The rules that solve most questions
- A ratio a : b splits a total into a + b equal parts.
- Distance = rate × time. Convert minutes to hours (divide by 60) before multiplying by a per-hour rate.
- Convert with fractions that equal 1, like 12 inches / 1 foot, so the units cancel.
- Square units scale by the square of the conversion: 1 square yard = 9 square feet.
Traps the wrong answers are built on
- Treating 2 hours 30 minutes as 2.30 hours instead of 2.5.
- Converting square units with the linear factor.
Worked example
A square rug measures 21 feet on each side. What is its area in square yards? (1 yard = 3 feet)
- A. 147
- B. 441
- C. 49
- D. 21
Answer: C. Convert the side first: 21 feet = 7 yards. Area = 7 × 7 = 49 square yards. Dividing 441 square feet by 3 is the trap: 1 square yard is 9 square feet, not 3.
Practice set
Answer each question to see whether you're right and why. When you finish, draw a new set: the numbers change every time.
0 of 10 answered · 0 correct · set 1
- Question 1Harder
A square rug measures 21 feet on each side. What is its area in square yards? (1 yard = 3 feet)
Show answer and explanation
Answer: C
Convert the side first: 21 feet = 7 yards.
Area = 7 × 7 = 49 square yards.
Dividing 441 square feet by 3 is the trap: 1 square yard is 9 square feet, not 3.
- Question 2Harder
A square rug measures 27 feet on each side. What is its area in square yards? (1 yard = 3 feet)
Show answer and explanation
Answer: C
Convert the side first: 27 feet = 9 yards.
Area = 9 × 9 = 81 square yards.
Dividing 729 square feet by 3 is the trap: 1 square yard is 9 square feet, not 3.
- Question 3Easier
How many inches are in 9 feet? (1 foot = 12 inches)
Show answer and explanation
Answer: A
Multiply by 12: 9 × 12 = 108 inches.
- Question 4Harder
A square rug measures 15 feet on each side. What is its area in square yards? (1 yard = 3 feet)
Show answer and explanation
Answer: B
Convert the side first: 15 feet = 5 yards.
Area = 5 × 5 = 25 square yards.
Dividing 225 square feet by 3 is the trap: 1 square yard is 9 square feet, not 3.
- Question 5Easier
A train travels at a constant speed of 55 miles per hour. How many miles does it travel in 3 hours?
Show answer and explanation
Answer: C
Convert the time to hours: 3 hours = 3 hours.
Distance = rate × time = 55 × 3 = 165 miles.
- Question 6Medium
The ratio of red marbles to blue marbles in a bag is 3 to 2. If the bag holds 55 marbles in total, how many are red?
Show answer and explanation
Answer: D
The ratio 3:2 splits the bag into 5 equal parts.
Each part is 55 / 5 = 11 marbles.
Red marbles: 3 × 11 = 33.
- Question 7Medium
The ratio of red marbles to blue marbles in a bag is 3 to 7. If the bag holds 60 marbles in total, how many are red?
Show answer and explanation
Answer: C
The ratio 3:7 splits the bag into 10 equal parts.
Each part is 60 / 10 = 6 marbles.
Red marbles: 3 × 6 = 18.
- Question 8Medium
The ratio of red marbles to blue marbles in a bag is 3 to 2. If the bag holds 25 marbles in total, how many are red?
Show answer and explanation
Answer: B
The ratio 3:2 splits the bag into 5 equal parts.
Each part is 25 / 5 = 5 marbles.
Red marbles: 3 × 5 = 15.
- Question 9Easier
How many inches are in 27 feet? (1 foot = 12 inches)
Show answer and explanation
Answer: D
Multiply by 12: 27 × 12 = 324 inches.
- Question 10Medium
The ratio of red marbles to blue marbles in a bag is 4 to 5. If the bag holds 108 marbles in total, how many are red?
Show answer and explanation
Answer: C
The ratio 4:5 splits the bag into 9 equal parts.
Each part is 108 / 9 = 12 marbles.
Red marbles: 4 × 12 = 48.
More Problem-Solving and Data Analysis practice
Questions people ask
Is this ratios, rates and units practice like the real SAT?
The questions follow the format of the digital SAT's Problem-Solving and Data Analysis domain: four answer choices built from common mistakes. They are written for this site; they are not official College Board questions.
How many practice questions are there?
As many as you want. Each math question is generated from a template with new numbers, and its answer is checked by code. Use "New set" for another ten.
Where is the domain on the test?
Problem-Solving and Data Analysis is one of the four content domains of the SAT Math section, alongside Algebra, Advanced Math, Geometry and Trigonometry.