ASVAB ARITHMETIC REASONING PRACTICE EXAM
130 Original Questions | Comprehensive Review | Detailed Rationales
TABLE OF CONTENTS
Section Topic Questions
1 Basic Arithmetic & Number Operations 1–15
2 Fractions, Decimals, & Percentages 16–30
3 Ratios, Proportions, & Rates 31–45
4 Distance, Rate, & Time Problems 46–55
5 Work & Combined Work Problems 56–65
6 Averages & Statistics 66–75
7 Simple Interest & Financial Math 76–85
8 Geometry: Area, Perimeter, & Volume 86–100
9 Algebraic Equations & Word Problems 101–115
10 Mixed/Advanced Problem Solving 116–130
SECTION 1: BASIC ARITHMETIC & NUMBER OPERATIONS
Questions 1–15
1. A delivery truck travels 1,248 miles over 6 days. If the truck travels the same number of miles each day, how many miles does it travel per day?
A) 198 miles
B) 208 miles
C) 218 miles
D) 228 miles
🔴 Correct Answer: B) 208 miles
Rationale: Divide the total miles by the number of days: 1,248 ÷ 6 = 208 miles per day.
2. What is the value of 24 + 16 ÷ 4 × 2 − 6?
A) 20
B) 22
C) 26
D) 32
🔴 Correct Answer: C) 26
Rationale: Follow order of operations (PEMDAS). First, perform division and multiplication from left to right: 16 ÷ 4 = 4, then 4 × 2 = 8. The expression
becomes 24 + 8 − 6 = 26. Addition and subtraction are then performed from left to right.
,3. A box contains 84 oranges. If 1/3 of the oranges are placed into bags with 7 oranges per bag, how many bags are needed?
A) 3 bags
B) 4 bags
C) 5 bags
D) 6 bags
🔴 Correct Answer: B) 4 bags
Rationale: First, find 1/3 of 84: 84 × 1/3 = 28 oranges. Then divide by 7 oranges per bag: 28 ÷ 7 = 4 bags.
4. A plumber charges $85 for a service call plus $65 per hour for labor. If a repair takes 4.5 hours, what is the total cost?
A) $292.50
B) $377.50
C) $382.50
D) $467.50
🔴 Correct Answer: B) $377.50
Rationale: Labor cost = $65 × 4.5 = $292.50. Add the service call fee: $292.50 + $85 = $377.50.
5. A rectangular garden is 24 feet long and 18 feet wide. What is the perimeter of the garden?
A) 42 feet
B) 72 feet
C) 84 feet
D) 432 feet
🔴 Correct Answer: C) 84 feet
Rationale: Perimeter of a rectangle = 2(length + width) = 2(24 + 18) = 2(42) = 84 feet.
6. Simplify: 5³ − 4² + 10
A) 109
B) 119
C) 129
D) 139
🔴 Correct Answer: B) 119
Rationale: 5³ = 125, 4² = 16. So 125 − 16 + 10 = 119.
7. A factory produces 2,400 units per day. If production increases by 15%, how many units are produced per day after the increase?
A) 2,520 units
B) 2,640 units
C) 2,760 units
D) 2,880 units
🔴 Correct Answer: C) 2,760 units
Rationale: Increase = 2,400 × 0.15 = 360 units. New total = 2,400 + 360 = 2,760 units.
8. What is the least common multiple (LCM) of 12, 18, and 24?
A) 48
B) 60
C) 72
D) 144
🔴 Correct Answer: C) 72
, Rationale: Prime factorization: 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.
9. A recipe calls for 2/3 cup of sugar. If you want to make 2.5 times the recipe, how much sugar is needed?
A) 1 1/3 cups
B) 1 2/3 cups
C) 2 cups
D) 2 1/3 cups
🔴 Correct Answer: B) 1 2/3 cups
Rationale: 2/3 × 2.5 = 2/3 × 5/2 = 10/6 = 5/3 = 1 2/3 cups.
10. What is the greatest common factor (GCF) of 48 and 72?
A) 12
B) 16
C) 24
D) 36
🔴 Correct Answer: C) 24
Rationale: Prime factorization: 48 = 2⁴ × 3, 72 = 2³ × 3². GCF = 2³ × 3 = 8 × 3 = 24.
11. A salesperson earns a commission of 8% on all sales. If total sales for the month are $42,500, what is the commission earned?
A) $3,200
B) $3,400
C) $3,600
D) $4,000
🔴 Correct Answer: B) $3,400
Rationale: Commission = $42,500 × 0.08 = $3,400.
12. Evaluate: √144 + √81 − √36
A) 9
B) 12
C) 15
D) 18
🔴 Correct Answer: C) 15
Rationale: √144 = 12, √81 = 9, √36 = 6. So 12 + 9 − 6 = 15.
13. A tank holds 3,600 gallons of water. If it is 65% full, how many gallons of water are in the tank?
A) 2,160 gallons
B) 2,340 gallons
C) 2,520 gallons
D) 2,700 gallons
🔴 Correct Answer: B) 2,340 gallons
Rationale: 3,600 × 0.65 = 2,340 gallons.
14. Simplify: (3/4 + 1/2) ÷ (5/8)
A) 1 1/5
B) 1 3/5
130 Original Questions | Comprehensive Review | Detailed Rationales
TABLE OF CONTENTS
Section Topic Questions
1 Basic Arithmetic & Number Operations 1–15
2 Fractions, Decimals, & Percentages 16–30
3 Ratios, Proportions, & Rates 31–45
4 Distance, Rate, & Time Problems 46–55
5 Work & Combined Work Problems 56–65
6 Averages & Statistics 66–75
7 Simple Interest & Financial Math 76–85
8 Geometry: Area, Perimeter, & Volume 86–100
9 Algebraic Equations & Word Problems 101–115
10 Mixed/Advanced Problem Solving 116–130
SECTION 1: BASIC ARITHMETIC & NUMBER OPERATIONS
Questions 1–15
1. A delivery truck travels 1,248 miles over 6 days. If the truck travels the same number of miles each day, how many miles does it travel per day?
A) 198 miles
B) 208 miles
C) 218 miles
D) 228 miles
🔴 Correct Answer: B) 208 miles
Rationale: Divide the total miles by the number of days: 1,248 ÷ 6 = 208 miles per day.
2. What is the value of 24 + 16 ÷ 4 × 2 − 6?
A) 20
B) 22
C) 26
D) 32
🔴 Correct Answer: C) 26
Rationale: Follow order of operations (PEMDAS). First, perform division and multiplication from left to right: 16 ÷ 4 = 4, then 4 × 2 = 8. The expression
becomes 24 + 8 − 6 = 26. Addition and subtraction are then performed from left to right.
,3. A box contains 84 oranges. If 1/3 of the oranges are placed into bags with 7 oranges per bag, how many bags are needed?
A) 3 bags
B) 4 bags
C) 5 bags
D) 6 bags
🔴 Correct Answer: B) 4 bags
Rationale: First, find 1/3 of 84: 84 × 1/3 = 28 oranges. Then divide by 7 oranges per bag: 28 ÷ 7 = 4 bags.
4. A plumber charges $85 for a service call plus $65 per hour for labor. If a repair takes 4.5 hours, what is the total cost?
A) $292.50
B) $377.50
C) $382.50
D) $467.50
🔴 Correct Answer: B) $377.50
Rationale: Labor cost = $65 × 4.5 = $292.50. Add the service call fee: $292.50 + $85 = $377.50.
5. A rectangular garden is 24 feet long and 18 feet wide. What is the perimeter of the garden?
A) 42 feet
B) 72 feet
C) 84 feet
D) 432 feet
🔴 Correct Answer: C) 84 feet
Rationale: Perimeter of a rectangle = 2(length + width) = 2(24 + 18) = 2(42) = 84 feet.
6. Simplify: 5³ − 4² + 10
A) 109
B) 119
C) 129
D) 139
🔴 Correct Answer: B) 119
Rationale: 5³ = 125, 4² = 16. So 125 − 16 + 10 = 119.
7. A factory produces 2,400 units per day. If production increases by 15%, how many units are produced per day after the increase?
A) 2,520 units
B) 2,640 units
C) 2,760 units
D) 2,880 units
🔴 Correct Answer: C) 2,760 units
Rationale: Increase = 2,400 × 0.15 = 360 units. New total = 2,400 + 360 = 2,760 units.
8. What is the least common multiple (LCM) of 12, 18, and 24?
A) 48
B) 60
C) 72
D) 144
🔴 Correct Answer: C) 72
, Rationale: Prime factorization: 12 = 2² × 3, 18 = 2 × 3², 24 = 2³ × 3. LCM = 2³ × 3² = 8 × 9 = 72.
9. A recipe calls for 2/3 cup of sugar. If you want to make 2.5 times the recipe, how much sugar is needed?
A) 1 1/3 cups
B) 1 2/3 cups
C) 2 cups
D) 2 1/3 cups
🔴 Correct Answer: B) 1 2/3 cups
Rationale: 2/3 × 2.5 = 2/3 × 5/2 = 10/6 = 5/3 = 1 2/3 cups.
10. What is the greatest common factor (GCF) of 48 and 72?
A) 12
B) 16
C) 24
D) 36
🔴 Correct Answer: C) 24
Rationale: Prime factorization: 48 = 2⁴ × 3, 72 = 2³ × 3². GCF = 2³ × 3 = 8 × 3 = 24.
11. A salesperson earns a commission of 8% on all sales. If total sales for the month are $42,500, what is the commission earned?
A) $3,200
B) $3,400
C) $3,600
D) $4,000
🔴 Correct Answer: B) $3,400
Rationale: Commission = $42,500 × 0.08 = $3,400.
12. Evaluate: √144 + √81 − √36
A) 9
B) 12
C) 15
D) 18
🔴 Correct Answer: C) 15
Rationale: √144 = 12, √81 = 9, √36 = 6. So 12 + 9 − 6 = 15.
13. A tank holds 3,600 gallons of water. If it is 65% full, how many gallons of water are in the tank?
A) 2,160 gallons
B) 2,340 gallons
C) 2,520 gallons
D) 2,700 gallons
🔴 Correct Answer: B) 2,340 gallons
Rationale: 3,600 × 0.65 = 2,340 gallons.
14. Simplify: (3/4 + 1/2) ÷ (5/8)
A) 1 1/5
B) 1 3/5
