SAT Problem-Solving & Data Analysis Domain Test

Calculator is allowed on all questions. Figures are not necessarily drawn to scale.

Question 1

A recipe uses 3 cups of flour for every 8 cookies. How many cups of flour are needed to make 24 cookies?

A) 1
B) 3
C) 4.5
D) 9

Show solution

Set up a proportion: $\dfrac{3}{8} = \dfrac{f}{24}$. Solving: $f = \dfrac{3 \times 24}{8} = 9$.

1. 1: Inverted the ratio, computing $\dfrac{3}{24} \times 8$ instead of $\dfrac{3}{8} \times 24$.
1. 3: Reported the scale factor ($24/8=3$) instead of using it to find the flour needed.
1. 4.5: Arithmetic slip, using $\dfrac{3}{8} \times 12$ instead of $\dfrac{3}{8} \times 24$ (halved the cookie count).

Answer: D

Question 2

A train moves 150 miles in 3 hours. At this rate, how many miles will it travel in 5 hours?

A) 125
B) 250
C) 300
D) 375

Show solution

Rate $= 150/3 = 50$ miles per hour. Distance in 5 hours: $50 \times 5 = 250$ miles.

1. 125: Used a rate of 25 mph instead of 50 mph, halving the correct rate.
1. 300: Multiplied the total distance (150) by 2 instead of using the hourly rate.
1. 375: Used a rate of 75 mph, computing $150/2$ instead of $150/3$.

Answer: B

Question 3

A car is 180 inches long. How many feet long is it? (1 foot = 12 inches)

Enter your answer:

Show solution

Divide by the number of inches per foot: $180 \div 12 = 15$ feet.

Answer: 15

Question 4

What is 15% of 80?

A) 8
B) 9.6
C) 12
D) 16

Show solution

$15\% \text{ of } 80 = 0.15 \times 80 = 12$.

1. 8: Used $10\%$ instead of $15\%$, computing $0.10 \times 80$.
1. 9.6: Arithmetic slip computing $0.15 \times 80$.
1. 16: Used $20\%$ instead of $15\%$, computing $0.20 \times 80$.

Answer: C

Question 5

The test scores of seven students are shown in the dot plot below. What is the mode of these scores?

Enter your answer:

Show solution

The mode is the value that appears most often. The dot plot shows two dots stacked above 85, while every other value appears only once, so the mode is $85$.

Answer: 85

Question 6

A bag contains 4 red marbles, 3 blue marbles, and 5 green marbles. If one marble is drawn at random, what is the probability that it is blue?

A) $\dfrac{1}{4}$
B) $\dfrac{1}{3}$
C) $\dfrac{5}{12}$
D) $\dfrac{3}{4}$

Show solution

Total marbles $= 4+3+5=12$. $P(\text{blue}) = \dfrac{3}{12} = \dfrac{1}{4}$.

1. $\dfrac{1}{3}$: Used the wrong denominator (9, forgetting one color) instead of the total of 12.
1. $\dfrac{5}{12}$: Reported the probability of green instead of blue.
1. $\dfrac{3}{4}$: Computed the probability of NOT drawing blue instead of drawing blue.

Answer: A

Question 7

A survey asked 200 people whether they own a car and whether they own a bike. The results are shown in the table below.

	Owns bike	No bike	Total
Owns car	60	90	150
No car	30	20	50
Total	90	110	200

What fraction of those surveyed own a car?

A) $\dfrac{1}{4}$
B) $\dfrac{3}{10}$
C) $\dfrac{9}{20}$
D) $\dfrac{3}{4}$

Show solution

From the table, 150 people own a car out of 200 total. $\dfrac{150}{200} = \dfrac{3}{4}$.

1. $\dfrac{1}{4}$: Reported those who do NOT own a car (50 out of 200) instead of those who do.
1. $\dfrac{3}{10}$: Reported only those who own both a car and a bike (60 out of 200) instead of all car owners.
1. $\dfrac{9}{20}$: Reported bike owners (90 out of 200) instead of car owners.

Answer: D

Question 8

The scatterplot below shows hours studied and test score for six students. Which of the following best describes the association between hours studied and test score?

A) No association
B) A strong positive association
C) A perfect positive association
D) A strong negative association

Show solution

As hours studied increases, test scores also tend to increase, following this upward trend closely but not perfectly. This describes a strong positive association.

1. No association: Failed to recognize the consistent upward pattern.
1. A perfect positive association: Overstated the strength — the points follow a clear upward trend but are not perfectly aligned on a single line.
1. A strong negative association: Misread the upward trend as downward.

Answer: B

Question 9

The cost $y$ of renting a car is proportional to the number of days $d$ rented. If 3 days of rental costs $\$135$, what is the cost of 7 days?

A) $\$180$
B) $\$225$
C) $\$315$
D) $\$360$

Show solution

The unit rate is $135/3 = \$45$ per day. Cost for 7 days: $45 \times 7 = \$315$.

1. $\$180$: Computed only the cost of the 4 additional days ($45 \times 4$) instead of the total cost for all 7 days.
1. $\$225$: Arithmetic slip finding the unit rate, then multiplying by the wrong number of days.
1. $\$360$: Used the correct unit rate but multiplied by 8 days instead of 7.

Answer: C

Question 10

A class of 24 students has an average score of 75 on a test. Another class of 16 students has an average score of 90 on the same test. What is the average score for all 40 students combined?

Enter your answer:

Show solution

Total combined score $= 24(75) + 16(90) = 1800 + 1440 = 3240$. Average for all 40 students: $3240/40 = 81$.

Answer: 81

Question 11

Dataset A and Dataset B are shown in the dot plots below. Both datasets have the same mean (10). Which statement is correct?

A) Dataset B has a greater standard deviation than Dataset A, since its values are farther from the mean.
B) Dataset A has a greater standard deviation than Dataset B.
C) Both datasets have the same standard deviation, since they have the same mean.
D) Standard deviation cannot be determined for either dataset.

Show solution

Standard deviation measures how spread out values are from the mean, not the mean itself. Dataset A’s values are all identical (no spread), while Dataset B’s values are spread widely around the same mean, so Dataset B has a greater standard deviation.

1. Dataset A has a greater standard deviation than Dataset B.: Reverses the correct relationship — Dataset A has zero spread.
1. Both datasets have the same standard deviation, since they have the same mean.: Confuses the mean (a measure of center) with standard deviation (a measure of spread) — equal means do not imply equal spread.
1. Standard deviation cannot be determined for either dataset.: Incorrect — the relative spread is clearly visible from the dot plots even without computing exact values.

Answer: A

Question 12

The boxplot below shows the distribution of test scores for a class. What is the interquartile range (IQR) of the data?

A) 14
B) 16
C) 28
D) 30

Show solution

The interquartile range is $Q_3 - Q_1 = 52 - 22 = 30$.

1. 14: Computed $Q_3 -$ median ($52-38$) instead of $Q_3 - Q_1$.
1. 16: Computed median $- Q_1$ ($38-22$) instead of $Q_3 - Q_1$.
1. 28: Computed max $- Q_3$ ($80-52$) instead of $Q_3 - Q_1$.

Answer: D

Question 13

A jar contains 5 red marbles and 7 blue marbles. If one marble is drawn at random and not replaced, then a second marble is drawn, what is the probability that both marbles are red? (Enter your answer as a decimal, rounded to the nearest hundredth.)

Enter your answer:

Show solution

Total marbles $= 12$. $P(\text{both red}) = \dfrac{5}{12} \times \dfrac{4}{11} = \dfrac{20}{132} = \dfrac{5}{33} \approx 0.15$.

Answer: 0.15

Question 14

A restaurant offers 4 appetizers, 6 entrees, and 3 desserts. How many different three-course meals can be created, choosing one of each?

A) 13
B) 72
C) 96
D) 144

Show solution

By the fundamental counting principle: $4 \times 6 \times 3 = 72$.

1. 13: Added the three counts instead of multiplying them.
1. 96: Used 4 for the dessert count by mistake, computing $4 \times 6 \times 4$.
1. 144: Mistakenly counted each combination twice, doubling the correct answer.

Answer: B

Question 15

The scatterplot below shows a data set along with its line of best fit, $\hat{y} = 2.5x + 10$. Using this line, what is the predicted value of $y$ when $x = 8$?

A) 10
B) 20
C) 30
D) 42.5

Show solution

Substitute $x=8$ into $\hat{y}=2.5x+10$: $\hat{y} = 2.5(8)+10 = 20+10 = 30$.

1. 10: Sign error on the intercept, computing $2.5(8)-10=10$ instead of $2.5(8)+10$.
1. 20: Forgot to add the intercept, computing $2.5(8)$ only.
1. 42.5: Arithmetic slip multiplying $2.5$ by $8$, then adding the intercept.

Answer: C

Question 16

The bar chart below shows a company’s monthly sales, in thousands of dollars. Which of the following best describes the effect of starting the vertical axis at 40 instead of 0?

A) It exaggerates the visual differences between the bars, making small changes in sales look more dramatic than they actually are.
B) It has no effect on how the data is interpreted.
C) It makes the bars look smaller than they actually are.
D) It only affects line graphs, not bar charts.

Show solution

Starting the vertical axis at a nonzero value compresses the visible range, so relatively small differences between bars appear as large proportional differences — exaggerating the visual impression of change.

1. It has no effect on how the data is interpreted.: Ignores that truncating the axis distorts the visual comparison between bars.
1. It makes the bars look smaller than they actually are.: Reverses the actual effect — truncation makes differences look larger, not smaller.
1. It only affects line graphs, not bar charts.: Incorrect — axis truncation distorts any chart type that relies on a zero baseline for visual comparison.

Answer: A

Question 17

A box contains 8 red marbles and 4 blue marbles. Two marbles are drawn without replacement. What is the probability that both are blue? (Enter your answer as a decimal, rounded to the nearest hundredth.)

Enter your answer:

Show solution

These are dependent events, since the marbles are not replaced. Total marbles $= 12$. $P(\text{both blue}) = \dfrac{4}{12} \times \dfrac{3}{11} = \dfrac{12}{132} = \dfrac{1}{11} \approx 0.09$.

Answer: 0.09

Question 18

A researcher observes that cities with more ice cream shops tend to have higher rates of drowning incidents. Which of the following best explains this association?

A) Eating ice cream directly causes drowning.
B) Drowning incidents cause an increase in ice cream shops.
C) There is no relationship between the two variables at all.
D) A third variable, such as warm weather, likely influences both ice cream shop prevalence and drowning incidents, rather than one causing the other.

Show solution

This is a classic confounding-variable scenario: warm weather (especially summer months) likely increases both ice cream sales and outdoor swimming, driving up both ice cream shop activity and drowning incidents, without either directly causing the other.

1. Eating ice cream directly causes drowning.: Mistakes correlation for direct causation without considering alternative explanations.
1. Drowning incidents cause an increase in ice cream shops.: Proposes a causal direction with no plausible mechanism connecting the two.
1. There is no relationship between the two variables at all.: Contradicts the stated observation that the two variables are associated — the question is about interpreting that association correctly, not denying it exists.

Answer: D

Question 19

A jacket originally priced at $80 is marked up by 25%, then later discounted by 20% off the new price. What is the final price?

A) $64
B) $80
C) $84
D) $100

Show solution

After the markup: $80 \times 1.25 = \$100$. After the discount: $100 \times 0.80 = \$80$.

1. $64: Applied only the discount, forgetting the markup: $80 \times 0.80$.
1. $84: Mistakenly combined the two percents into a single net change ($25\%-20\%=5\%$) and applied it directly to the original price.
1. $100: Applied only the markup, forgetting the discount.

Answer: B

Question 20

A student has scores of 82, 88, and 91 on three tests, each weighted equally. What score must the student earn on a fourth test (also weighted equally) to have an overall average of 88 across all four tests?

A) 85
B) 88
C) 91
D) 94

Show solution

For an average of 88 across 4 tests, the total must be $88 \times 4 = 352$. The first three tests sum to $82+88+91=261$. The fourth score must be $352-261=91$.

1. 85: Arithmetic slip computing the required total or the difference.
1. 88: Mistakenly reported the target average itself, without realizing a specific fourth score is needed to reach it.
1. 94: Sign error computing the deficit, overshooting the required score.

Answer: C