Word problems test your ability to apply mathematical concepts to real-world situations. This section of the ASVAB is called Arithmetic Reasoning and requires logical thinking, equation setup, and problem-solving strategies.
1. Understanding Arithmetic Reasoning
Arithmetic reasoning involves applying math to practical scenarios.
What is Arithmetic Reasoning?
- Solving real-world math problems using addition, subtraction, multiplication, division, ratios, percentages, and algebra.
- Focuses on understanding the problem and applying the right math skills.
Key Facts About ASVAB Word Problems:
- No calculators allowed—you must work out problems manually.
- Scratch paper is encouraged—use it to write down key information and work through steps.
- Common problem types include: rate/time/distance, proportions, percentages, budgeting, and geometry applications.
2. Steps to Solve Word Problems
Follow these five steps to break down and solve word problems efficiently.
Step 1: Read the Problem Completely
- Understand the scenario before attempting to solve it.
- Read carefully to avoid overlooking key details.
Step 2: Identify What the Question Is Asking
- Look for clue words (e.g., “total,” “difference,” “times”) to determine the operation needed.
- Rephrase the problem in your own words if necessary.
Step 3: Extract Relevant Information
- Identify important numbers and eliminate unnecessary details.
- Write down given values and label them clearly.
Step 4: Set Up an Equation
- Translate the problem into a mathematical equation.
- Use variables (x, y) if necessary for unknown values.
Step 5: Solve and Review
- Perform the required calculations.
- Double-check the answer to ensure it makes sense.
- Plug the answer back into the problem for verification.
3. Identifying Clue Words
Word problems often contain keywords that indicate which operation to use.
Addition Clue Words:
- Sum, total, increased by, combined, together, more than
Example:
“John has 5 apples, and Sarah gives him 3 more. How many does he have in total?”
5+3=85 + 3 = 85+3=8
Subtraction Clue Words:
- Difference, fewer than, less than, decreased by, remaining
Example:
“A store had 200 items, and 75 were sold. How many remain?”
200−75=125200 – 75 = 125200−75=125
Multiplication Clue Words:
- Product, times, of, per dozen, double, triple, squared, cubic
Example:
“A box holds 6 rows of 4 bottles each. How many bottles are in the box?”
6×4=246 \times 4 = 246×4=24
Division Clue Words:
- Ratio, quotient, per, out of, split evenly, shared among
Example:
“A 12-pack of soda is split evenly among 4 friends. How many sodas does each get?”
12÷4=312 \div 4 = 312÷4=3
Equals Clue Words:
- Is, was, amounts to, results in, gives, will be
Example:
“The total bill is $45. Each person pays an equal share. How much does each person pay if there are 3 people?”
x=45÷3x = 45 \div 3x=45÷3
4. Problem-Solving Strategies
Use these strategies to simplify and solve word problems accurately.
Unit Analysis (Keeping Track of Units):
- Always write down the units (miles, gallons, feet, dollars) in problems.
- Convert units if necessary (e.g., minutes to hours).
Example:
“A car travels 60 miles in 2 hours. What is its speed in miles per hour?”
60 miles2 hours=30 mph\frac{60 \text{ miles}}{2 \text{ hours}} = 30 \text{ mph}2 hours60 miles=30 mph
Eliminating Distractions:
- Some problems contain extra information meant to confuse you.
- Ignore numbers that don’t contribute to solving the question.
Example:
“Lisa bought 4 notebooks for $3 each and also looked at pens but didn’t buy them. What was her total cost?”
4×3=124 \times 3 = 124×3=12
(The pens are irrelevant!)
Breaking Down Multi-Step Problems:
- Solve in logical steps rather than rushing to the final answer.
- Use order of operations (PEMDAS) when needed.
Example:
“A family of 5 spends $250 on groceries per week. How much do they spend in a month?”
- Weekly expense: $250
- Weeks in a month: 4
- Total monthly expense:
250×4=1000250 \times 4 = 1000250×4=1000
5. Common Word Problem Applications
Word problems appear in real-life situations. Be prepared for these types.
Volume and Area Calculations
- Used for measuring spaces, construction, and packaging.
- Example: “Find the area of a rectangular yard that is 20 feet long and 15 feet wide.”
Area=20×15=300 square feet\text{Area} = 20 \times 15 = 300 \text{ square feet}Area=20×15=300 square feet
Savings and Budgeting Problems
- Used in financial planning and business.
- Example: “Jake wants to save $1,200 in a year. How much should he save per month?”
120012=100 per month\frac{1200}{12} = 100 \text{ per month}121200=100 per month
Ratio and Proportion Problems
- Used in recipes, scale drawings, and financial comparisons.
- Example: “A map scale shows that 1 inch = 5 miles. How many miles do 3 inches represent?”
3×5=15 miles3 \times 5 = 15 \text{ miles}3×5=15 miles
6. Visual Aids for Problem-Solving
Use visual tools to organize and simplify problems.
Drawing Diagrams
- Sketch shapes, objects, or number lines to clarify problems.
- Example: A triangle problem may be easier to solve by drawing the figure.
Using Tables or Lists
- Organize data to recognize patterns and relationships.
- Example: A store’s sale prices can be organized into a table for easier calculations.
| Item | Original Price | Discount | Final Price |
| Shirt | $20 | 20% off | $16 |
| Jeans | $50 | 30% off | $35 |
Final Review
- Read the problem carefully and identify key information.
- Use clue words to determine the correct operation.
- Set up an equation and solve step by step.
- Apply logical strategies like unit analysis and breaking down steps.
- Use diagrams and tables when necessary.