SAT Problem Solving & Data Analysis
Practice Questions
Problem Solving & Data Analysis tests your ability to interpret real-world data, work with ratios and percentages, and draw valid conclusions from statistics. A calculator is available throughout Math, but these questions still depend on careful reading of tables and graphs.
About Problem Solving & Data Analysis
Problem Solving & Data Analysis questions make up roughly 15% of the Math section. The built-in calculator is available throughout Math, including this domain. The work centers on quantitative reasoning in contexts such as budgets, survey results, medical studies, and scientific data sets: extracting meaning from charts, identifying limits in a statistical claim, and translating percentage relationships into concrete numbers.
The five core skills tested here span a wide practical range. Ratio and proportion questions ask you to scale quantities, convert units, or set up and solve proportional equations. Percentage problems require you to move between percent, decimal, and fraction forms and to compute multi-step percent changes without losing track of the correct base. Statistics questions cover measures of center, spread, and shape of distributions, and may require reading values from tables or histograms before doing arithmetic.
Probability and statistical inference round out the domain. Two-way tables require you to identify the relevant sample space. Inference questions ask what a study's design permits you to conclude: an observational study supports association rather than causation; a random sample can support generalization to its sampled population; and a non-representative sample limits the scope of a conclusion.
What You'll Practice
- Setting up and solving proportional equations
- Computing single and multi-step percent change
- Reading and interpreting two-way tables and bar charts
- Calculating mean, median, range, and standard deviation conceptually
- Finding simple and conditional probabilities
- Evaluating study design and scope of valid inference
Why Problem Solving & Data Analysis Matters for Your Score
This domain connects arithmetic to claims about real data. Ratios, percentages, study design, and statistical interpretation also appear in subjects such as economics, biology, and psychology, making the underlying reasoning useful beyond a single test section.
Problem Solving & Data Analysis Subtopics
Each subtopic page combines its available practice questions with concept explanations, common mistakes, and strategy tips tailored to that specific skill.
Ratios, Rates, and Proportional Relationships
Questions asking you to set up proportional equations, convert units, and scale quantities in real-world contexts.
Percentages and Percent Change
Questions covering percent conversions, percent increase and decrease, and multi-step percentage problems with real-world price or quantity contexts.
Statistics, Data Interpretation, and Distributions
Questions requiring you to calculate and interpret measures of center and spread, read graphs and tables, and understand the shape of data distributions.
Probability and Conditional Probability
Questions asking you to find simple, compound, and conditional probabilities, often from two-way frequency tables.
Statistical Inference and Study Design
Questions testing whether you can identify what a study's design allows you to validly conclude, including generalizability and causality.
Problem Solving Sample Questions
More questionsPick an answer and hit Check Answer to see the detailed explanation. Questions are from easy, medium, and hard difficulty levels.
A recipe calls for 3 cups of flour for every 2 cups of sugar. If a baker wants to use 9 cups of flour, how many cups of sugar are needed?
Show explanation
Correct answer: B. 6
Explanation
Set up a proportion: 3/2 = 9/x. Cross-multiplying gives 3x = 18, so x = 6. The baker needs 6 cups of sugar.
After a 20% increase, the price of a laptop is $960. What was the original price?
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Correct answer: D. $800
Explanation
Original × 1.20 = $960. Original = $960 / 1.20 = $800.
A dataset has a mean of 50 and a median of 42. Which of the following best describes the likely shape of the distribution?
Show explanation
Correct answer: A. Skewed right (mean > median)
Explanation
When the mean > median, the distribution is skewed right—the tail extends toward the higher values, pulling the mean above the median.
A bag contains 5 red, 3 green, and 2 blue marbles. If one marble is drawn at random, what is the probability of drawing a green marble?
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Correct answer: C. 3/10
Explanation
Total marbles = 5 + 3 + 2 = 10. P(green) = 3/10.
A poll of 1,000 randomly selected adults in a city found that 62% support a new transit policy, with a margin of error of ±3%. Which of the following is the best interpretation?
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Correct answer: D. Between 59% and 65% of all adults in the city are estimated to support the policy
Explanation
Margin of error creates an interval estimate: 62% ± 3% = [59%, 65%]. This interval applies to the city's adult population (the sampling frame), not the country.
Train A leaves City X at 60 mph heading toward City Y, which is 300 miles away. Train B leaves City Y at the same time heading toward City X at 90 mph. How many miles from City X will the trains meet?
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Correct answer: C. 120
Explanation
Combined closing speed = 60 + 90 = 150 mph. Time to meet = 300 / 150 = 2 hours. Distance from City X = 60 × 2 = 120 miles.
A jacket originally costs $80. It is on sale for 25% off. What is the sale price of the jacket?
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Correct answer: A. $60
Explanation
Discount = 25% × $80 = $20. Sale price = $80 − $20 = $60.
A class of 20 students has a mean score of 78. After one more student takes the test, the mean drops to 77. What score did the new student receive?
Show explanation
Correct answer: A. 57
Explanation
Original total = 20 × 78 = 1,560. New total needed for mean of 77 with 21 students = 21 × 77 = 1,617. New student's score = 1,617 − 1,560 = 57.
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Strategy Tips for Problem Solving
Always identify the base before computing a percent
The single most common error in this domain is using the wrong number as 100%. Before calculating, ask: 'percent of what?' If a price increases by 20% and then decreases by 20%, the base for the decrease is the higher price—so you end up below the original.
Read every axis label on graphs
Graphs may use non-standard scales, dual axes, or counts rather than percentages. Read both axis labels and the legend before calculating; otherwise, a correct operation can be applied to the wrong quantity.
For probability, box off the correct sample space
Conditional probability questions tell you a condition has already been met—'given that the person is a senior…'—so your denominator is only that subgroup, not the full table total. Physically circle or mentally isolate the row or column that forms the new sample space.
Use elimination on inference questions
On inference questions, reject choices that claim causation from an observational study or generalize beyond the sampled population. Prefer the statement whose scope and certainty match what the design supports; words such as 'associated' or 'suggests' are often better calibrated than 'proves' or 'causes.'
Frequently Asked Questions — Problem Solving
Can I use a calculator on Problem Solving & Data Analysis questions?
Yes. The built-in graphing calculator is available throughout the current digital SAT Math section. Decide question by question whether it clarifies the work; a proportion or table lookup may be simpler to set up directly.
How much statistics do I need to know?
You need a solid conceptual grasp of mean, median, mode, range, and standard deviation—but you will never be asked to compute a standard deviation by hand on the test. Questions about spread typically ask you to compare two distributions or identify which change would affect a statistic.
What types of graphs appear most often?
Bar charts, scatterplots, line graphs, and two-way frequency tables are the most common. Histograms and box plots appear occasionally. You will not need to interpret more exotic chart types like radar or bubble charts.
Do I need to know hypothesis testing or p-values?
Not the formal procedures. The test covers the conceptual logic of inference: whether a sample was randomly selected, whether you can generalize beyond the sample, and whether you can infer causation vs. association. Specific p-value calculations or null hypothesis mechanics are not tested.
How do I improve quickly on this domain?
Practice reading real data sources—tables, news graphics, or short research summaries—and ask yourself what conclusion is and is not supported. The reasoning skills transfer directly to the test's inference questions. For computation, drill two-step percent problems until the base-identification step is automatic.
Other Math Topics
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