Digital SAT chapter 3: Math · Problem-Solving and Data Analysis practice questions with answers

By Team Megalecture · Updated 4 Nov 2026

133 exam-style questions on Math · Problem-Solving and Data Analysis, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

133 questions · 6 topics · 10 per test

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What chapter 3 covers

Ten Math · Problem-Solving and Data Analysis questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A faucet leaks 3 drops of water every 2 seconds. If 20 drops of water make 1 milliliter, how many liters of water does the faucet leak in one day? (1 liter = 1,000 milliliters)

  1. A
    2.88
  2. B
    6.48
  3. C
    64.8
  4. D
    6,480
Show answer

Answer: B. One day has 24 × 60 × 60 = 86,400 seconds, so the faucet leaks 1.5 × 86,400 = 129,600 drops, which is 129,600 ÷ 20 = 6,480 milliliters, or 6.48 liters. 2.88 turns the rate upside down (2/3 drop per second), and 6,480 stops at milliliters.

2. Machine A makes 45 parts per hour, and Machine B makes 30 parts per hour. If both machines work at the same time, how many minutes will it take them to make a total of 300 parts?

  1. A
    240
  2. B
    400
  3. C
    480
  4. D
    1,200
Show answer

Answer: A. Together the machines make 45 + 30 = 75 parts per hour, so 300 parts take 300 ÷ 75 = 4 hours, or 240 minutes. 400 is the time for Machine A alone, and 480 uses the average of the two rates instead of their sum.

3. A farmer randomly selected 200 tomato plants from the plants in her greenhouse. She randomly assigned 100 of them to receive a new fertilizer and the other 100 to receive no fertilizer. On average, the plants that received the fertilizer produced significantly more tomatoes. Which conclusion is best supported?

  1. A
    The new fertilizer causes an increase in the number of tomatoes produced by plants in her greenhouse.
  2. B
    The new fertilizer causes an increase in the number of tomatoes produced by all tomato plants.
  3. C
    The new fertilizer is associated with more tomatoes, but it cannot be concluded that it causes the increase.
  4. D
    The new fertilizer increases the number of tomatoes only for the 200 plants in the study.
Show answer

Answer: A. Random assignment of the fertilizer allows a cause-and-effect conclusion, and because the 200 plants were randomly selected from her greenhouse, the conclusion applies to the plants in her greenhouse. It cannot be extended to all tomato plants, which were not sampled.

4. The function A(m) = 800(1.015)m models the balance, in dollars, of a savings account m months after it was opened. Which of the following is closest to the percent increase in the predicted balance each year?

  1. A
    1.5%
  2. B
    18%
  3. C
    19.6%
  4. D
    119.6%
Show answer

Answer: C. In 12 months the balance is multiplied by 1.01512 ≈ 1.196, an increase of about 19.6%. 1.5% is the monthly increase, 18% adds twelve 1.5% increases without compounding, and 119.6% is the new balance as a percent of the old one.

5. A cheetah can run at a speed of 30 meters per second for short bursts. What is this speed in kilometers per hour? (1 kilometer = 1,000 meters)

  1. A
    1.8
  2. B
    8.3
  3. C
    108
  4. D
    1,800
Show answer

Answer: C. 30 meters per second × 3,600 seconds per hour = 108,000 meters per hour, which is 108 kilometers per hour. 1,800 is the speed in meters per minute, 1.8 is kilometers per minute, and 8.3 divides by 3.6 instead of multiplying.

6. A chemist has 400 milliliters of a solution that is 15% acid by volume. How many milliliters of pure water must be added to make a solution that is 10% acid by volume?

  1. A
    20
  2. B
    40
  3. C
    200
  4. D
    600
Show answer

Answer: C. The solution contains 0.15 × 400 = 60 milliliters of acid. For 60 milliliters to be 10% of the new solution, the total must be 600 milliliters, so 600 − 400 = 200 milliliters of water must be added. 600 is the final volume, not the amount added.

7. Two models are proposed for the value y, in dollars, of a collectible card x years after it was issued: a linear model, y = 50 + 20x, and an exponential model, y = 50(1.25)x. What is the smallest positive integer x for which the exponential model predicts a greater value than the linear model?

  1. A
    3
  2. B
    4
  3. C
    5
  4. D
    6
Show answer

Answer: C. At x = 4 the models give 130 and 50(1.25)4 ≈ 122.1, so the linear model is still greater. At x = 5 they give 150 and about 152.6, so x = 5 is the first positive integer for which the exponential model is greater.

8. A basketball player makes 80% of her free throws, and each free throw is independent of the others. If she attempts 2 free throws, what is the probability that she makes at least one of them?

  1. A
    0.32
  2. B
    0.64
  3. C
    0.80
  4. D
    0.96
Show answer

Answer: D. She misses both with probability 0.2 × 0.2 = 0.04, so the probability that she makes at least one is 1 − 0.04 = 0.96. 0.64 is the probability of making both, and 0.32 is the probability of making exactly one.

9. Researchers took a random sample of students from each of two schools. At School X, the sample mean daily study time was 2.4 hours, with an associated margin of error of 0.3 hour. At School Y, the sample mean was 2.1 hours, with an associated margin of error of 0.4 hour. Which conclusion is best supported?

  1. A
    The mean daily study time of all students at School X is greater than that of all students at School Y.
  2. B
    Every student at School X studies more each day than every student at School Y.
  3. C
    The mean daily study time of all students at School Y is between 2.1 and 2.5 hours.
  4. D
    The data do not show that the mean daily study time at School X is greater than at School Y, because the intervals of plausible values overlap.
Show answer

Answer: D. The plausible values are 2.1 to 2.7 hours for School X and 1.7 to 2.5 hours for School Y. These intervals overlap, so the two schools could have the same mean, and the data do not show that the mean at School X is greater.

10. A line of best fit for a data set passes through the points (2, 15) and (10, 55). Based on this line, what is the predicted value of y when x = 7?

  1. A
    35
  2. B
    38.5
  3. C
    40
  4. D
    45
Show answer

Answer: C. The slope is (55 − 15)/(10 − 2) = 5, and 15 = 5(2) + b gives b = 5, so the line is y = 5x + 5 and y = 40 when x = 7. 35 leaves out the intercept, and 38.5 treats y as proportional to x (7/10 of 55).

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Math · Problem-Solving and Data Analysis: questions students ask

How many Math · Problem-Solving and Data Analysis practice questions are there?

133, each with the answer and a short explanation, across 6 topics: Ratios, rates, proportions and units, Percentages, One-variable data, Two-variable data, Probability, Samples, studies and margin of error. Every chapter test draws ten of them, so you can take it many times.

Is the Digital SAT chapter 3 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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