SAT Problem-Solving and Data Analysis Practice Questions

Problem-Solving and Data Analysis is the smallest math domain, around 5 to 7 questions, but it is calculator-friendly territory where prepared students should drop nothing. It covers ratios and rates, percentages, probability, margin of error, and reading one- and two-variable data.

Its questions are wordier than the rest of SAT math, and that is the real skill being tested: extracting the one relevant relationship from a paragraph of context. Slow down on the setup, and the arithmetic is rarely hard.

1. Question 1Percentages · medium

   A survey was conducted in Madison to estimate the percent of adult residents who support the addition of streetlights at every corner in their town. Based on the survey, it is estimated that 40% of all adult residents of Madison support the addition of streetlights at every corner in their town, with an associated margin of error of 6%. Which of the following is the most appropriate conclusion about all adult residents of Madison?

   APlausible values for the percent of all adult residents of Madison who support the addition of streetlights at every corner in their town are between 34% and 46%.

   BThe addition of streetlights at every corner in the town is supported by exactly 34% of all adult residents of Madison.

   CPlausible values for the percent of all adult residents of Madison who support the addition of streetlights at every corner in their town are either less than 34% or more than 46%.

   DThe addition of streetlights at every corner in the town is supported by more than 46% of all adult residents of Madison.
   Show answer & explanation

   Correct answer: A

   Plausible values for the percent of all adult residents of Madison who support the addition of streetlights at every corner in their town are between 34% and 46%.

   Option A ✓Option BOption COption D

   Option A is correct

   1. A survey estimate with a margin of error defines an interval of plausible values: estimate ± margin.

   2. Here that is $40\% \pm 6\%$, giving the interval from 34% to 46%.

   3. The correct conclusion states exactly that: the true percent of supporting residents plausibly lies between 34% and 46%. A margin of error never pins down an exact value and never pushes the estimate outside its own interval.

   Answer: A.

2. Question 2Probability and conditional probability · hard

   A researcher selected 26 guinea pigs from one habitat and 19 wild cavies from another habitat at random in Venezuela. A field of a specific size within each habitat was divided into equally-sized virtual squares, and the animals were allowed to wander in the field for a fixed amount of time. To observe their behavior, the researcher counted the number of times the guinea pigs and wild cavies crossed the virtual squares in their field during early adolescence and again during late adolescence. The researcher found that in early adolescence, the number of virtual squares the wild cavies crossed was significantly more than the number of virtual squares the guinea pigs crossed. The researcher also found that the number of virtual squares crossed by both the wild cavies and the guinea pigs decreased from early adolescence to late adolescence. Based on the researcher's findings, which of the following statements is an appropriate conclusion that can be drawn from this study?

   AThe statistically significant difference in behavior between the two age groups was caused by aging.

   BThe statistically significant difference in behavior between the two age groups was caused by the differences in habitat.

   CThe statistically significant difference in behavior during early adolescence between the two groups of animals can be generalized to all guinea pigs and wild cavies.

   DThe statistically significant difference in behavior during early adolescence between the two groups of animals can only be generalized to the habitats in the study.
   Show answer & explanation

   Correct answer: D

   The statistically significant difference in behavior during early adolescence between the two groups of animals can only be generalized to the habitats in the study.

   Option AOption BOption COption D ✓

   Option D is correct

   1. This is a study-design question, and two features of the design decide everything. The animals were selected at random from their habitats, and nothing was randomly assigned by the researcher.

   2. Random selection lets results generalize — but only to the populations that were sampled: guinea pigs from the one habitat and wild cavies from the other.

   3. Random assignment is what would permit cause-and-effect conclusions, and there was none: the researcher didn't assign animals to species, habitats, or ages. So no causal claim survives.

   4. That leaves exactly one defensible conclusion: the observed difference can be generalized, but only to the two habitats in the study.

   Answer: D.

3. Question 3Ratios, rates, proportional relationships, and units · hard

   On average, a certain tree grows 87 centimeters every $m$ months. At this rate, which expression represents the number of centimeters, on average, the tree grows every $k$ years?

   A$\frac{29m}{4k}$

   B$\frac{29k}{4m}$

   C$\frac{1{,}044m}{k}$

   D$\frac{1{,}044k}{m}$
   Show answer & explanation

   Correct answer: D

   $\frac{1{,}044k}{m}$

   Option AOption BOption COption D ✓

   Option D is correct

   1. The growth rate is $\tfrac{87}{m}$ centimeters per month (87 cm spread over $m$ months).

   2. $k$ years is $12k$ months.

   3. Multiply rate by time: $\tfrac{87}{m} \cdot 12k = \tfrac{1044k}{m}$ centimeters.

   4. A units check confirms it: $\tfrac{\text{cm}}{\text{month}} \times \text{months}$ leaves centimeters, as required.

   Answer: D.

4. Question 4Two-variable data: Models and scatterplots · easy

   Line $t$ in the $xy$-plane has a slope of $-\tfrac{1}{3}$ and passes through the point $(9,4)$. Which equation defines line $t$?

   A$y = 7x - \tfrac{1}{3}$

   B$y = 9x + 4$

   C$y = -\tfrac{x}{3} + 4$

   D$y = -\tfrac{x}{3} + 7$
   Show answer & explanation

   Correct answer: D

   $y = -\tfrac{x}{3} + 7$

   Option AOption BOption COption D ✓

   Option D is correct

   1. Start from slope-intercept form with the given slope: $y = -\tfrac{1}{3}x + b$.

   2. The line passes through $(9, 4)$, so substitute: $4 = -\tfrac{1}{3}(9) + b = -3 + b$.

   3. Solve: $b = 7$. The equation is $y = -\tfrac{x}{3} + 7$.

   4. Check: at $x = 9$, $y = -3 + 7 = 4$. ✓

   Answer: D.

5. Question 5One-variable data: Distributions and measures of center and spread · medium

   Ari examined a set of 85 plants. The lightest plant had a mass of 2.8 kilograms (kg) and the heaviest plant had a mass of 6.2 kg. Chihiro examined the same set of 85 plants and also an additional plant with a mass of 11.6 kg. Which of the following must be true about the set of plants that Ari examined and the set of plants that Chihiro examined?

   AThe standard deviation of the masses, in kg, of the plants that Ari examined is greater than the standard deviation of the masses, in kg, of the plants that Chihiro examined.

   BThe range of the masses, in kg, of the plants that Ari examined is greater than the range of the masses, in kg, of the plants that Chihiro examined.

   CThe median of the masses, in kg, of the plants that Ari examined is less than the median of the masses, in kg, of the plants that Chihiro examined.

   DThe mean of the masses, in kg, of the plants that Ari examined is less than the mean of the masses, in kg, of the plants that Chihiro examined.
   Show answer & explanation

   Correct answer: D

   The mean of the masses, in kg, of the plants that Ari examined is less than the mean of the masses, in kg, of the plants that Chihiro examined.

   Option AOption BOption COption D ✓

   Option D is correct

   1. Chihiro's set is Ari's 85 plants plus one more at 11.6 kg — heavier than every plant Ari examined (max 6.2 kg).

   2. Adding a value larger than a data set's mean must raise the mean. Since 11.6 exceeds even the maximum, it certainly exceeds the mean, so Chihiro's mean is strictly greater than Ari's.

   3. "Must be true" is the bar, and only the mean statement clears it: the other statistics either move the wrong way (range and standard deviation grow with the outlier, not shrink) or aren't forced to move at all (the median can stay put).

   Answer: D.

6. Question 6Percentages · easy

   Julia purchased 800 feet of fencing. She used 60% of this fencing to surround a vegetable garden. How many feet of fencing did Julia use to surround the vegetable garden?

   A$12$

   B$30$

   C$480$

   D$740$
   Show answer & explanation

   Correct answer: C

   $480$

   Option AOption BOption C ✓Option D

   Option C is correct

   1. "60% of this fencing" means 60% of the 800 feet purchased.

   2. Convert and multiply: $0.60 \times 800 = 480$ feet.

   3. Sanity check: 60% is a bit more than half, and 480 is a bit more than half of 800. ✓

   Answer: C.

7. Question 7Probability and conditional probability · medium

   A machine fills bags with approximately 11 ounces of sugar. To test the accuracy of the filling process, 132 bags of sugar were selected at random and weighed. Based on the sample, it is estimated that the average weight of all bags of sugar filled by the machine in an 8-hour period is 10.83 ounces, with an associated margin of error of 0.2 ounce. Which of the following is the best interpretation of this estimate?

   APlausible values for the average weight of all bags of sugar filled by the machine are between 10.63 ounces and 11.03 ounces.

   BPlausible values for the average weight of all bags of sugar filled by the machine are less than 10.63 ounces or greater than 11.03 ounces.

   CThe average weight of all bags of sugar filled by the machine is greater than 10.98 ounces.

   DThe average weight of all bags of sugar filled by the machine is less than 10.98 ounces.
   Show answer & explanation

   Correct answer: A

   Plausible values for the average weight of all bags of sugar filled by the machine are between 10.63 ounces and 11.03 ounces.

   Option A ✓Option BOption COption D

   Option A is correct

   1. The estimate is 10.83 ounces with a margin of error of 0.2 ounce, so the interval of plausible values is $10.83 \pm 0.2$.

   2. That runs from 10.63 to 11.03 ounces.

   3. The best interpretation states the interval: plausible values for the true average weight lie between 10.63 and 11.03 ounces. Note the interval brackets the machine's target of 11 — the process may well be fine.

   Answer: A.

8. Question 8Ratios, rates, proportional relationships, and units · hard

   A certain investment account offers a special interest rate for the first 4 months the account is open followed by a lower interest rate for the remainder of the time the account is open. Bennett opened one of these accounts with an original account balance of $900 and did not make any other deposits or withdrawals. 4 months after Bennett opened the account, the balance had increased by 0.6% of the original balance. 6 months after Bennett opened the account, the balance had increased by an additional 0.1% of the balance at the end of the first 4 months. Every 2 months after the first 6 months, the balance had increased by an additional 0.1% of the balance 2 months before. Which of the following equations could represent the account balance $B(x)$, in dollars, $x$ months after the account was opened, where $x \ge 4$?

   A$B(x) = 905.40(1.001)^{2x - 8}$

   B$B(x) = 905.40(1.001)^{\frac{x}{2} - \frac{4}{2}}$

   C$B(x) = 905.40(1.001)^{\frac{x}{2} - 4}$

   D$B(x) = 905.40(1.001)^{2x - 4}$
   Show answer & explanation

   Correct answer: B

   $B(x) = 905.40(1.001)^{\frac{x}{2} - \frac{4}{2}}$

   Option AOption B ✓Option COption D

   Option B is correct

   1. After the first 4 months the balance is $900 + 0.6\% \cdot 900 = 905.40$ dollars — that's the 905.40 out front, the starting point for the second phase.

   2. From month 4 onward, the balance grows 0.1% every 2 months, i.e. one factor of 1.001 per 2-month step.

   3. Between month 4 and month $x$ there are $\tfrac{x - 4}{2}$ such steps, so $B(x) = 905.40(1.001)^{\frac{x-4}{2}}$, which is exactly $905.40(1.001)^{\frac{x}{2} - \frac{4}{2}}$.

   4. Check at $x = 6$: exponent $= 1$, one growth step — matches the problem's "6 months after opening" description. ✓

   Answer: B.

9. Question 9Two-variable data: Models and scatterplots · easy

   For the linear function $h$, $h(0) = 0$ and $h(11) = 5$. Which equation defines $h$?

   A$h(x) = \frac{5}{11}x$

   B$h(x) = \frac{5}{11}x + 5$

   C$h(x) = \frac{11}{5}x$

   D$h(x) = \frac{11}{5}x + 11$
   Show answer & explanation

   Correct answer: A

   $h(x) = \frac{5}{11}x$

   Option A ✓Option BOption COption D

   Option A is correct

   1. $h(0) = 0$ means the line passes through the origin — the $y$-intercept is 0, so $h(x) = mx$ with no constant term.

   2. The slope comes from the two points: $m = \tfrac{5 - 0}{11 - 0} = \tfrac{5}{11}$.

   3. So $h(x) = \tfrac{5}{11}x$. Check: $h(11) = \tfrac{5}{11} \cdot 11 = 5$. ✓

   Answer: A.

10. Question 10Percentages · easy

    A furniture company is selling all tables with a 20% discount off their original price for the month of October. What is the discount, in dollars, on a table with an original price of $130?

    A$110$

    B$90$

    C$52$

    D$26$
    Show answer & explanation

    Correct answer: D

    $26$

    Option AOption BOption COption D ✓

    Option D is correct

    1. The question asks for the discount itself, in dollars — not the sale price.

    2. The discount is 20% of the original price: $0.20 \times 130 = 26$ dollars.

    3. (The sale price would then be $130 - 26 = 104$ dollars, but that's not what was asked.)

    Answer: D.