Free SAT Math Problem Solving and Data Analysis Practice Test — Questions and Answers

Question 1: A survey of 200 students found that 60% prefer science over history. How many students prefer science?

60
100
120 (Correct answer)
140

Correct answer: 120

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

Question 2: A data set has values: 4, 7, 7, 10, 12. What is the median?

7 (Correct answer)
8
9
10

Correct answer: 7

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

Question 3: A recipe calls for 2.5 cups of flour for every 12 cookies. How many cups are needed for 48 cookies?

5
8
10 (Correct answer)
12

Correct answer: 10

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

Question 4: A car travels 180 miles on 6 gallons of gas. At the same rate, how many gallons are needed for 300 miles?

8
9
10 (Correct answer)
12

Correct answer: 10

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

Question 5: The following data shows test scores: 70, 75, 80, 80, 85, 90, 95. What is the mean?

80
82 (Correct answer)
82.1
85

Correct answer: 82

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

Question 6: A store marks up prices by 30%. If an item costs $40 wholesale, what is the retail price?

$44
$52 (Correct answer)
$56
$70

Correct answer: $52

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

Question 7: 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?

40
60
80 (Correct answer)
100

Correct answer: 80

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

Question 8: Which measure of central tendency is most affected by an outlier?

Mode
Median
Mean (Correct answer)
Range

Correct answer: Mean

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

Question 9: A price decreases from $80 to $60. What is the percent decrease?

20%
25% (Correct answer)
30%
33%

Correct answer: 25%

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

Question 10: 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?

40
43 (Correct answer)
50
63

Correct answer: 43

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

Question 11: In a scatter plot, the data points cluster closely around a line going from lower-left to upper-right. This indicates:

A strong negative correlation
No correlation
A strong positive correlation (Correct answer)
A perfect positive correlation

Correct answer: A strong positive correlation

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

Question 12: A bag has 5 red, 3 blue, and 2 green marbles. What is the probability of drawing a blue marble?

0.2
0.25
0.3 (Correct answer)
0.5

Correct answer: 0.3

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

Question 13: A data set: 3, 5, 5, 7, 8, 10, 10, 10. What is the mode?

5
7
8
10 (Correct answer)

Correct answer: 10

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

Question 14: A runner completes a 5K race in 25 minutes. What is her average speed in minutes per kilometer?

4 min/km
5 min/km (Correct answer)
6 min/km
7 min/km

Correct answer: 5 min/km

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

Question 15: 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?

202 to 248
203 to 247
225 ± 22
Between 204 and 246 (Correct answer)

Correct 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.

Question 16: If a data set has a range of 20 and the maximum value is 35, what is the minimum value?

5
10
15 (Correct answer)
55

Correct answer: 15

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

Question 17: A train travels at 60 mph for 2 hours and then at 80 mph for 1 hour. What is the total distance?

180 miles
200 miles (Correct answer)
220 miles
260 miles

Correct answer: 200 miles

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

Question 18: A data table shows that as hours of study increase, test scores also increase. This is an example of:

Causation
Negative correlation
No relationship
Positive correlation (Correct answer)

Correct answer: Positive correlation

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

Question 19: The box plot of a data set shows Q1 = 30, median = 45, Q3 = 60. What is the interquartile range (IQR)?

15
30 (Correct answer)
45
60

Correct answer: 30

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

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

$55
$60 (Correct answer)
$65
$70

Correct answer: $60

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

Question 21: A histogram shows the number of students who scored in each range. The bars show: 60–70: 5 students, 70–80: 12 students, 80–90: 8 students, 90–100: 3 students. What percentage scored 80 or above?

25%
30%
35% (Correct answer)
39%

Correct answer: 35%

Total = 5+12+8+3 = 28. Students scoring 80+: 8+3 = 11. Percentage = 11/28 ≈ 39.3%. Closest is D, but the intended answer per standard rounding is approximately 39%. Answer is D.

Question 22: A company's revenue grows from $2 million to $2.5 million. What is the percent increase?

20%
25% (Correct answer)
30%
50%

Correct answer: 25%

Percent increase = (change/original) × 100 = (0.5/2) × 100 = 25%.

Question 23: A data set: 10, 14, 18, 22, 26. What is the mean?

16
18 (Correct answer)
20
22

Correct answer: 18

Sum = 10+14+18+22+26 = 90. Mean = 90/5 = 18.

Question 24: In a study, 30% of participants reported headaches after taking a new pill, versus 25% in the placebo group. The difference between groups is:

5 percentage points (Correct answer)
20%
5%
6 percentage points

Correct answer: 5 percentage points

30% - 25% = 5 percentage points. (This is a difference in absolute percentages, not a relative change.)

Question 25: If the probability of rain on any given day is 0.4, what is the probability it does NOT rain?

0.4
0.5
0.6 (Correct answer)
0.8

Correct answer: 0.6

P(not rain) = 1 - P(rain) = 1 - 0.4 = 0.6.

Question 26: A line of best fit for a scatter plot passes through (0, 3) and (4, 11). What does the slope represent?

The starting value
The rate of change per unit increase in x (Correct answer)
The total change
The average y-value

Correct answer: The rate of change per unit increase in x

Slope = (11-3)/(4-0) = 8/4 = 2. In context, the slope represents how much y increases for each 1-unit increase in x — the rate of change.

Question 27: A survey finds the average number of hours of TV watched per week is 14 with a standard deviation of 3. What range captures one standard deviation above and below the mean?

10 to 17
11 to 17 (Correct answer)
11 to 18
12 to 18

Correct answer: 11 to 17

One SD below: 14 - 3 = 11. One SD above: 14 + 3 = 17. The range is 11 to 17.

Question 28: Two events A and B are independent. P(A) = 0.5 and P(B) = 0.4. What is P(A and B)?

0.1
0.2 (Correct answer)
0.45
0.9

Correct answer: 0.2

For independent events: P(A and B) = P(A) × P(B) = 0.5 × 0.4 = 0.2.

Question 29: A company produces items with a defect rate of 2%. If 500 items are produced, about how many are expected to be defective?

5
10 (Correct answer)
15
20

Correct answer: 10

Expected defective = 2% × 500 = 0.02 × 500 = 10 items.

Question 30: The median of a data set is most useful when:

You want to find the most common value
All values are equally important
The data contains extreme outliers (Correct answer)
The data has no repeated values

Correct answer: The data contains extreme outliers

The median is the middle value when data is ordered and is resistant to outliers, making it the best measure of center when extreme values are present.

Question 31: A unit rate problem: If 4 pounds of apples cost $6, what is the cost per pound?

$1.25
$1.50 (Correct answer)
$1.75
$2.00

Correct answer: $1.50

Unit rate = $6 ÷ 4 pounds = $1.50 per pound.

Question 32: A graph shows that as a car's age increases, its value decreases. This shows:

Positive correlation
No correlation
Negative correlation (Correct answer)
Perfect positive correlation

Correct answer: Negative correlation

When one variable increases and the other decreases, this is a negative correlation.

Question 33: A data set has mean 50 and standard deviation 5. A value of 65 is how many standard deviations above the mean?

2
3 (Correct answer)
4
5

Correct answer: 3

z-score = (value - mean) / SD = (65 - 50) / 5 = 15/5 = 3 standard deviations above the mean.

Question 34: A restaurant survey shows that 40% of customers order a salad, 35% order soup, and 15% order both. What percentage orders at least one of these?

50%
55%
60% (Correct answer)
75%

Correct answer: 60%

P(A or B) = P(A) + P(B) - P(A and B) = 40% + 35% - 15% = 60%.

Question 35: The line of best fit for data on advertising spending (x) and sales (y) is y = 200x + 500. What do sales equal when $3 thousand is spent on advertising?

$900
$1,100 (Correct answer)
$1,100 thousand
$2,000

Correct answer: $1,100

Substitute x = 3: y = 200(3) + 500 = 600 + 500 = 1,100.

Question 36: A random sample of 50 students shows an average study time of 3 hours per night. The margin of error is ±0.5 hours. Which statement is correct?

All students study exactly 3 hours
The true average is likely between 2.5 and 3.5 hours (Correct answer)
No student studies less than 2.5 hours
The sample is too small to draw conclusions

Correct answer: The true average is likely between 2.5 and 3.5 hours

A margin of error of ±0.5 means the true population mean likely falls between 3 - 0.5 = 2.5 and 3 + 0.5 = 3.5 hours.

Question 37: A bag has 4 red and 6 blue marbles. What is the probability of drawing two red marbles in a row without replacement?

2/15 (Correct answer)
4/25
1/5
2/5

Correct answer: 2/15

P(first red) = 4/10. P(second red | first red) = 3/9. P(both) = 4/10 × 3/9 = 12/90 = 2/15.

Free SAT Math Problem Solving and Data Analysis Practice Test

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