Free SAT Math Problem Solving and Data Analysis Practice Test Flashcards

A survey of 200 students found that 60% prefer science over history. How many students prefer science?

Answer: 120

60% of 200 = 0.60 × 200 = 120 students.

A data set has values: 4, 7, 7, 10, 12. What is the median?

Answer: 7

Arranged in order: 4, 7, 7, 10, 12. The middle value (3rd of 5) is 7.

A recipe calls for 2.5 cups of flour for every 12 cookies. How many cups are needed for 48 cookies?

Answer: 10

Set up a proportion: 2.5/12 = x/48. Cross-multiply: 12x = 120. x = 10 cups.

A car travels 180 miles on 6 gallons of gas. At the same rate, how many gallons are needed for 300 miles?

Answer: 10

Rate = 180/6 = 30 miles per gallon. Gallons needed = 300/30 = 10 gallons.

The following data shows test scores: 70, 75, 80, 80, 85, 90, 95. What is the mean?

Answer: 82

Sum = 70+75+80+80+85+90+95 = 575. Mean = 575/7 ≈ 82.1. Closest answer is B. 82.

A store marks up prices by 30%. If an item costs $40 wholesale, what is the retail price?

Answer: $52

Markup = 30% × $40 = $12. Retail price = $40 + $12 = $52.

A pie chart shows 25% for sports, 40% for music, 20% for art, and 15% for drama. If 200 students were surveyed, how many prefer music?

Answer: 80

40% of 200 = 0.40 × 200 = 80 students.

Which measure of central tendency is most affected by an outlier?

Answer: Mean

The mean uses all values in its calculation, so extreme outliers pull it significantly. The median is resistant to outliers.

A price decreases from $80 to $60. What is the percent decrease?

Answer: 25%

Percent decrease = (change/original) × 100 = (20/80) × 100 = 25%.

A class of 30 students has a mean score of 74. A new student joins and the class mean drops to 73. What was the new student's score?

Answer: 43

Original total = 30 × 74 = 2220. New total = 31 × 73 = 2263. New student's score = 2263 - 2220 = 43.

In a scatter plot, the data points cluster closely around a line going from lower-left to upper-right. This indicates:

Answer: A strong positive correlation

Data clustering tightly around a line going up to the right shows a strong positive correlation.

A bag has 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?

Answer: 0.3

Total marbles = 5+3+2 = 10. P(blue) = 3/10 = 0.3.

A data set: 3, 5, 5, 7, 8, 10, 10, 10. What is the mode?

Answer: 10

The mode is the most frequently occurring value. 10 appears 3 times, more than any other value.

A runner completes a 5K race in 25 minutes. What is her average speed in minutes per kilometer?

Answer: 5 min/km

Speed = 25 minutes ÷ 5 km = 5 minutes per kilometer.

A poll of 500 people shows 45% approve of a new policy. What is the margin of error if 95% confidence intervals are used with a margin of ±4.4%? How many people approve within that range?

Answer: Between 204 and 246

45% of 500 = 225. Margin = 4.4% of 500 = 22. So the range is 203 to 247. Choice B is most accurate: 203 to 247 people.

If a data set has a range of 20 and the maximum value is 35, what is the minimum value?

Answer: 15

Range = max - min. So 20 = 35 - min. Min = 35 - 20 = 15.

A train travels at 60 mph for 2 hours and then at 80 mph for 1 hour. What is the total distance?

Answer: 200 miles

Distance = rate × time. First part: 60 × 2 = 120 miles. Second: 80 × 1 = 80 miles. Total = 120 + 80 = 200 miles.

A data table shows that as hours of study increase, test scores also increase. This is an example of:

Answer: Positive correlation

When two variables both increase together, they show a positive correlation. Note: correlation does not prove causation.

The box plot of a data set shows Q1 = 30, median = 45, Q3 = 60. What is the interquartile range (IQR)?

Answer: 30

IQR = Q3 - Q1 = 60 - 30 = 30.

An item is on sale for 20% off its original price of $75. What is the sale price?

Answer: $60

Discount = 20% × $75 = $15. Sale price = $75 - $15 = $60.