# SAT Problem-Solving and Data Analysis: rates, percentages, data

Problem-Solving and Data Analysis is about 15% of the Digital SAT Math section, 5 to 7 questions across seven skill points. Worked items on percent change, centers of data and margin of error.

## The short answer

Problem-Solving and Data Analysis is about 15% of the Digital SAT Math section, 5 to 7 of the 40 operational questions. It is the domain of ratios, rates, units and percentages. It also covers one-variable and two-variable data, probability, and inference from sample statistics. Margin of error sits here, and so does judging a claim made from an observational study or an experiment. Seven skill points share those few questions, so breadth matters more than depth.

## Key facts

- **Section:** Math
- **Domain:** Problem-Solving and Data Analysis
- **Domain share:** ~=15% of the section, 5-7 questions
- **Question format:** Multiple choice and student-produced response
- **Skill points in this domain:** 7, the most of any Math domain
- **Math section:** 44 questions, 40 operational, 70 minutes

Question counts, timings and domain shares come from College Board's test pages and the Digital SAT Suite Specifications Overview, checked 28 September 2026.

## How it's scored

One mark per question, and this is the widest domain per mark on the test. Seven named skill points share 5 to 7 questions, so no single topic is guaranteed to appear. That makes the domain a poor place to specialize and a good place to cover everything once.

College Board names seven skill and knowledge testing points here:

- Ratios, rates, proportional relationships, and units
- Percentages
- One-variable data: distributions and measures of center and spread
- Two-variable data: models and scatterplots
- Probability and conditional probability
- Inference from sample statistics and margin of error
- Evaluating statistical claims: observational studies and experiments

The last two ask you to judge rather than to calculate. The correct answer is often the most cautious statement in the list. A sample supports a range, and a study without random assignment cannot show cause.

> Write the units beside every number you copy down. Most misses in this domain are unit errors: minutes reported as hours, or a rate read upside down.

## Problem-Solving and Data Analysis examples

Worked examples written for this page. Answer each one before you open the model response: memorizing a response is scored as an irrelevant answer in the real test.

**Example 1 -- two percent changes in a row**

Prompt: A shop raises the price of a lamp from $40 by 25%, then takes 20% off the new price. What is the final price of the lamp?

- A. $38.00
- B. $40.00
- C. $42.00
- D. $45.00
Answer: B.

Model response: B, $40.00. The increase is 25% of $40, which is $10, so the new price is $50. The discount is 20% of $50, which is $10, so the final price is $40. The two changes cancel exactly, and the lamp ends where it started.

Why it scores: Percent changes apply to different bases, so they never simply add or subtract. Subtracting 20 from 25 and calling it a 5% rise gives $42, which is the option most people pick.

**Example 2 -- the gap between two centers**

Prompt: Seven students read the following numbers of books over a summer: 2, 3, 3, 5, 8, 9, and 40. How much greater is the mean of the data than the median? Type your answer.

Write your response.

Model response: 5. The values are already in order, so the median is the fourth of seven, which is 5. The sum is 2 + 3 + 3 + 5 + 8 + 9 + 40 = 70, and 70 / 7 = 10, so the mean is 10. The mean is 10 - 5 = 5 greater than the median.

Why it scores: One extreme value pulls the mean far from the median and leaves the median untouched. The question asks for the gap, not for either center, so answering 10 or 5 without subtracting is a wasted calculation.

**Example 3 -- a rate, then a unit change**

Prompt: A printer produces 18 pages per minute at a steady rate. How many hours does it take to print 5,400 pages?

- A. 3
- B. 5
- C. 50
- D. 300
Answer: B.

Model response: B, 5. Dividing, 5,400 / 18 = 300, so the job takes 300 minutes. There are 60 minutes in an hour, and 300 / 60 = 5, so it takes 5 hours. Check: 18 pages per minute for 300 minutes is 5,400 pages.

Why it scores: Option D is the right arithmetic with the wrong unit, and it is there because the question says hours while the rate is given per minute. Labeling 300 as minutes the moment you write it down prevents the miss.

**Example 4 -- what a margin of error licenses you to say**

Prompt: In a survey of 400 randomly selected town residents, 62% supported a new library, with a margin of error of 4 percentage points. Which conclusion is best supported by these results?

- A. Exactly 62% of all residents support the library.
- B. The share of all residents who support the library is likely between 58% and 66%.
- C. Fewer than half of all residents support the library.
- D. Residents of nearby towns also support the library.
Answer: B.

Model response: B. The margin of error turns the sample figure into a range: 62% - 4% = 58% at the low end and 62% + 4% = 66% at the high end. A sample supports a plausible range for the whole town, not one exact value.

Why it scores: Option A ignores the margin of error, option C contradicts the data, and option D goes beyond the population that was sampled. The cautious statement about the sampled group is the pattern to expect in these items.

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## Common mistakes

| What costs marks | Do this instead |
| --- | --- |
| Adding or subtracting two percent changes as if they shared a base. | Apply each change to the amount in front of it. A 25% rise then a 20% cut is not a 5% rise. |
| Answering with a center when the question asks for the gap between two centers. | Read the last clause again. "How much greater" means subtract, and it needs both numbers first. |
| Reporting the right number in the wrong unit. | Label every intermediate number as you write it. Convert only at the end, and check the unit the question names. |
| Stating an exact population value from a sample. | A margin of error gives a range around the sample figure, and the range applies only to the group that was sampled. |

**Turn correct answers into a score** The SAT score calculator maps correct answers per module onto a 400-1600 range with College Board's own table, and superscores across test dates. [Open the SAT score calculator](/sat/score-calculator)

## How to practice

1. Drill percent change in both directions: find the new amount from a percent, and find the percent from two amounts. The second form is the one people skip.
2. For each small data set you meet, write the mean, the median and the range. Then say in one line which one an outlier moved.
3. Cover all seven skill points at least once before you drill any of them twice. With 5 to 7 questions on offer, a gap costs more than a weak spot.
4. On every survey or study item, name the group that was sampled before you look at the options. Half the wrong answers describe some other group.

## Common questions

### How many Problem-Solving and Data Analysis questions are on the SAT?

About 5 to 7 of the 40 operational Math questions, which is roughly 15% of the section. It is tied with Geometry and Trigonometry as the smallest Math domain.

### What statistics does the SAT Math section test?

Measures of center and spread for one-variable data, models and scatterplots for two-variable data, and probability including conditional probability. It also tests inference from sample statistics with a margin of error, and evaluating claims from observational studies and experiments.

### Is Problem-Solving and Data Analysis the easiest Math domain?

It is the smallest, not the easiest. Seven skill points share 5 to 7 questions, so the range of content per question is wider here than anywhere else in Math.

**Sources**
- [College Board: what's on the SAT Math section (checked 28 September 2026)](https://satsuite.collegeboard.org/sat/whats-on-the-test/math)
- [College Board: Digital SAT Suite of Assessments Specifications Overview (PDF)](https://satsuite.collegeboard.org/media/pdf/digital-sat-test-spec-overview.pdf)
- [College Board: how SAT scores are calculated (checked 28 September 2026)](https://satsuite.collegeboard.org/sat/scores/understanding-scores/how-scores-are-calculated)

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