SAT Ratios Practice Questions | Download PDF
70 SAT-style ratio and proportion practice questions with answer choices, full solutions, student-produced responses, and SAT trap notes
Quick Answer
SAT ratios practice questions test whether students can simplify ratios, find equivalent ratios, solve proportions, calculate unit rates, use scales, compare similar figures, and build real-world models. This guide includes 70 SAT-style questions that move from basic part-to-part and part-to-total ratios to harder problems involving mixtures, scale factors, inverse proportions, area, volume, and multi-step relationships.
What Should You Know Before Practicing SAT Ratios?
- A ratio compares quantities in a specific order.
- Equivalent ratios are created by multiplying or dividing every term by the same nonzero number.
- When a total is given, add all ratio parts before finding the value of one part.
- A unit rate compares a quantity with one unit of another quantity.
- Direct proportions grow together, while inverse proportions move in opposite directions.
- Length scales linearly, area scales by the square of the factor, and volume scales by the cube.
- Real-world questions may express ratios as fractions, decimals, rates, percentages, probabilities, or map scales.
In This Guide – 70 SAT Ratios Practice Questions
- What does the SAT test in ratio questions?
- How does the SAT test basic ratios?
- How are unit rates and proportions tested?
- How do scale and similarity questions use ratios?
- How are ratios used in real-world models?
- What do hard SAT ratio questions look like?
- What do student-produced response ratio questions look like?
- What mistakes cost students points?
- How should students study ratios in 2 weeks?
- Frequently asked questions
Start With SAT Math Topic-Wise Practice
When combined with a weekly scoring plan, a mock test review, and focused SAT math correction, ratio practice becomes even more beneficial.
Download the SAT Prep Guide E-Book
Use the SAT Prep Guide E-Book to organize ratio and proportion practice, review SAT math techniques, and connect each practice set to a particular strategy for raising your score.
Download SAT Prep E-Book GuideWhat Does the SAT Test in Ratio Questions?
Ratio questions can be found throughout SAT Math because ratios connect algebra, data analysis, geometry, percentages, and real-world modeling. You can be requested to simplify a comparison, calculate a unit rate, decipher a map scale, divide a total in a specific ratio, find a missing number in a proportion, or compare the areas and volumes of comparable figures.
The best approach is to label each quantity while keeping the designated order. Next, ascertain whether the task produces a total, a unit rate, a scale factor, a difference, or a fixed amount of effort…
| Skill Area | What It Tests | Common SAT Trap | Practice Set |
|---|---|---|---|
| Ratio basics | Simplifying, scaling, and dividing totals | Reversing the requested order | Q1-Q15 |
| Unit rates and proportions | Rates, missing values, direct and inverse relationships | Using the wrong units or direction | Q16-Q30 |
| Scale and similarity | Maps, models, similar figures, area, and volume | Forgetting to square or cube a scale factor | Q31-Q45 |
| Real-world ratio models | Mixtures, budgets, probability, speed, and percentages | Using part-to-part when part-to-total is needed | Q46-Q55 |
| Hard mixed questions | Combined ratios, changing groups, inverse rates, and scale area | Applying only one relationship | Q56-Q70 |
SAT strategy: Ascertain whether the given number represents the difference, the whole, one part, or numerous parts. Keep the same order when writing the ratio with labels.
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How Does the SAT Test Basic Ratios?
Simplifying ratios, identifying equivalent ratios, dividing totals, and linking a known item to its matching ratio term are the main topics of these problems.
RATIO BASICS
EASY
Question 1
What is the simplified form of the ratio 12:18?
Which choice is correct?
A) 2:3
B) 3:2
C) 6:9
D) 4:9
Show full solution
Correct answer: A) 2:3
Divide both parts of 12:18 by their greatest common factor, 6. The result is 2:3.
SAT trap: A ratio should be simplified by dividing both terms by the same number.
RATIO BASICS
EASY
Question 2
A class has 15 boys and 10 girls. What is the ratio of boys to girls in simplest form?
Which choice is correct?
A) 2:3
B) 3:2
C) 5:2
D) 3:5
Show full solution
Correct answer: B) 3:2
The ratio is 15:10. Divide both terms by 5 to get 3:2.
SAT trap: Read the requested order carefully. Boys to girls is not the same as girls to boys.
RATIO BASICS
EASY
Question 3
The ratio of red marbles to blue marbles is 4:7. If there are 33 marbles in total, how many are red?
Which choice is correct?
A) 8
B) 12
C) 18
D) 21
Show full solution
Correct answer: B) 12
There are 4 + 7 = 11 total ratio parts. Each part represents 33/11 = 3 marbles. Red marbles = 4(3) = 12.
SAT trap: Use the sum of the ratio parts when the total number is given.
RATIO BASICS
EASY
Question 4
The ratio of red pens to blue pens is 5:3. If there are 18 blue pens, how many red pens are there?
Which choice is correct?
A) 24
B) 27
C) 30
D) 36
Show full solution
Correct answer: C) 30
Three ratio parts represent 18 pens, so one part represents 6 pens. Red pens = 5(6) = 30.
SAT trap: Match the known quantity to the correct part of the ratio before scaling.
RATIO BASICS
EASY
Question 5
If x:y = 3:5 and x = 24, what is the value of y?
Which choice is correct?
A) 32
B) 36
C) 40
D) 45
Show full solution
Correct answer: C) 40
Since 3 ratio parts equal 24, one part equals 8. Therefore y = 5(8) = 40.
SAT trap: Do not add 2 to 24. Ratios scale multiplicatively.
RATIO BASICS
EASY
Question 6
Which ratio is equivalent to 6:8?
Which choice is correct?
A) 9:10
B) 12:18
C) 15:20
D) 18:20
Show full solution
Correct answer: C) 15:20
The ratio 6:8 simplifies to 3:4. The ratio 15:20 also simplifies to 3:4.
SAT trap: Equivalent ratios must have the same multiplicative scale factor for both terms.
RATIO BASICS
MEDIUM
Question 7
Two numbers are in the ratio 2:9 and have a sum of 55. What is the larger number?
Which choice is correct?
A) 10
B) 35
C) 40
D) 45
Show full solution
Correct answer: D) 45
The ratio has 2 + 9 = 11 parts. Each part is 55/11 = 5. The larger number is 9(5) = 45.
SAT trap: The larger number corresponds to the larger ratio term.
RATIO BASICS
EASY
Question 8
Three identical pens cost $4.50. At the same rate, how much do 8 pens cost?
Which choice is correct?
A) $10.50
B) $12.00
C) $13.50
D) $16.00
Show full solution
Correct answer: B) $12.00
One pen costs $4.50/3 = $1.50. Eight pens cost 8($1.50) = $12.00.
SAT trap: Find the cost per one item before scaling to the requested number.
RATIO BASICS
EASY
Question 9
If a:b = 7:4 and b = 20, what is the value of a?
Which choice is correct?
A) 28
B) 30
C) 35
D) 40
Show full solution
Correct answer: C) 35
Four ratio parts equal 20, so one part equals 5. Then a = 7(5) = 35.
SAT trap: The scale factor must multiply both terms of the ratio.
RATIO BASICS
MEDIUM
Question 10
What is the simplified ratio 0.6:1.5?
Which choice is correct?
A) 2:3
B) 2:5
C) 3:5
D) 5:2
Show full solution
Correct answer: B) 2:5
Multiply both terms by 10 to get 6:15, then divide both by 3 to get 2:5.
SAT trap: Clear decimals from both terms before simplifying.
RATIO BASICS
MEDIUM
Question 11
What is the simplified ratio (1/2):(3/4)?
Which choice is correct?
A) 1:3
B) 2:3
C) 3:2
D) 4:3
Show full solution
Correct answer: B) 2:3
Multiply both terms by the least common denominator, 4. This gives 2:3.
SAT trap: A ratio containing fractions can be simplified by multiplying both terms by a common denominator.
RATIO BASICS
MEDIUM
Question 12
A class has 14 girls and 21 boys. What is the ratio of girls to the total number of students?
Which choice is correct?
A) 2:3
B) 2:5
C) 3:5
D) 5:2
Show full solution
Correct answer: B) 2:5
The total number of students is 14 + 21 = 35. The ratio is 14:35, which simplifies to 2:5.
SAT trap: Part-to-total ratios use the total as the second quantity, not the other category.
RATIO BASICS
HARD
Question 13
If m:n = 5:8 and n:p = 4:3, what is m:p?
Which choice is correct?
A) 5:3
B) 5:6
C) 8:3
D) 10:9
Show full solution
Correct answer: B) 5:6
Make the n terms equal. Since m:n = 5:8 and n:p = 4:3, multiply the second ratio by 2 to get n:p = 8:6. Therefore m:p = 5:6.
SAT trap: When combining ratios, first make the shared quantity equal in both ratios.
RATIO BASICS
MEDIUM
Question 14
Three quantities are in the ratio 4:6:9 and have a total of 57. What is the largest quantity?
Which choice is correct?
A) 18
B) 24
C) 27
D) 36
Show full solution
Correct answer: C) 27
There are 4 + 6 + 9 = 19 parts. Each part is 57/19 = 3. The largest quantity is 9(3) = 27.
SAT trap: For a three-part ratio, add all three terms before finding one part.
RATIO BASICS
MEDIUM
Question 15
The ratio of adults to children at an event is 3:2. If there are 21 adults, how many children are there?
Which choice is correct?
A) 12
B) 14
C) 18
D) 28
Show full solution
Correct answer: B) 14
Three ratio parts equal 21, so one part equals 7. Children = 2(7) = 14.
SAT trap: Keep the category order aligned with the ratio order.
Download More SAT Math Topic-Wise Practice Questions
Strengthen ratios, proportions, percentages, rates, and algebra through focused topic-wise question sets.
How Are Unit Rates and Proportions Tested on the SAT?
These questions use constant rates, direct proportions, inverse relationships, and missing values. Keep units aligned before calculating.
UNIT RATES AND PROPORTIONS
EASY
Question 16
A car travels 180 miles in 3 hours at a constant speed. What is its unit rate in miles per hour?
Which choice is correct?
A) 45
B) 50
C) 60
D) 90
Show full solution
Correct answer: C) 60
Divide distance by time: 180/3 = 60 miles per hour.
SAT trap: A unit rate has a denominator of 1, so divide by the number of hours.
UNIT RATES AND PROPORTIONS
EASY
Question 17
Five notebooks cost $12.50. At the same rate, how much do 8 notebooks cost?
Which choice is correct?
A) $18.00
B) $20.00
C) $22.50
D) $25.00
Show full solution
Correct answer: B) $20.00
One notebook costs $12.50/5 = $2.50. Eight notebooks cost 8($2.50) = $20.00.
SAT trap: Do not multiply 12.50 by 8. First find the price for one notebook.
UNIT RATES AND PROPORTIONS
EASY
Question 18
A recipe uses 3 cups of flour to make 12 muffins. How many cups of flour are needed to make 20 muffins at the same rate?
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: B) 5
The rate is 3/12 = 1/4 cup per muffin. For 20 muffins, use 20(1/4) = 5 cups.
SAT trap: Set up the units consistently so cups correspond to muffins.
UNIT RATES AND PROPORTIONS
EASY
Question 19
On a map, 1 inch represents 25 miles. How many miles are represented by 3.6 inches?
Which choice is correct?
A) 75
B) 80
C) 90
D) 100
Show full solution
Correct answer: C) 90
Multiply the map distance by the scale: 3.6(25) = 90 miles.
SAT trap: A scale is a rate. Multiply only when converting from map units to actual units.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 20
Eight identical machines produce 240 parts in 6 hours. At the same rate, how many parts will 3 machines produce in 4 hours?
Which choice is correct?
A) 40
B) 60
C) 80
D) 120
Show full solution
Correct answer: B) 60
The rate per machine-hour is 240/(8·6) = 5 parts. Three machines working 4 hours provide 12 machine-hours, so they produce 12(5) = 60 parts.
SAT trap: Account for both the number of machines and the number of hours.
UNIT RATES AND PROPORTIONS
EASY
Question 21
If 7/9 = x/27, what is the value of x?
Which choice is correct?
A) 18
B) 19
C) 21
D) 24
Show full solution
Correct answer: C) 21
The denominator 9 is multiplied by 3 to get 27, so multiply 7 by 3. Thus x = 21.
SAT trap: Scale the numerator and denominator by the same factor.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 22
If 4/15 = 12/x, what is the value of x?
Which choice is correct?
A) 30
B) 36
C) 45
D) 60
Show full solution
Correct answer: C) 45
Cross-multiply: 4x = 15(12) = 180. Therefore x = 45.
SAT trap: Cross products are equal, but keep each product on the correct diagonal.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 23
If 0.75/3 = x/10, what is the value of x?
Which choice is correct?
A) 2
B) 2.5
C) 3
D) 7.5
Show full solution
Correct answer: B) 2.5
Since 0.75/3 = 0.25, x/10 = 0.25. Therefore x = 2.5.
SAT trap: Decimals do not change the proportion method. Simplify one side carefully.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 24
Six workers can complete a job in 8 days at the same constant rate. How many days would 12 workers need to complete the same job?
Which choice is correct?
A) 2
B) 4
C) 6
D) 16
Show full solution
Correct answer: B) 4
The job requires 6(8) = 48 worker-days. With 12 workers, the time is 48/12 = 4 days.
SAT trap: Workers and time are inversely proportional for a fixed amount of work.
UNIT RATES AND PROPORTIONS
EASY
Question 25
Four gallons of paint cover 120 square feet. At the same rate, how many square feet will 7 gallons cover?
Which choice is correct?
A) 180
B) 200
C) 210
D) 240
Show full solution
Correct answer: C) 210
One gallon covers 120/4 = 30 square feet. Seven gallons cover 7(30) = 210 square feet.
SAT trap: Find coverage per gallon before multiplying.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 26
A 2.5-kilogram bag of rice costs $18. At the same rate, what is the cost of 4 kilograms?
Which choice is correct?
A) $24.80
B) $27.20
C) $28.80
D) $32.00
Show full solution
Correct answer: C) $28.80
The unit price is $18/2.5 = $7.20 per kilogram. Four kilograms cost 4($7.20) = $28.80.
SAT trap: Dividing by a decimal is often easier after converting it to a fraction or using a calculator carefully.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 27
A train travels 150 miles in 2.5 hours at a constant speed. How far will it travel in 4.25 hours?
Which choice is correct?
A) 225 miles
B) 240 miles
C) 255 miles
D) 270 miles
Show full solution
Correct answer: C) 255 miles
The speed is 150/2.5 = 60 miles per hour. In 4.25 hours, the train travels 60(4.25) = 255 miles.
SAT trap: Use the constant unit rate, not the original total distance.
UNIT RATES AND PROPORTIONS
EASY
Question 28
A drink recipe uses 12 liters for 8 people. How many liters are needed for 14 people at the same rate?
Which choice is correct?
A) 18
B) 20
C) 21
D) 24
Show full solution
Correct answer: C) 21
The rate is 12/8 = 1.5 liters per person. For 14 people, use 14(1.5) = 21 liters.
SAT trap: Check that the final amount grows when the number of people grows.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 29
A scale drawing uses 5 centimeters to represent 2 meters. How many meters are represented by 12.5 centimeters?
Which choice is correct?
A) 4
B) 5
C) 6.25
D) 8
Show full solution
Correct answer: B) 5
The scale is 2/5 = 0.4 meter per centimeter. Therefore 12.5 centimeters represents 12.5(0.4) = 5 meters.
SAT trap: Keep drawing units and actual units in the same positions in the proportion.
UNIT RATES AND PROPORTIONS
MEDIUM
Question 30
If x/14 = 9/21, what is the value of x?
Which choice is correct?
A) 5
B) 6
C) 7
D) 8
Show full solution
Correct answer: B) 6
Simplify 9/21 to 3/7. Since x/14 = 3/7, x = 14(3/7) = 6.
SAT trap: Simplifying the known fraction can make the proportion faster.
Build Accuracy With Targeted SAT Math Practice
Use focused practice to improve unit rates, proportions, scale problems, and real-world SAT Math modeling.
How Do Scale and Similarity Questions Use Ratios?
Scale questions connect drawings, models, maps, similar figures, areas, volumes, and coordinate dilations. Convert units before applying a scale.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 31
A drawing uses a scale of 1:50. If an actual wall is 6 meters long, how long is it on the drawing in centimeters?
Which choice is correct?
A) 6 cm
B) 10 cm
C) 12 cm
D) 30 cm
Show full solution
Correct answer: C) 12 cm
Convert 6 meters to 600 centimeters. At a 1:50 scale, the drawing length is 600/50 = 12 centimeters.
SAT trap: Convert both lengths to the same unit before applying the scale.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 32
The length and width of a rectangle are in the ratio 5:3. If the perimeter is 64, what is the area of the rectangle?
Which choice is correct?
A) 192
B) 224
C) 240
D) 256
Show full solution
Correct answer: C) 240
Let the length be 5k and the width be 3k. Then 2(5k + 3k) = 64, so 16k = 64 and k = 4. The dimensions are 20 and 12, giving area 240.
SAT trap: A perimeter includes two lengths and two widths.
SCALE AND SIMILAR FIGURES
EASY
Question 33
Two similar triangles have a small-to-large side ratio of 2:3. If a side of the smaller triangle is 8, what is the corresponding side of the larger triangle?
Which choice is correct?
A) 10
B) 12
C) 14
D) 16
Show full solution
Correct answer: B) 12
The scale factor from small to large is 3/2. The corresponding side is 8(3/2) = 12.
SAT trap: Use the direction of the scale factor that matches the requested figure.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 34
A model uses a scale of 1:200. If the model height is 7.5 centimeters, what is the actual height in meters?
Which choice is correct?
A) 7.5 m
B) 10 m
C) 15 m
D) 150 m
Show full solution
Correct answer: C) 15 m
The actual height is 7.5(200) = 1,500 centimeters, which is 15 meters.
SAT trap: After scaling, convert centimeters to meters by dividing by 100.
SCALE AND SIMILAR FIGURES
EASY
Question 35
A photograph has a height-to-width ratio of 4:6. If the width is enlarged to 15 inches, what is the new height?
Which choice is correct?
A) 8 inches
B) 10 inches
C) 12 inches
D) 22.5 inches
Show full solution
Correct answer: B) 10 inches
The ratio 4:6 simplifies to 2:3. If the width is 15, the height is 15(2/3) = 10 inches.
SAT trap: Keep height matched with the first ratio term and width with the second.
SCALE AND SIMILAR FIGURES
HARD
Question 36
On a rectangular map, 1 centimeter represents 8 kilometers. A region measures 3 centimeters by 5 centimeters on the map. What is its actual area?
Which choice is correct?
A) 120 square kilometers
B) 320 square kilometers
C) 640 square kilometers
D) 960 square kilometers
Show full solution
Correct answer: D) 960 square kilometers
The actual dimensions are 3(8) = 24 kilometers and 5(8) = 40 kilometers. The area is 24(40) = 960 square kilometers.
SAT trap: For area, scale both dimensions before multiplying.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 37
At the same time of day, a 6-foot person casts a 4-foot shadow. A tree casts an 18-foot shadow. How tall is the tree?
Which choice is correct?
A) 24 feet
B) 27 feet
C) 30 feet
D) 36 feet
Show full solution
Correct answer: B) 27 feet
The height-to-shadow ratio is 6/4 = 3/2. The tree height is 18(3/2) = 27 feet.
SAT trap: Match height with height and shadow with shadow in the proportion.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 38
The perimeters of two similar polygons are in the ratio 5:8. If the smaller perimeter is 45, what is the larger perimeter?
Which choice is correct?
A) 64
B) 68
C) 72
D) 80
Show full solution
Correct answer: C) 72
Set 45/x = 5/8. The scale factor is 45/5 = 9, so x = 8(9) = 72.
SAT trap: Perimeters of similar figures scale by the same factor as corresponding side lengths.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 39
A figure is enlarged by a linear scale factor of 1.5. By what factor does its area change?
Which choice is correct?
A) 1.5
B) 2
C) 2.25
D) 3
Show full solution
Correct answer: C) 2.25
Area scales by the square of the linear factor. Therefore the area factor is 1.5² = 2.25.
SAT trap: Area does not scale linearly. Square the side-length scale factor.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 40
A solid is enlarged by a linear scale factor of 3. By what factor does its volume change?
Which choice is correct?
A) 3
B) 9
C) 18
D) 27
Show full solution
Correct answer: D) 27
Volume scales by the cube of the linear factor. Therefore the volume factor is 3³ = 27.
SAT trap: For three-dimensional figures, cube the linear scale factor.
SCALE AND SIMILAR FIGURES
HARD
Question 41
A blueprint uses 1/4 inch to represent 2 feet. How many inches on the blueprint represent a 15-foot wall?
Which choice is correct?
A) 1.5 inches
B) 1.75 inches
C) 1.875 inches
D) 2 inches
Show full solution
Correct answer: C) 1.875 inches
The blueprint rate is 1/4 inch per 2 feet, or 1/8 inch per foot. For 15 feet, the drawing length is 15/8 = 1.875 inches.
SAT trap: Convert the scale to a per-foot rate before multiplying.
SCALE AND SIMILAR FIGURES
EASY
Question 42
The side lengths of a triangle are in the ratio 3:4:5. If the perimeter is 72, what is the longest side?
Which choice is correct?
A) 18
B) 24
C) 30
D) 36
Show full solution
Correct answer: C) 30
The ratio has 3 + 4 + 5 = 12 parts. Each part is 72/12 = 6. The longest side is 5(6) = 30.
SAT trap: Use all three side-ratio terms when the perimeter is given.
SCALE AND SIMILAR FIGURES
HARD
Question 43
The ratio of corresponding side lengths of two similar figures is 7:9. If the area of the smaller figure is 196, what is the area of the larger figure?
Which choice is correct?
A) 252
B) 288
C) 324
D) 378
Show full solution
Correct answer: C) 324
The area ratio is 7²:9² = 49:81. Since 196/49 = 4, the larger area is 81(4) = 324.
SAT trap: Square the side-length ratio when comparing areas.
SCALE AND SIMILAR FIGURES
MEDIUM
Question 44
Every linear dimension of a cylinder is doubled. By what factor does the cylinder’s volume increase?
Which choice is correct?
A) 2
B) 4
C) 6
D) 8
Show full solution
Correct answer: D) 8
Doubling every linear dimension gives a volume scale factor of 2³ = 8.
SAT trap: Volume depends on three dimensions, so the scale factor is cubed.
SCALE AND SIMILAR FIGURES
EASY
Question 45
A point (-3, 5) is dilated about the origin by a scale factor of 2. What is the image of the point?
Which choice is correct?
A) (-6, 10)
B) (-1.5, 2.5)
C) (6, 10)
D) (-6, 5)
Show full solution
Correct answer: A) (-6, 10)
Multiply both coordinates by 2: (-3·2, 5·2) = (-6, 10).
SAT trap: A dilation multiplies both coordinates by the same scale factor.
Connect Ratio Practice With Your SAT Score Plan
Combine practice questions with mock-test review, timing work, and a weekly correction strategy.
How Are Ratios Used in Real-World SAT Models?
Real-world ratio questions may involve mixtures, budgets, probability, speed, percentages, staffing, or voting. Translate the context into labeled ratio parts.
REAL-WORLD RATIO MODELS
EASY
Question 46
A drink is mixed in a water-to-syrup ratio of 5:2. If 28 liters of drink are made, how many liters are syrup?
Which choice is correct?
A) 6
B) 8
C) 10
D) 20
Show full solution
Correct answer: B) 8
There are 5 + 2 = 7 parts. Each part is 28/7 = 4 liters. Syrup = 2(4) = 8 liters.
SAT trap: Use the syrup term, not the water term, after finding one ratio part.
REAL-WORLD RATIO MODELS
EASY
Question 47
An alloy contains copper and zinc in a ratio of 7:3. How many kilograms of copper are in 50 kilograms of the alloy?
Which choice is correct?
A) 15
B) 21
C) 30
D) 35
Show full solution
Correct answer: D) 35
There are 10 total ratio parts. Each part is 50/10 = 5 kilograms. Copper = 7(5) = 35 kilograms.
SAT trap: The total alloy corresponds to the sum of both ratio terms.
REAL-WORLD RATIO MODELS
MEDIUM
Question 48
A solution is 30% acid by volume. How many liters of acid are in 40 liters of solution?
Which choice is correct?
A) 8
B) 10
C) 12
D) 14
Show full solution
Correct answer: C) 12
Thirty percent is the ratio 30:100, or 3:10. Acid = 0.30(40) = 12 liters.
SAT trap: A percent is a ratio out of 100.
REAL-WORLD RATIO MODELS
EASY
Question 49
A coffee blend contains beans A and B in a ratio of 2:3. If the blend weighs 25 pounds, how many pounds are beans B?
Which choice is correct?
A) 10
B) 12
C) 15
D) 18
Show full solution
Correct answer: C) 15
There are 5 total parts. Each part is 25/5 = 5 pounds. Beans B = 3(5) = 15 pounds.
SAT trap: Identify which blend component matches the requested ratio term.
REAL-WORLD RATIO MODELS
MEDIUM
Question 50
A school maintains a student-to-teacher ratio of 18:1. How many teachers are needed for 504 students?
Which choice is correct?
A) 24
B) 28
C) 32
D) 36
Show full solution
Correct answer: B) 28
Divide the number of students by 18 students per teacher: 504/18 = 28 teachers.
SAT trap: The teacher count is the number of complete groups of 18 students.
REAL-WORLD RATIO MODELS
MEDIUM
Question 51
The ratio of favorable outcomes to total outcomes is 3:8. In 40 trials, how many favorable outcomes would be expected at the same rate?
Which choice is correct?
A) 12
B) 15
C) 18
D) 24
Show full solution
Correct answer: B) 15
The favorable fraction is 3/8. Expected favorable outcomes = 40(3/8) = 15.
SAT trap: Use favorable-to-total as a fraction, not favorable-to-unfavorable.
REAL-WORLD RATIO MODELS
MEDIUM
Question 52
A monthly budget is divided among rent, food, and savings in the ratio 5:3:2. If the total budget is $3,000, how much is allocated to savings?
Which choice is correct?
A) $300
B) $500
C) $600
D) $900
Show full solution
Correct answer: C) $600
There are 10 total parts. Each part is $3,000/10 = $300. Savings receives 2($300) = $600.
SAT trap: The savings category is 2 out of 10 total parts.
REAL-WORLD RATIO MODELS
EASY
Question 53
The speeds of car A and car B are in the ratio 4:5. If car B travels at 75 miles per hour, what is the speed of car A?
Which choice is correct?
A) 55 mph
B) 60 mph
C) 65 mph
D) 70 mph
Show full solution
Correct answer: B) 60 mph
Five ratio parts equal 75, so one part equals 15. Car A travels at 4(15) = 60 miles per hour.
SAT trap: Match car B with the second ratio term.
REAL-WORLD RATIO MODELS
EASY
Question 54
Red paint and white paint are mixed in a ratio of 3:5. How many liters of red paint are needed for 32 liters of mixture?
Which choice is correct?
A) 10
B) 12
C) 16
D) 20
Show full solution
Correct answer: B) 12
There are 8 total parts. Each part is 32/8 = 4 liters. Red paint = 3(4) = 12 liters.
SAT trap: The mixture total corresponds to all ratio parts together.
REAL-WORLD RATIO MODELS
MEDIUM
Question 55
Votes in favor and votes against a proposal are in the ratio 7:5. If 144 votes were cast, how many were in favor?
Which choice is correct?
A) 60
B) 72
C) 84
D) 96
Show full solution
Correct answer: C) 84
There are 12 total parts. Each part is 144/12 = 12 votes. Votes in favor = 7(12) = 84.
SAT trap: Use the sum of favor and against parts for the total number of votes.
Review Every Ratio Mistake Before Your Next Mock Test
Classify each error as a setup, order, unit, scale, or calculation mistake before moving to the next set.
What Do Hard SAT Ratio Questions Look Like?
Hard ratio questions combine multiple relationships, changing quantities, inverse rates, or area scales. Build the structure before calculating.
HARD MIXED RATIO QUESTIONS
HARD
Question 56
If a:b = 2:3 and b:c = 4:5, what is a:c?
Which choice is correct?
A) 2:5
B) 8:15
C) 3:5
D) 8:12
Show full solution
Correct answer: B) 8:15
Make the b terms equal. Multiply 2:3 by 4 to get a:b = 8:12. Multiply 4:5 by 3 to get b:c = 12:15. Therefore a:c = 8:15.
SAT trap: The shared quantity must have the same numerical value before the outer terms can be compared.
HARD MIXED RATIO QUESTIONS
HARD
Question 57
If x:y = 5:7 and y:z = 14:9, what is x:z?
Which choice is correct?
A) 5:9
B) 10:9
C) 10:14
D) 14:9
Show full solution
Correct answer: B) 10:9
Multiply x:y = 5:7 by 2 to get x:y = 10:14. Since y:z = 14:9, x:z = 10:9.
SAT trap: Scale the first ratio so the shared y term matches 14.
HARD MIXED RATIO QUESTIONS
HARD
Question 58
The ratio of boys to girls in a club is 4:5. After 6 boys join, the numbers of boys and girls are equal. How many girls were originally in the club?
Which choice is correct?
A) 24
B) 30
C) 36
D) 45
Show full solution
Correct answer: B) 30
Let boys = 4k and girls = 5k. After 6 boys join, 4k + 6 = 5k, so k = 6. The original number of girls was 5(6) = 30.
SAT trap: Only the number of boys changes, so add 6 to one side of the equation.
HARD MIXED RATIO QUESTIONS
HARD
Question 59
The ratio of red beads to blue beads is 3:4. After 6 red beads are added, the ratio becomes 1:1. How many beads were there originally?
Which choice is correct?
A) 35
B) 42
C) 48
D) 54
Show full solution
Correct answer: B) 42
Let red = 3k and blue = 4k. Then 3k + 6 = 4k, so k = 6. The original total was 3(6) + 4(6) = 42.
SAT trap: The final 1:1 ratio means the two updated category amounts are equal.
HARD MIXED RATIO QUESTIONS
MEDIUM
Question 60
Two numbers are in the ratio 7:11 and differ by 20. What is their sum?
Which choice is correct?
A) 70
B) 80
C) 90
D) 100
Show full solution
Correct answer: C) 90
The difference in ratio parts is 11 – 7 = 4. Four parts equal 20, so one part equals 5. The numbers are 35 and 55, and their sum is 90.
SAT trap: When a difference is given, use the difference between the ratio terms.
HARD MIXED RATIO QUESTIONS
HARD
Question 61
A mixture contains acid and water in a ratio of 2:5. There are 28 liters of mixture. How many liters of water must be added to make the acid-to-water ratio 1:4?
Which choice is correct?
A) 8
B) 10
C) 12
D) 16
Show full solution
Correct answer: C) 12
Each of the seven parts of the original combination is four liters. Eight liters of acid and twenty liters of water. Eight liters of acid and thirty-two liters of water are needed for an acid-to-water ratio of 1:4. 32 minus 20 is 12 liters.
SAT trap: The amount of acid stays fixed because only water is added.
HARD MIXED RATIO QUESTIONS
MEDIUM
Question 62
There is a 20% price increase. The new price is five times the prior amount.Sixth. What was the initial cost if the current price is $72?
Which choice is correct?
A) $54
B) $60
C) $64
D) $66
Show full solution
Correct answer: B) $60
Six ratio parts equal $72, so one part equals $12. The original price is 5($12) = $60.
SAT trap: A 20% increase means new price is 120% of original, giving the ratio 100:120 = 5:6.
HARD MIXED RATIO QUESTIONS
HARD
Question 63
The scale of a map is 1:25,000. On the map, a region is four square centimeters in size. In square kilometers, how big is it?
Which choice is correct?
A) 0.04
B) 0.10
C) 0.25
D) 1.00
Show full solution
Correct answer: C) 0.25
One centimeter is equivalent to 25,000 centimeters, or 250 meters, on this scale. Consequently, 250² = 62,500 square meters is equivalent to 1 square centimeter. 250,000 square meters, or 0.25 square kilometers, are equivalent to four square centimeters.
SAT trap:Square the linear scale for area, then carefully convert to square units.
HARD MIXED RATIO QUESTIONS
HARD
Question 64
A job can be finished by eight personnel in fifteen days. Four more employees join after they have been working for five days. Assuming equal steady rates, how many extra days will it take to complete the job?
Which choice is correct?
A) 5
B) 6
C) 6 2/3
D) 10
Show full solution
Correct answer: C) 6 2/3
8(15) = 120 worker-days are needed to complete the task. The initial workers finish 8(5) = 40 worker-days in 5 days, leaving 80. The remaining time with 12 employees is 80/12 = 20/3 = 6 2/3 days..
SAT trap: Subtract completed work before applying the new worker rate.
HARD MIXED RATIO QUESTIONS
HARD
Question 65
The distance covered by two cars is the same. The ratio between their speeds is 3:4. How many minutes does the slower car take if the faster car takes forty-five minutes
Which choice is correct?
A) 50
B) 55
C) 60
D) 75
Show full solution
Correct answer: C) 60
Time is inversely related to speed over the same distance. As a result, the time ratio is 4:3. The slower car takes 4(15) = 60 minutes if three parts equal 45 minutes and one part is 15.
SAT trap: For equal distances, faster speed means less time, so invert the speed ratio.
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What Do Student-Produced Response Ratio Questions Look Like?
Instead of selecting from four options, student-produced response questions need a numerical response. Enter only the final value and display the ratio configuration.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 66
Two numbers are in the ratio 9:11 and have a sum of 100. What is the smaller number?
Enter your answer as a student-produced response.
Show full solution
Correct answer: 45
There are 9 + 11 = 20 parts. Each part is 100/20 = 5. The smaller number is 9(5) = 45.
SAT trap: Enter only the numerical answer in a student-produced response.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 67
If (x + 2)/18 = 5/6, what is the value of x?
Enter your answer as a student-produced response.
Show full solution
Correct answer: 13
Cross-multiply or multiply both sides by 18: x + 2 = 18(5/6) = 15. Therefore x = 13.
SAT trap: After finding x + 2, subtract 2 to isolate x.
STUDENT-PRODUCED RESPONSE
HARD
Question 68
A scale model uses a ratio of 1:125. An actual object is 25 meters long. What is the model length in centimeters?
Enter your answer as a student-produced response.
Show full solution
Correct answer: 20
Convert 25 meters to 2,500 centimeters. Divide by 125: 2,500/125 = 20 centimeters.
SAT trap: Convert the actual length to the same unit requested for the model.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
A mixture contains two ingredients in the ratio 3:7 and has a total mass of 80 grams. How many grams are the first ingredient?
Enter your answer as a student-produced response.
Show full solution
Correct answer: 24
There are 10 total parts. Each part is 80/10 = 8 grams. The first ingredient is 3(8) = 24 grams.
SAT trap: The first ingredient corresponds to the first ratio term.
STUDENT-PRODUCED RESPONSE
HARD
Question 70
If a:b = 4:9 and b:c = 3:5, and a = 28, what is the value of c?
Enter your answer as a student-produced response.
Show full solution
Correct answer: 105
Make the b terms equal. Multiply b:c = 3:5 by 3 to get b:c = 9:15. Therefore a:b:c = 4:9:15. Since a = 28, the scale factor is 7, so c = 15(7) = 105.
SAT trap: Build a three-part ratio before applying the known value of a.
What Mistakes Cost Students Points on SAT Ratio Questions?
| Common Mistake | Why It Happens | Better SAT Habit |
|---|---|---|
| Reversing the ratio | The quantities are read in the wrong order | Write labels above both terms |
| Using one ratio term as the total | The student skips adding all parts | Circle whether the number is a part, total, or difference |
| Mismatching units | Centimeters, meters, hours, or minutes are mixed | Convert before setting up the proportion |
| Treating inverse variation as direct | More workers or greater speed is assumed to mean more time | Ask whether one quantity should increase or decrease |
| Using a linear factor for area or volume | The scale factor is not squared or cubed | Use k for length, k² for area, and k³ for volume |
| Changing the wrong category | An added or removed amount is applied to both groups | Write the before-and-after quantities separately |
How Should Students Study SAT Ratios in 2 Weeks?
| Days | Practice Focus | Goal |
|---|---|---|
| Days 1-2 | Simplifying and equivalent ratios | Preserve order and scale both terms correctly |
| Days 3-4 | Part-to-part, part-to-total, totals, and differences | Recognize what the given number represents |
| Days 5-6 | Unit rates and proportions | Keep units aligned and solve efficiently |
| Days 7-8 | Maps, models, similarity, area, and volume | Use linear, squared, and cubed scale factors correctly |
| Days 9-10 | Mixtures, percentages, budgets, speed, and probability | Translate contexts into labeled ratios |
| Days 11-12 | Hard mixed and inverse proportion questions | Combine multiple relationships without skipping steps |
| Days 13-14 | Timed mixed set and error review | Correct repeated setup, unit, and scale mistakes |
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