2
An aircraft travels 600 miles with a tailwind in 2 hours, and returns the same distance against the wind in 3 hours. What is the aircraft's speed in still air?
  • 200 mph
  • 250 mph
  • 275 mph
  • 300 mph
With wind: (plane + wind) = 300 mph. Against: (plane - wind) = 200 mph. Plane speed = (300+200)/2 = 250 mph.
Sample Question 3
If a box contains 24 items and 1/4 are defective, how many are NOT defective?
  • 6
  • 12
  • 18
  • 20
Defective = 24 × 1/4 = 6. Not defective = 24 - 6 = 18.

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.