SAT Math - 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 2 cups of milk. At this rate, how many cups of flour are needed for 8 cups of milk?
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The scale factor from 2 cups of milk to 8 cups is 4.
Therefore, the amount of flour is \(3(4)=12\) cups.
Answer: C
Question 2
A car travels 180 miles in 3 hours at a constant speed. What is the car’s speed, in miles per hour?
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Speed is distance divided by time: \(180\div3=60\) miles per hour.
Answer: B
Question 3
A jacket originally costs $80 and is discounted by 25%. What is the sale price, in dollars?
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The discount is \(0.25(80)=20\) dollars.
The sale price is \(80-20=60\) dollars.
Answer: 60
Question 4
The numbers 4, 7, 7, 9, and 13 form a data set. What is the median?
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The values are already ordered.
The middle value is \(7\).
The median is \(7\).
Answer: A
Question 5
A bag contains 5 red marbles and 15 blue marbles. If one marble is selected at random, what is the probability that it is red?
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Use \(P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}\).
There are \(5+15=20\) marbles total and 5 are red, so \(P(\text{red})=\frac{5}{20}=\frac14\).
Answer: B
Question 6
A map uses a scale of 1 inch to represent 12 miles. Two towns are 3.5 inches apart on the map. How many miles apart are the towns?
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Multiply the map distance by the scale: \(3.5(12)=42\) miles.
Answer: 42
Question 7
The table shows the number of customers at a store on four days. On which day was the number of customers greatest?
| Day | Customers |
|---|---|
| Monday | 42 |
| Tuesday | 55 |
| Wednesday | 48 |
| Thursday | 60 |
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The greatest value in the table is \(60\), which occurred on Thursday.
Answer: D
Question 8
A survey of 200 students found that 70 prefer soccer. What percent of the students prefer soccer?
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\(\frac{70}{200}=0.35\), which is \(35\%\).
Answer: B
Question 9
A store increases the price of an item from $50 to $62. What is the percent increase?
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The increase is \(62-50=12\).
Relative to the original price, \(\frac{12}{50}=0.24\).
The percent increase is \(24\%\).
Answer: C
Question 10
A runner completes 5 kilometers in 24 minutes at a constant rate. At this rate, how many minutes will it take the runner to complete 7.5 kilometers?
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The time scales proportionally: \(24\left(\frac{7.5}{5}\right)=24(1.5)=36\) minutes.
Answer: 36
Question 11
The table summarizes a survey of 120 students. If a Grade 9 student is selected at random, what is the probability that the student plays an instrument?
| Plays an instrument | Does not play an instrument | Total | |
|---|---|---|---|
| Grade 9 | 36 | 24 | 60 |
| Grade 10 | 28 | 32 | 60 |
| Total | 64 | 56 | 120 |
Show solution
Use conditional probability: \(P(\text{instrument}\mid\text{Grade 9})=\frac{\text{Grade 9 and instrument}}{\text{Grade 9}}\).
Substitute the counts: \(P=\frac{36}{60}=\frac35\).
Answer: C
Question 12
The mean of five numbers is 18. Four of the numbers are 12, 16, 19, and 21. What is the fifth number?
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The sum of all five numbers is \(5(18)=90\).
The four known numbers sum to \(68\).
The fifth number is \(90-68=22\).
Answer: B
Question 13
A student’s course grade is based on tests worth 60% and homework worth 40%. The student’s test average is 82 and homework average is 94. What is the student’s course average?
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The weighted average is \(0.60(82)+0.40(94)=49.2+37.6=86.8\).
Answer: B
Question 14
The scatterplot compares hours studied and test score. Which statement best describes the association?
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Points close to an upward-sloping trend indicate a strong positive association.
Answer: D
Question 15
In a random sample of 80 voters, 52 support a proposal. Based on this sample, how many of 500 voters would be expected to support the proposal?
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The sample proportion is \(\frac{52}{80}=0.65\).
Applying this proportion to 500 voters gives \(0.65(500)=325\).
Answer: 325
Question 16
A data set has a mean of 40 and a standard deviation of 3. A second data set has a mean of 40 and a standard deviation of 9. Which statement is true?
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A larger standard deviation indicates greater spread around the mean.
Since \(9>3\), the second data set has greater spread.
Answer: A
Question 17
A survey estimates that 48% of a city’s residents support a new park, with a margin of error of 4 percentage points. Which value is a plausible percentage of all city residents who support the park?
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The estimate gives a plausible interval from \(48\%-4\%=44\%\) to \(48\%+4\%=52\%\).
Since \(51\%\) is within that interval, it is a reasonable estimate.
Answer: C
Question 18
In a group of 120 students, 70 take biology, 55 take chemistry, and 25 take both. If one student is selected at random, what is the probability that the student takes biology or chemistry?
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Use inclusion-exclusion: \(|B\cup C|=|B|+|C|-|B\cap C|\).
So \(|B\cup C|=70+55-25=100\) students.
Use \(P(\text{event})=\frac{\text{favorable outcomes}}{\text{total outcomes}}\): \(P=\frac{100}{120}=\frac56\).
Answer: C
Question 19
A school has 900 students. A stratified random sample includes 36 of the 240 seniors and the same sampling fraction from each other grade. How many students are in the full sample?
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The sampling fraction is \(\frac{36}{240}=0.15\).
Applying the same fraction to all 900 students gives \(0.15(900)=135\).
Answer: 135
Question 20
The scatterplot shows five data points. Which equation is the best linear model for the data?
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For \(y=3x+5\), the predicted values are 11, 17, 23, 29, and 35, which are very close to all five observed values.
The other equations produce substantially larger deviations.
Answer: D