Guided Practice
Learn
This guided practice lesson walks you through quantitative reasoning problems step-by-step. You will apply skills from financial mathematics and statistical literacy to solve real-world scenarios with instructor guidance.
Key Strategies for Quantitative Reasoning
- Read carefully: Identify what the question is actually asking before starting calculations.
- Extract data: Underline or note the key numbers and relationships given in the problem.
- Choose the right approach: Decide whether you need percentages, ratios, statistics, or financial formulas.
- Estimate first: Use mental math to get a ballpark answer before detailed calculations.
- Check units: Ensure your final answer has the correct units and makes sense in context.
When to Use Each Technique
Quantitative reasoning problems often combine multiple skills. Here is a quick reference:
- Percentage change: Comparing values over time, discounts, tax calculations
- Ratios and proportions: Scaling recipes, unit conversions, comparing rates
- Mean/median/mode: Summarizing data sets, identifying typical values
- Interest calculations: Loans, savings accounts, investment growth
- Data interpretation: Reading graphs, tables, and charts accurately
Examples
Work through these guided examples. Each one demonstrates a complete problem-solving process.
Example 1: Percentage Increase
Problem: A store's monthly revenue increased from $45,000 to $52,200. What was the percentage increase?
Step 1: Find the difference: $52,200 - $45,000 = $7,200
Step 2: Divide by the original: $7,200 / $45,000 = 0.16
Step 3: Convert to percentage: 0.16 x 100 = 16%
Answer: The revenue increased by 16%.
Example 2: Comparing Statistical Measures
Problem: Test scores: 72, 85, 88, 88, 91, 95. Which is greater, the mean or the median?
Step 1: Calculate the mean: (72+85+88+88+91+95)/6 = 519/6 = 86.5
Step 2: Find the median: With 6 values, average the 3rd and 4th: (88+88)/2 = 88
Step 3: Compare: Median (88) > Mean (86.5)
Answer: The median is greater than the mean by 1.5 points.
Example 3: Compound Interest
Problem: $2,000 is invested at 4% annual interest, compounded annually. What is the value after 3 years?
Step 1: Use the formula A = P(1 + r)^t
Step 2: Substitute: A = 2000(1 + 0.04)^3 = 2000(1.04)^3
Step 3: Calculate: A = 2000 x 1.124864 = $2,249.73
Answer: The investment will be worth $2,249.73 after 3 years.
Practice
Try these problems on your own. Apply the strategies and techniques you learned.
Problem 1: A laptop originally priced at $1,200 is on sale for $960. What is the percentage discount?
Problem 2: The data set {15, 22, 22, 25, 30, 35, 40} has what mean and mode?
Problem 3: If inflation is 3% per year, what will a $50 item cost in 5 years?
Problem 4: A car travels 280 miles using 8 gallons of gas. At the same rate, how many gallons are needed for 420 miles?
Problem 5: Company A's stock went from $45 to $54. Company B's stock went from $80 to $92. Which had a greater percentage increase?
Problem 6: The median of 5 consecutive even numbers is 24. What is the sum of all 5 numbers?
Problem 7: A savings account earns 2.5% simple interest per year. How much interest is earned on $3,000 after 4 years?
Problem 8: In a survey, 45% of 800 respondents preferred Brand A. How many people is that?
Problem 9: If the ratio of teachers to students is 1:18 and there are 540 students, how many teachers are there?
Problem 10: A population of 50,000 grows by 2% per year. What will the population be after 2 years?
Check Your Understanding
Test yourself with these review questions.
Question 1: What is the first step you should take when approaching a quantitative reasoning problem?
Question 2: Explain when you would use mean versus median to describe a data set.
Question 3: What is the difference between simple interest and compound interest?
Next Steps
- Review any problems that felt challenging
- Proceed to Word Problems for more practice with contextual scenarios
- Return to these guided examples when you need a refresher