SAT Math Practice Test: Ratios, Rates and Percentages
- Ratios, Rates and Percentages
- 10 questions
- 15 minutes
These 10 questions practice ratios, rates, proportional relationships, unit conversion and percentages from the SAT Problem-Solving and Data Analysis domain. Write the units next to every number; they show whether to multiply or divide.
Tap an option to mark your answer. You can change your mind, or tap the same option again to leave the question blank. The correct answers and explanations appear when you finish the test.Tap an option to answer; tap it again to leave the question blank.
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Question 1
A jacket cost $80. Its price was increased by 15%, and later the new price was decreased by 15%. What was the final price of the jacket?
Correct answer: A
The final price is 80 × 1.15 × 0.85 = $78.20. The two changes do not cancel: the 15% decrease is taken from $92, a larger amount than the original $80.
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Question 2
A car travels at a constant speed of 66 feet per second. What is this speed in miles per hour? (1 mile = 5,280 feet)
Correct answer: B
In one hour the car travels 66 × 3,600 = 237,600 feet, and 237,600 ÷ 5,280 = 45 miles. So the speed is 45 miles per hour.
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Question 3
A painter mixes blue paint and white paint in a ratio of 5 to 3. How many liters of blue paint are in 24 liters of this mixture?
Correct answer: C
The mixture has 5 + 3 = 8 equal parts, so each part is 3 liters and the blue paint is 5 × 3 = 15 liters. The choice 9 is the amount of white paint, and 40 comes from 24 × 5/3.
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Question 4
35% of what number is 84?
Correct answer: C
If 0.35n = 84, then n = 84 ÷ 0.35 = 240. The choice 29.4 is 35% of 84, which reverses the question.
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Question 5
The price of a pair of headphones dropped from $250 to $210. By what percent did the price decrease?
Correct answer: A
The decrease is $40, and 40 ÷ 250 = 0.16, or 16%. The choice 19% divides by the new price, $210, instead of the original price.
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Question 6
A machine fills 450 bottles every 6 minutes. At this rate, how many bottles does the machine fill in 2.5 hours?
Correct answer: D
The rate is 450 ÷ 6 = 75 bottles per minute, and 2.5 hours is 150 minutes, so the machine fills 75 × 150 = 11,250 bottles. The choice 1,125 multiplies 450 by 2.5 without converting hours to minutes.
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Question 7
On a map, 1 inch represents 12 miles. Two towns are 57 miles apart. How far apart, in inches, are the towns on the map?
Correct answer: B
Divide the real distance by the number of miles per inch: 57 ÷ 12 = 4.75 inches. The choice 684 multiplies 57 by 12, which uses the scale backward.
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Question 8
A club's membership grew from 240 to 300 members in one year. If membership grows by the same percent the next year, how many members will the club have?
Correct answer: D
The growth was 60 ÷ 240 = 25%, and 300 × 1.25 = 375. The choice 360 adds the same 60 members again, which is the same amount but a smaller percent.
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Question 9
The quantity y is directly proportional to x, and y = 18 when x = 4. What is the value of y when x = 10?
Correct answer: C
The constant of proportionality is 18 ÷ 4 = 4.5, so y = 4.5 × 10 = 45. The choice 24 adds 6 to 18, treating the relationship as linear with a slope of 1.
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Question 10
A chemist adds 300 milliliters of pure water to 200 milliliters of a solution that is 30% salt. What percent of the new solution is salt?
Correct answer: B
The salt stays 0.30 × 200 = 60 mL, and the total volume becomes 500 mL, so the solution is 60 ÷ 500 = 12% salt. The choice 20% divides 60 by 300, the water added, instead of the total.
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