SAT Math quiz

SAT Problem-Solving and Data Analysis Quizzes

Practice 10 SAT Problem-Solving and Data Analysis questions involving ratios, rates, percentages, units, probability, data distributions, scatterplots, sampling, inference, and evaluating statistical claims. Use hints when needed and review the explanation after each answer.

1 Question 1 of 10
Not answered

A recipe uses flour and sugar in a ratio of 5:2. If 3.5 cups of sugar are used, how many cups of flour are needed?

Hint: Scale both parts of the 5:2 ratio by the same factor.
Explanation: The sugar part 2 is scaled to 3.5 by multiplying by 1.75. Apply the same factor to the flour part: 5 × 1.75 = 8.75 cups.
2 Question 2 of 10
Not answered

A car travels 315 miles using 10.5 gallons of fuel. At the same rate, how many gallons are needed to travel 450 miles?

Hint: First find miles per gallon, then use that unit rate for 450 miles.
Explanation: The car travels 315 ÷ 10.5 = 30 miles per gallon. To travel 450 miles, it needs 450 ÷ 30 = 15 gallons.
3 Question 3 of 10
Not answered

A laboratory solution has a mass of 2.4 kilograms. What is its mass in grams?

Hint: There are 1,000 grams in 1 kilogram.
Explanation: 2.4 kilograms × 1,000 grams per kilogram = 2,400 grams.
4 Question 4 of 10
Not answered

A jacket price increases from $80 to $94. What is the percent increase?

Hint: Find the increase, then divide by the original price.
Explanation: The increase is $94 - $80 = $14. Then 14 ÷ 80 = 0.175 = 17.5%.
5 Question 5 of 10
Not answered

A bag contains 6 red, 5 blue, and 4 green marbles. If one marble is selected at random, what is the probability that it is not green?

Hint: Count all marbles that are red or blue, then divide by the total number of marbles.
Explanation: There are 15 marbles total and 11 are not green. Therefore, the probability is 11/15.
6 Question 6 of 10
Not answered

The data set 12, 14, 14, 15, 16, 18, 31 has one high outlier. Which measure of center is most resistant to the outlier?

Hint: Choose the measure of center that depends mainly on position rather than the magnitude of every value.
Explanation: The median is resistant to extreme values because it depends on the middle position in the ordered data, not on the size of every observation.
7 Question 7 of 10
Not answered

A scatterplot shows a strong negative association between x and y. Which statement best describes the relationship?

Hint: A negative association means larger x-values generally correspond to smaller y-values.
Explanation: A strong negative association means that as x increases, y tends to decrease. Association alone does not establish causation.
8 Question 8 of 10
Not answered

A survey of 400 randomly selected students at a large high school finds that 46% prefer a later start time. Which conclusion is most appropriate?

Hint: Think about the population from which the random sample was selected.
Explanation: Because the students were randomly selected from that high school, the sample can be used to estimate the preference of the school population. It does not justify claims about all teenagers or about causation.
9 Question 9 of 10
Not answered

A study finds that students who report more hours of sleep also tend to have higher test scores. Which statement is justified by this result alone?

Hint: An observational association does not by itself establish a cause-and-effect relationship.
Explanation: The study supports an association between reported sleep and test scores, but without a controlled experiment it does not establish causation.
10 Question 10 of 10
Not answered

Two classes have the same mean test score of 82. Class A has a standard deviation of 3, and Class B has a standard deviation of 9. Which statement is true?

Hint: Standard deviation measures how spread out values are around the mean.
Explanation: Because Class B has the larger standard deviation, its scores are more spread out around the mean than Class A scores.

Your result

You answered 0 out of 10 questions correctly.

SAT Data Reasoning Lab

Problem-Solving and Data Analysis connects arithmetic to real data, units, probability, and statistical reasoning

These 10 questions practice ratios, rates, unit conversion, percentages, probability, measures of center and spread, scatterplots, random sampling, inference, and evaluating statistical claims. The emphasis is on interpreting what a number means in context, not merely computing it.

Ratios & rates
Percentages & units
Probability & distributions
Inference & claims
Ratios and unit rates

SAT ratio problems reward normalization: reduce the relationship to one unit, then scale

Ratio scaling

A 5:2 flour-to-sugar ratio becomes easier once the sugar scale factor is known.

3.5 ÷ 2 = 1.75 → 5 × 1.75 = 8.75 cups

Unit rate

Fuel problems are often shortest when converted to miles per gallon first.

315 ÷ 10.5 = 30 mpg → 450 ÷ 30 = 15 gallons
Unit discipline

Units are part of the calculation

2.4 kg
× 1,000 g/kg
= 2,400 g

Percent change uses the original value as the base

For a price increase from $80 to $94, the $14 change is compared with $80, not $94.

change = 94 − 80 = 14
14 ÷ 80 = 0.175
percent increase = 17.5%
Probability model

A probability is favorable outcomes divided by all possible outcomes in the model

With 15 marbles total and 4 green, there are 11 outcomes that are not green.

11 not green4 green
Distribution lab

Center and spread answer different questions about a data set

Outlier resistance

The median is less affected by a very large observation than the mean.

12141415161831
Standard deviation

If two groups have the same mean, the larger standard deviation indicates greater spread around that mean.

Scatterplot reading

Association describes a pattern; it does not prove a cause

A strong negative association means that larger x-values tend to occur with smaller y-values. It does not mean x necessarily causes y to decrease.

Sampling and inference

The sample design determines how far a conclusion can reasonably be generalized

Sample400 randomly selected students
Populationstudents at that high school
Valid inferenceestimate the school-wide proportion
Statistical claims

A valid statistical statement must match the design of the study

Supported

Students who report more sleep also tend to have higher test scores. This describes an association.

Not supported by association alone

More sleep causes higher test scores. A causal claim needs stronger study design than an observed association.

Skill diagnostic

Review the reasoning category behind each missed question

Rates & ratiosunit rates, proportional scaling, contextual comparisons
Units & percentagesconversion factors, original-value base, percent change
Probability & distributionsfavorable outcomes, center, spread, outliers
Inference & claimsrandom samples, population limits, association vs causation