SAT Math Practice Test: Problem-Solving and Data Analysis
- Problem-Solving and Data Analysis
- 11 questions
- 15 minutes
These questions practice the SAT Problem-Solving and Data Analysis domain: ratios, rates, percentages, unit conversions, statistics, probability and data in tables. Write the units next to every number; conversion mistakes become easy to spot.
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Question 1
The price of a jacket was $80. The price was increased by 15%, and later the new price was decreased by 25%. The final price is what percent less than the original price of $80?
Correct answer: C
After the increase the price is 80(1.15) = $92, and after the decrease it is 92(0.75) = $69. The drop of $11 is 11 ÷ 80 = 13.75% of the original price; simply combining +15% and −25% to get 10% ignores that the two percents apply to different amounts.
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Question 2
A machine fills 45 bottles per minute, and each bottle holds 750 milliliters. How many liters does the machine fill in 2 hours? (1 liter = 1,000 milliliters)
Correct answer: B
In 2 hours, or 120 minutes, the machine fills 45 × 120 = 5,400 bottles, and 5,400 × 0.75 liter = 4,050 liters. The choice 5,400 is the number of bottles, and 4,050,000 is the amount in milliliters.
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Question 3
In a school chess club, the ratio of juniors to seniors is 3 to 5. After 6 more juniors join the club and no seniors join or leave, the ratio of juniors to seniors becomes 3 to 4. How many seniors are in the club?
Correct answer: C
Let the club have 3k juniors and 5k seniors. Then (3k + 6) ÷ 5k = 3/4 gives 12k + 24 = 15k, so k = 8 and there are 5(8) = 40 seniors. The choice 24 is the original number of juniors.
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Question 4
The mean of Dana's first five quiz scores is 84. After she takes a sixth quiz, the mean of all six scores is 86. What is her score on the sixth quiz?
Correct answer: D
The five scores total 5 × 84 = 420, and the six scores must total 6 × 86 = 516, so the sixth score is 516 − 420 = 96. A sixth score of 86 would raise the mean only to about 84.3.
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Question 5
A data set consists of 9 different positive numbers. If the greatest number in the data set is increased by 40, which statement about the mean and the median of the data set must be true?
Correct answer: B
The sum of the data increases by 40, so the mean increases by 40/9. The median is the 5th number in order, and making the greatest number even larger does not change which number is in the middle.
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Question 6
A survey asked 200 students at a high school whether they prefer online or in-person classes. The results are shown in the table.
Online In-person Total Grade 11 38 62 100 Grade 12 54 46 100 Total 92 108 200 If one of the students who prefer online classes is selected at random, what is the probability that the student is in grade 12?
Correct answer: A
The condition limits the choice to the 92 students who prefer online classes, and 54 of them are in grade 12, so the probability is 5492 = 2746. The choice 27100 divides by all 200 students, and 2750 divides by the 100 students in grade 12.
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Question 7
A biology class measured the height of a plant once a week. The line of best fit for the data is y = 2.4x + 18, where y is the plant's height, in centimeters, x weeks after the first measurement. What is the best interpretation of 2.4 in this context?
Correct answer: A
The number 2.4 is the slope, the predicted change in height for each 1-week increase in x. The predicted height at the first measurement (x = 0) is 18 centimeters, not 2.4 centimeters.
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Question 8
In a town, 40% of the residents own a dog, and 25% of the dog owners also own a cat. If 3,600 residents own both a dog and a cat, how many residents live in the town?
Correct answer: D
Residents who own both pets make up 25% of 40%, or 0.25 × 0.40 = 0.10 of the town, so the town has 3,600 ÷ 0.10 = 36,000 residents. The choice 14,400 is the number of dog owners, not the number of residents.
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Question 9
A metal block has a mass of 2.34 kilograms. The density of the metal is 7.8 grams per cubic centimeter. What is the volume of the block, in cubic centimeters? (1 kilogram = 1,000 grams)
Correct answer: C
Volume = mass ÷ density = 2,340 grams ÷ 7.8 grams per cubic centimeter = 300 cubic centimeters. The choice 0.3 skips the conversion from kilograms to grams, and 18,252 multiplies instead of dividing.
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Question 10
Data set X: 4, 8, 8, 8, 12
Data set Y: 4, 4, 8, 12, 12Which statement correctly compares the two data sets?
Correct answer: A
Both sets add up to 40, so both means are 8. In set Y four of the five values are 4 away from the mean, while in set X three values equal the mean, so set Y is more spread out and has the greater standard deviation.
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Question 11
A polling organization surveyed a random sample of 500 registered voters in a city. Of those surveyed, 56% said they support a proposal to build a new public library. The margin of error for this estimate is 4 percentage points. Which conclusion is best supported by the survey?
Correct answer: B
A margin of error describes uncertainty about the whole population, so the true percentage among all registered voters in the city is plausibly 56% ± 4%. The sample percentage itself is known exactly, and a sample from one city says nothing about other cities.
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