SAT practice test

SAT Problem Solving and Data Analysis Practice Test

Ratios, percents, statistics, probability, scatterplots. 15% of Math. Here are 10 SAT problem solving and data analysis questions, each with the answer and the reason.

Updated 2026-11-14 by the Tigertest team. Original questions written to the digital SAT specifications. Not affiliated with College Board. Score estimates are unofficial.

1. 1.

   The monthly price of a transit pass increased from $80 to $92. By what percent did the price increase?

   • A.

     $12\%$

   • B.

     $13\%$

   • C.

     $15\%$

   • D.

     $115\%$

   Answer: C.

   Percent change is the change divided by the original amount: $\frac{92 - 80}{80} = \frac{12}{80} = 0.15$, so the price increased by $15\%$. The choice $13\%$ divides the change by the new price, $\frac{12}{92} \approx 0.13$, instead of the original price. The choice $12\%$ reports the dollar change as if it were a percent, and $115\%$ is the ratio $\frac{92}{80}$ of the new price to the old price, not the increase.

2. 2.

   The lists give the points scored by two basketball players in each of $5$ games.

   Player A: $12, 14, 16, 18, 20$

   Player B: $8, 14, 16, 18, 24$

   Which of the following statements is true?

   • A.

     The two players have the same mean score, and the standard deviation of Player B's scores is greater than the standard deviation of Player A's scores.

   • B.

     The mean score of Player B is greater than the mean score of Player A.

   • C.

     The median score of Player A is greater than the median score of Player B.

   • D.

     The standard deviations of the two lists are equal because the medians are equal.

   Answer: A.

   Both lists sum to $80$, so both means are $\frac{80}{5} = 16$, and each list has $16$ as its middle value, so the medians are also equal. Standard deviation measures spread about the mean: Player B's scores reach $8$ points from the mean ($8$ and $24$) while Player A's stay within $4$, so B's standard deviation is greater. The choice claiming B's mean is greater is tempting because B has the single highest score, $24$, but the low score of $8$ balances it exactly. Equal medians say nothing about spread, so the choice claiming the standard deviations are equal because the medians are equal is false.

3. 3.

   A city planner surveyed a random sample of $400$ households in a city. In the sample, $54\%$ of the households owned at least one pet, with an associated margin of error of $5\%$. Which of the following conclusions is best supported by these results?

   • A.

     It is plausible that the percent of all households in the city that own at least one pet is between $49\%$ and $59\%$.

   • B.

     Exactly $54\%$ of all households in the city own at least one pet.

   • C.

     Between $49\%$ and $59\%$ of the households in the sample own at least one pet.

   • D.

     If the planner had surveyed $800$ households instead, the margin of error would be larger.

   Answer: A.

   The margin of error gives an interval of plausible values for the population percent: $54\% \pm 5\%$, or $49\%$ to $59\%$, for all households in the city. The sample percent itself is known exactly ($54\%$ of the $400$ households), so the interval does not describe the sample; it describes the uncertainty in generalizing from the sample to the city. The choice 'exactly $54\%$' treats the sample result as the population value with no uncertainty, the most common error. A larger random sample would make the margin of error smaller, not larger.

4. 4.

   A cyclist rides $54$ kilometers in $2.25$ hours at a constant speed. What is the cyclist's speed in meters per minute? ($1$ kilometer $= 1{,}000$ meters)

   • A.

     $24$

   • B.

     $240$

   • C.

     $400$

   • D.

     $1{,}440$

   Answer: C.

   First find the speed in kilometers per hour: $\frac{54}{2.25} = 24$ km per hour. Convert kilometers to meters by multiplying by $1{,}000$ and hours to minutes by dividing by $60$: $\frac{24 \times 1000}{60} = 400$ meters per minute. The choice $24$ is the speed in km per hour without converting. The choice $1{,}440$ multiplies $24$ by $60$ instead of dividing and skips the conversion from kilometers to meters, and $240$ divides by $100$ instead of $60$, as if an hour had $100$ minutes.

5. 5.

   A company has $80$ employees, of whom $50$ work remotely and the rest work in the office. Of the remote employees, $30$ have more than five years of experience, and of the office employees, $12$ have more than five years of experience. If an employee with more than five years of experience is selected at random, what is the probability that the employee works remotely?

   • A.

     $\frac{5}{7}$

   • B.

     $\frac{3}{8}$

   • C.

     $\frac{3}{5}$

   • D.

     $\frac{21}{40}$

   Answer: A.

   The condition restricts the choice to employees with more than five years of experience, so the denominator is that group: $30 + 12 = 42$ employees. Of them, $30$ work remotely, so the probability is $\frac{30}{42} = \frac{5}{7}$. The choice $\frac{3}{8}$ uses all $80$ employees as the denominator, ignoring the condition. The choice $\frac{3}{5}$ answers a different question, the probability that a remote employee has more than five years of experience, and $\frac{21}{40}$ is the fraction of all employees with more than five years of experience.

6. 6.

   A garden hose fills a $60$-gallon tub in $8$ minutes at a constant rate. At this rate, how many gallons does the hose deliver per hour?

   • A.

     $7.5$

   • B.

     $450$

   • C.

     $480$

   • D.

     $750$

   Answer: B.

   First find the rate per minute: $\frac{60}{8} = 7.5$ gallons per minute. An hour has $60$ minutes, so multiply: $7.5 \times 60 = 450$ gallons per hour. The choice $7.5$ is the rate per minute, left unconverted. The choice $480$ multiplies $60 \times 8$ instead of dividing, and $750$ uses $100$ minutes in an hour.

7. 7.

   In a parking garage, the ratio of electric cars to gasoline cars is $2:7$. If the garage holds $126$ cars, all of them electric or gasoline, how many of the cars are electric?

   • A.

     $18$

   • B.

     $28$

   • C.

     $36$

   • D.

     $98$

   Answer: B.

   The ratio $2:7$ splits the cars into $2 + 7 = 9$ equal parts. Each part is $\frac{126}{9} = 14$ cars, so there are $2(14) = 28$ electric cars and $7(14) = 98$ gasoline cars. The choice $36$ comes from $\frac{126}{7} \times 2$, which divides by $7$ instead of by the $9$ total parts, as if the ratio were electric cars to all cars. The choice $98$ is the number of gasoline cars.

8. 8.

   At a high school with $1{,}200$ students, $35\%$ of the students take a world language course. Of the students who take a world language course, $40\%$ take Spanish. How many students at the school take Spanish?

   • A.

     $60$

   • B.

     $168$

   • C.

     $420$

   • D.

     $480$

   Answer: B.

   Apply the percents in order. First, $35\%$ of $1{,}200$ is $0.35 \times 1{,}200 = 420$ students in a world language course. Then $40\%$ of those $420$ is $0.40 \times 420 = 168$. Equivalently, $0.35 \times 0.40 = 0.14$, so $14\%$ of all students take Spanish. The choice $480$ takes $40\%$ of the whole school, but the $40\%$ applies only to language students; $420$ stops after the first step, and $60$ subtracts the percents ($5\%$ of $1{,}200$).

9. 9.

   The commute times, in minutes, of $7$ employees at an office are $12$, $15$, $18$, $20$, $22$, $25$ and $28$. A new employee whose commute time is $95$ minutes joins the office. When the new time is included, how do the mean and the median of the commute times change?

   • A.

     The mean increases by more than the median increases.

   • B.

     The median increases by more than the mean increases.

   • C.

     The mean and the median increase by the same amount.

   • D.

     The mean increases, and the median does not change.

   Answer: A.

   Before: the sum is $140$, so the mean is $\frac{140}{7} = 20$, and the median is the $4$th value, $20$. After: the sum is $235$, so the mean is $\frac{235}{8} = 29.375$, an increase of about $9.4$; the median of $8$ values is the mean of the $4$th and $5$th values, $\frac{20 + 22}{2} = 21$, an increase of $1$. An outlier pulls the mean strongly because its full value enters the sum, but it shifts the median by only one position. The choice saying the median does not change misses that adding a value moves the middle of the list.

10. 10.

    Two researchers each estimate the mean number of hours per week that students at a large university spend at part-time jobs. Researcher 1 uses a random sample of $150$ students, and Researcher 2 uses a random sample of $600$ students from the same university. Which of the following is most likely true?

    • A.

      Researcher 2's estimate has a smaller margin of error than Researcher 1's.

    • B.

      Researcher 2's estimate has a larger margin of error than Researcher 1's.

    • C.

      The two estimates have the same margin of error because both samples are random.

    • D.

      Researcher 2's estimate must equal the true mean for all students at the university.

    Answer: A.

    When samples are drawn at random from the same population, a larger sample tends to give an estimate closer to the population value, so its margin of error is smaller. Researcher 2's sample is $4$ times as large, so Researcher 2's margin of error is most likely smaller. The strongest trap says the margins are equal because both samples are random: random selection removes bias, but it does not make sample size irrelevant. No sample guarantees the estimate equals the true mean; a margin of error describes a range of plausible values.