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SAT Math Practice: Problem Solving and Data Analysis

Practise ratios, percentages, unit conversion, scatterplots and probability in SAT-style problems, with worked examples.

  • ⏱ 3 min read
  • ✏️ 3 worked examples
  • 🎯 5 practice questions
  • 📶 Intermediate
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Curriculum fit: Digital SAT Math, Problem-Solving and Data Analysis domain. Practice questions here are original, not official SAT questions. US: middle school and high school ratios, statistics and probability.

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What Is It?

This domain tests everyday quantitative reasoning: ratios and rates, percentages, unit conversions, reading tables and graphs, and basic statistics and probability. Most questions are set in a real-world context.

Careful reading matters as much as calculation. Identify what is being asked, the units involved and which numbers are relevant.

old 80new 100Percent change(new − old) ÷ old × 100(100 − 80) ÷ 80 × 100 = 25%Meansum of values ÷ how manyProbabilityfavourable ÷ total outcomes
Percent change compares the change with the original amount. Always divide by the old value, not the new one.

Key Formulas and Ideas

  • Percent change = (new − old) ÷ old × 100.
  • Mean = sum of values ÷ number of values.
  • Probability = favourable outcomes ÷ total outcomes.
  • Unit conversion: multiply by conversion factors written as fractions equal to 1, so units cancel.

Worked Examples

Example 1

Unit Conversion

Question

Convert 60 miles per hour to feet per second (1 mile = 5280 feet).

  1. Multiply by 5280 feet per mile and divide by 3600 seconds per hour.
  2. 60 × 5280 ÷ 3600 = 316 800 ÷ 3600 = 88.

✓ Answer 88 feet per second

Example 2

Percent Change

Question

A price increases by 20%, then the new price decreases by 20%. What is the overall change?

  1. Multiply: 1.20 × 0.80 = 0.96.
  2. 0.96 means a decrease of 4%.

✓ Answer A 4% decrease

Example 3

Mean

Question

The mean of 5 numbers is 12. A sixth number, 18, is added. What is the new mean?

  1. Sum of the first five: 5 × 12 = 60.
  2. New sum: 60 + 18 = 78.
  3. New mean: 78 ÷ 6 = 13.

✓ Answer 13

Common Mistakes to Avoid

  • Averaging percentages instead of multiplying the factors.
  • Not converting units consistently.
  • Using the wrong base for a percent change.
  • Reading the scale of a graph incorrectly.

Practice Questions

0 of 5 answered
Q1A price rises from $40 to $50. What is the percent change?
Q2The mean of 4 numbers is 10. What is their sum?
Q3A bag has 3 red and 7 blue marbles. P(red) = ?
Q4Convert 2 hours to seconds.
Q5A recipe uses 3 cups of flour for 12 cookies. How much flour for 30 cookies?

Frequently Asked Questions

Does the standard deviation need to be calculated?

You may be asked to compare the spread of data sets without computing it. Check the College Board's content descriptions for the current details.

How do I handle a scatterplot question?

Look at the overall trend and the line of best fit, and decide whether a prediction is inside the data range.

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Sources and Review

Reviewed by StudyMorrow editorial review on 5 Nov 2026.