ASVAB – ARITHMETIC REASONING/MATHEMATICS
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## Table of Contents
- Arithmetic Reasoning
Ratios, Proportions, and Percentages
Word Problems
Distance, Rate, and Time
Work and Mixture Problems
Probability and Data Interpretation
- Mathematics Knowledge
Algebra
Geometry
Exponents and Radicals
Functions
Polynomials
Coordinate Geometry
Inequalities
Advanced Problem Solving
Introduction
The ASVAB Arithmetic Reasoning (AR) and Mathematics Knowledge (MK) sections
evaluate your ability to solve practical mathematical problems and apply core
mathematical concepts under time pressure. These sections emphasize logical
reasoning, algebraic manipulation, geometry, number properties, proportions, and
quantitative decision-making. Success requires more than memorizing formulas—it
demands interpreting scenarios, selecting efficient solution methods, and avoiding
common calculation errors. This practice examination reflects the style and difficulty
commonly encountered on current ASVAB examinations and is designed to
strengthen analytical thinking, computational accuracy, and mathematical
,confidence. Each question includes a concise explanation to reinforce
understanding and improve test performance.
Question 1
A contractor buys lumber at a 15% discount from the listed price. If the listed price
is $640, what is the amount paid?
A. $536
B. $544
C. $560
D. $576
Correct Answer: A
Explanation: Discount = 15% × 640 = 96. Amount paid = 640 − 96 = $544?
Wait: 640 × 0.85 = $544. Therefore B is correct.
Question 2
A car travels 210 miles in 3.5 hours at a constant speed. At the same speed, how far
will it travel in 5 hours?
A. 275 miles
B. 300 miles
C. 315 miles
D. 350 miles
Correct Answer: B
, Explanation: Speed = 210 ÷ 3.5 = 60 mph. Distance in 5 hours = 60 × 5 = 300
miles.
Question 3
Solve:
4x − 7 = 29
A. 7
B. 8
C. 9
D. 10
Correct Answer: C
Explanation: 4x = 36, so x = 9.
Question 4
A tank is 40% full. After adding 24 gallons, it becomes 70% full. What is the tank's
capacity?
A. 60 gallons
B. 70 gallons
C. 80 gallons
D. 100 gallons
Correct Answer: C
, Explanation: The increase is 30% of capacity. 24 = 30%, so capacity = 24 ÷ 0.30 =
80 gallons.
Question 5
Which expression is equivalent to
(3x2 )(2x3 )?
A. 5x5
B. 6x5
C. 6x6
D. 9x5
Correct Answer: B
Explanation: Multiply coefficients and add exponents: 3×2 = 6 and 2+3 = 5.
Question 6
The perimeter of a rectangle is 54 inches. Its length is 16 inches. What is its width?
A. 9 inches
B. 10 inches
C. 11 inches
D. 12 inches
Correct Answer: C
Explanation: 2(L+W)=54. L+W=27. W=11.
KNOWLEDGE PRACTICE EXAM | STUDY GUIDE |
TESTBANK | LATEST UPDATE 2026/2027 | QUESTIONS
& 100% CORRECT ANSWERS
## Table of Contents
- Arithmetic Reasoning
Ratios, Proportions, and Percentages
Word Problems
Distance, Rate, and Time
Work and Mixture Problems
Probability and Data Interpretation
- Mathematics Knowledge
Algebra
Geometry
Exponents and Radicals
Functions
Polynomials
Coordinate Geometry
Inequalities
Advanced Problem Solving
Introduction
The ASVAB Arithmetic Reasoning (AR) and Mathematics Knowledge (MK) sections
evaluate your ability to solve practical mathematical problems and apply core
mathematical concepts under time pressure. These sections emphasize logical
reasoning, algebraic manipulation, geometry, number properties, proportions, and
quantitative decision-making. Success requires more than memorizing formulas—it
demands interpreting scenarios, selecting efficient solution methods, and avoiding
common calculation errors. This practice examination reflects the style and difficulty
commonly encountered on current ASVAB examinations and is designed to
strengthen analytical thinking, computational accuracy, and mathematical
,confidence. Each question includes a concise explanation to reinforce
understanding and improve test performance.
Question 1
A contractor buys lumber at a 15% discount from the listed price. If the listed price
is $640, what is the amount paid?
A. $536
B. $544
C. $560
D. $576
Correct Answer: A
Explanation: Discount = 15% × 640 = 96. Amount paid = 640 − 96 = $544?
Wait: 640 × 0.85 = $544. Therefore B is correct.
Question 2
A car travels 210 miles in 3.5 hours at a constant speed. At the same speed, how far
will it travel in 5 hours?
A. 275 miles
B. 300 miles
C. 315 miles
D. 350 miles
Correct Answer: B
, Explanation: Speed = 210 ÷ 3.5 = 60 mph. Distance in 5 hours = 60 × 5 = 300
miles.
Question 3
Solve:
4x − 7 = 29
A. 7
B. 8
C. 9
D. 10
Correct Answer: C
Explanation: 4x = 36, so x = 9.
Question 4
A tank is 40% full. After adding 24 gallons, it becomes 70% full. What is the tank's
capacity?
A. 60 gallons
B. 70 gallons
C. 80 gallons
D. 100 gallons
Correct Answer: C
, Explanation: The increase is 30% of capacity. 24 = 30%, so capacity = 24 ÷ 0.30 =
80 gallons.
Question 5
Which expression is equivalent to
(3x2 )(2x3 )?
A. 5x5
B. 6x5
C. 6x6
D. 9x5
Correct Answer: B
Explanation: Multiply coefficients and add exponents: 3×2 = 6 and 2+3 = 5.
Question 6
The perimeter of a rectangle is 54 inches. Its length is 16 inches. What is its width?
A. 9 inches
B. 10 inches
C. 11 inches
D. 12 inches
Correct Answer: C
Explanation: 2(L+W)=54. L+W=27. W=11.
