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 train leaves Station A at 9 AM traveling at 60 mph. Another train leaves Station B (120 miles away) at 10 AM traveling toward A at 40 mph. At what time do they meet?
  • 10:30 AM
  • 11:00 AM
  • 11:30 AM
  • 12:00 PM
By 10 AM, first train traveled 60 miles. Distance between = 60 miles. Combined speed = 100 mph. Time = 60/100 = 0.6 hr = 36 min. Meet at 10:36 AM ≈ 11 AM.
Sample Question 2
If a tank can be filled by Pipe A in 4 hours and by Pipe B in 6 hours, how long will it take to fill the tank if both pipes are used?
  • 2 hours
  • 2.4 hours
  • 5 hours
  • 10 hours
Rate A = 1/4, Rate B = 1/6. Combined rate = 1/4 + 1/6 = 5/12. Time = 12/5 = 2.4 hours.
Sample Question 3
Water flows into a tank at 5 gallons/minute and out at 2 gallons/minute. If the tank holds 60 gallons and is empty, how long to fill it?
  • 12 minutes
  • 15 minutes
  • 20 minutes
  • 30 minutes
Net rate = 5 - 2 = 3 gallons/minute. Time = 60/3 = 20 minutes.

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.