SAT Proportions Practice Questions | Download PDF
70 SAT-style proportion practice questions with answer choices, full solutions, student-produced responses, and SAT trap notes
Quick Answer
SAT proportions practice questions test whether students can identify equivalent relationships, solve missing-value equations, use direct and inverse proportions, work with percentages, interpret scale drawings, and model real-world situations. This guide includes 70 SAT-style questions that begin with basic proportions and move into recipes, prices, speed, similar figures, percent relationships, inverse variation, mixtures, and multi-step models.
What Should You Know Before Practicing SAT Proportions?
- A proportion states that two ratios or rates are equal.
- Corresponding quantities must appear in matching positions.
- Cross-multiplication works because the cross products of equivalent fractions are equal.
- Direct proportions increase or decrease together by the same scale factor.
- Inverse proportions have a constant product, so one quantity increases while the other decreases.
- Percent proportions compare part to whole and percent to 100.
- Similarity questions may require linear, area, or volume scale relationships.
In This Guide – 70 SAT Proportions Practice Questions
- What does the SAT test in proportion questions?
- How does the SAT test basic proportions?
- How are direct proportions used in real-world problems?
- How do percent, scale, and similarity proportions work?
- How does the SAT test inverse proportions?
- What do hard SAT proportion questions look like?
- What do student-produced response questions look like?
- What mistakes cost students points?
- How should students study proportions in 2 weeks?
- Frequently asked questions
Start With SAT Math Topic-Wise Practice
Proportion practice becomes more useful when it is connected to a weekly score plan, mock test review, and targeted SAT Math correction.
Download the SAT Prep Guide E-Book
Use the SAT Prep Guide E-Book to organize proportions, percentages, rates, and similarity practice and connect every practice set with a clear score improvement plan.
Download SAT Prep E-Book GuideWhat Does the SAT Test in Proportion Questions?
Proportion questions appear throughout SAT Math because proportional relationships connect algebra, data analysis, percentages, geometry, rates, and real-world modeling. Students may need to solve an equation, scale a recipe or price, interpret a map, compare similar figures, calculate a missing percentage, or recognize an inverse relationship.
The strongest method is to label each quantity, place corresponding units in the same order, and decide whether the relationship is direct, inverse, percent-based, or geometric before calculating.
| Skill Area | What It Tests | Common SAT Trap | Practice Set |
|---|---|---|---|
| Basic proportions | Equivalent fractions and missing values | Mismatching corresponding quantities | Q1-Q15 |
| Direct proportions | Prices, recipes, rates, maps, and production | Using an additive pattern instead of a scale factor | Q16-Q30 |
| Percent, scale, and similarity | Part-whole relationships and geometric scaling | Using a linear factor for area or volume | Q31-Q45 |
| Inverse proportions | Workers, machines, time, speed, and fixed products | Treating an inverse relationship as direct | Q46-Q55 |
| Hard mixed proportions | Variable expressions, mixtures, samples, and multi-step models | Applying only one of several changing factors | Q56-Q70 |
SAT strategy: Write units beside each value. If the units do not line up vertically in your proportion, the setup probably needs to be reversed.
Download Free SAT Study Resources For U.S. Students
To begin your preparation with organized practice, download our free SAT Prep E-Book, SAT Math Question Bank, and SAT English Question Bank. These tools are intended to assist students in comprehending the style of the Digital SAT, increasing their accuracy, and boosting their self-assurance prior to test day.
How Does the SAT Test Basic Proportions?
These questions focus on equivalent fractions, missing values, cross-multiplication, and equations in which the variable appears inside a numerator or denominator.
PROPORTION BASICS
EASY
Question 1
Solve x/5 = 12/15 for x.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: B) 4
Cross-multiply: 15x = 5(12) = 60. Divide by 15 to get x = 4.
SAT trap: Keep corresponding quantities in the same positions before cross-multiplying.
PROPORTION BASICS
EASY
Question 2
Solve 7/9 = x/27 for x.
Which choice is correct?
A) 18
B) 21
C) 24
D) 27
Show full solution
Correct answer: B) 21
The denominator 9 is multiplied by 3 to become 27, so multiply 7 by 3. Thus x = 21.
SAT trap: Equivalent fractions require the same scale factor in the numerator and denominator.
PROPORTION BASICS
EASY
Question 3
Solve 4/x = 10/25 for x.
Which choice is correct?
A) 8
B) 10
C) 12
D) 16
Show full solution
Correct answer: B) 10
Cross-multiply: 4(25) = 10x. Therefore 100 = 10x and x = 10.
SAT trap: Do not multiply the two numerators together and the two denominators together.
PROPORTION BASICS
EASY
Question 4
Solve x/14 = 9/21 for x.
Which choice is correct?
A) 5
B) 6
C) 7
D) 9
Show full solution
Correct answer: B) 6
The fraction 9/21 simplifies to 3/7. Since x/14 = 3/7, x = 6.
SAT trap: Simplifying first can make a proportion much faster to solve.
PROPORTION BASICS
MEDIUM
Question 5
Solve 3/8 = 15/x for x.
Which choice is correct?
A) 24
B) 32
C) 40
D) 45
Show full solution
Correct answer: C) 40
Cross-multiply: 3x = 8(15) = 120. Divide by 3 to get x = 40.
SAT trap: When the variable is in a denominator, cross-multiply before dividing.
PROPORTION BASICS
EASY
Question 6
Solve 12/18 = x/15 for x.
Which choice is correct?
A) 8
B) 10
C) 12
D) 14
Show full solution
Correct answer: B) 10
Simplify 12/18 to 2/3. Then x/15 = 2/3, so x = 10.
SAT trap: Use the simplified ratio rather than treating 12 and 18 as unrelated values.
PROPORTION BASICS
MEDIUM
Question 7
Solve (x + 2)/10 = 3/5 for x.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: B) 4
Multiply both sides by 10: x + 2 = 6. Subtract 2, so x = 4.
SAT trap: The entire expression x + 2 is the numerator.
PROPORTION BASICS
MEDIUM
Question 8
Solve 5/(x – 1) = 15/24 for x.
Which choice is correct?
A) 7
B) 8
C) 9
D) 10
Show full solution
Correct answer: C) 9
Simplify 15/24 to 5/8. Then 5/(x – 1) = 5/8, so x – 1 = 8 and x = 9.
SAT trap: After finding x – 1, remember to solve for x.
PROPORTION BASICS
MEDIUM
Question 9
Solve x/6 = (x + 4)/10 for x.
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: C) 6
Cross-multiply: 10x = 6(x + 4) = 6x + 24. Then 4x = 24, so x = 6.
SAT trap: Distribute the 6 to both terms inside the parentheses.
PROPORTION BASICS
MEDIUM
Question 10
Solve (2x – 1)/9 = 5/3 for x.
Which choice is correct?
A) 7
B) 8
C) 9
D) 10
Show full solution
Correct answer: B) 8
Multiply both sides by 9: 2x – 1 = 15. Add 1 and divide by 2 to get x = 8.
SAT trap: Clear the denominator before isolating x.
PROPORTION BASICS
EASY
Question 11
Solve 18/24 = 3/x for x.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: B) 4
Simplify 18/24 to 3/4. Since 3/x = 3/4, x = 4.
SAT trap: A proportion can often be solved by recognizing equivalent fractions.
PROPORTION BASICS
MEDIUM
Question 12
Solve (x + 5)/12 = 7/4 for x.
Which choice is correct?
A) 14
B) 16
C) 18
D) 21
Show full solution
Correct answer: B) 16
Multiply by 12: x + 5 = 21. Subtract 5 to get x = 16.
SAT trap: The denominator applies to the complete numerator x + 5.
PROPORTION BASICS
MEDIUM
Question 13
Solve 0.4/1.6 = x/20 for x.
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: B) 5
The fraction 0.4/1.6 equals 1/4. Therefore x/20 = 1/4 and x = 5.
SAT trap: Decimals can be simplified into a familiar fraction before solving.
PROPORTION BASICS
MEDIUM
Question 14
Solve 2.5/4 = x/24 for x.
Which choice is correct?
A) 12
B) 15
C) 18
D) 20
Show full solution
Correct answer: B) 15
Cross-multiply: 4x = 2.5(24) = 60. Divide by 4 to get x = 15.
SAT trap: Keep decimal multiplication accurate before dividing.
PROPORTION BASICS
EASY
Question 15
If 3:x = 12:28, what is the value of x?
Which choice is correct?
A) 6
B) 7
C) 8
D) 9
Show full solution
Correct answer: B) 7
Write 3/x = 12/28. Simplify 12/28 to 3/7, so x = 7.
SAT trap: Preserve the order of both ratios when converting colon notation to fractions.
Strengthen Your SAT Algebra Foundation
Use topic-wise practice to connect proportions with equations, functions, percentages, and real SAT Math timing.
How Are Direct Proportions Used in Real-World Problems?
Direct proportions model situations in which both quantities change by the same multiplicative factor, including cost, recipes, distance, production, map scales, and constant rates.
DIRECT PROPORTIONS
EASY
Question 16
Six notebooks cost $9. At the same rate, how much do 10 notebooks cost?
Which choice is correct?
A) $12
B) $15
C) $18
D) $21
Show full solution
Correct answer: B) $15
Set 6/9 = 10/x or find the unit cost: $9/6 = $1.50. Then 10 notebooks cost $15.
SAT trap: Compare notebooks with notebooks and cost with cost.
DIRECT PROPORTIONS
EASY
Question 17
Four cups of flour make 24 cookies. At the same rate, how many cookies can be made with 10 cups?
Which choice is correct?
A) 48
B) 54
C) 60
D) 64
Show full solution
Correct answer: C) 60
The recipe makes 24/4 = 6 cookies per cup. With 10 cups, it makes 60 cookies.
SAT trap: A direct proportion increases both quantities by the same scale factor.
DIRECT PROPORTIONS
EASY
Question 18
A car travels 180 miles in 3 hours at a constant speed. How far will it travel in 5 hours?
Which choice is correct?
A) 240 miles
B) 270 miles
C) 300 miles
D) 360 miles
Show full solution
Correct answer: C) 300 miles
The speed is 180/3 = 60 miles per hour. In 5 hours, the car travels 60(5) = 300 miles.
SAT trap: Use the constant unit rate before scaling to the new time.
DIRECT PROPORTIONS
MEDIUM
Question 19
Eight tickets cost $52. At the same price per ticket, what is the cost of 15 tickets?
Which choice is correct?
A) $91.50
B) $95.00
C) $97.50
D) $104.00
Show full solution
Correct answer: C) $97.50
Each ticket costs $52/8 = $6.50. Then 15 tickets cost 15($6.50) = $97.50.
SAT trap: Do not round the unit price before completing the multiplication.
DIRECT PROPORTIONS
EASY
Question 20
Three gallons of paint cover 750 square feet. At the same coverage rate, how many square feet will 5 gallons cover?
Which choice is correct?
A) 1,000
B) 1,125
C) 1,250
D) 1,500
Show full solution
Correct answer: C) 1,250
One gallon covers 750/3 = 250 square feet. Five gallons cover 1,250 square feet.
SAT trap: The covered area is directly proportional to the amount of paint.
DIRECT PROPORTIONS
EASY
Question 21
A machine produces 45 parts in 6 minutes. At the same rate, how many parts does it produce in 14 minutes?
Which choice is correct?
A) 90
B) 100
C) 105
D) 112
Show full solution
Correct answer: C) 105
The machine produces 45/6 = 7.5 parts per minute. In 14 minutes, it produces 7.5(14) = 105 parts.
SAT trap: A rate may be a decimal and still produce a whole-number result.
DIRECT PROPORTIONS
EASY
Question 22
Five liters of paint cover 140 square meters. At the same rate, how many square meters will 8 liters cover?
Which choice is correct?
A) 196
B) 210
C) 224
D) 240
Show full solution
Correct answer: C) 224
One liter covers 140/5 = 28 square meters. Eight liters cover 28(8) = 224 square meters.
SAT trap: Find the amount for one unit before multiplying by the new quantity.
DIRECT PROPORTIONS
EASY
Question 23
On a map, 1 inch represents 24 miles. How many miles are represented by 3.5 inches?
Which choice is correct?
A) 72
B) 78
C) 84
D) 96
Show full solution
Correct answer: C) 84
Multiply the map length by the scale: 3.5(24) = 84 miles.
SAT trap: Map distance and real distance must remain in corresponding positions.
DIRECT PROPORTIONS
MEDIUM
Question 24
A map scale shows that 2 centimeters represent 15 kilometers. What actual distance is represented by 8.4 centimeters?
Which choice is correct?
A) 56 km
B) 60 km
C) 63 km
D) 67.5 km
Show full solution
Correct answer: C) 63 km
The scale is 15/2 = 7.5 kilometers per centimeter. Then 8.4(7.5) = 63 kilometers.
SAT trap: Do not treat 8.4 as if it were 8; retain the decimal throughout.
DIRECT PROPORTIONS
MEDIUM
Question 25
A recipe uses 3 cups of rice for 8 servings. How many cups are needed for 12 servings?
Which choice is correct?
A) 4
B) 4.5
C) 5
D) 6
Show full solution
Correct answer: B) 4.5
Set 3/8 = x/12. Cross-multiply: 8x = 36, so x = 4.5 cups.
SAT trap: A proportional answer does not always need to be a whole number.
DIRECT PROPORTIONS
EASY
Question 26
Seven ounces of cheese cost $4.90. At the same rate, how much do 12 ounces cost?
Which choice is correct?
A) $7.20
B) $8.00
C) $8.40
D) $9.10
Show full solution
Correct answer: C) $8.40
The unit price is $4.90/7 = $0.70 per ounce. Twelve ounces cost $8.40.
SAT trap: Use dollars per ounce, not ounces per dollar, when finding cost.
DIRECT PROPORTIONS
MEDIUM
Question 27
A student reads 9 pages in 12 minutes at a constant rate. How many pages can the student read in 30 minutes?
Which choice is correct?
A) 18
B) 20
C) 22.5
D) 27
Show full solution
Correct answer: C) 22.5
The reading rate is 9/12 = 0.75 page per minute. In 30 minutes, the student reads 22.5 pages.
SAT trap: The mathematical model can produce a fractional page even if a practical answer might be rounded.
DIRECT PROPORTIONS
MEDIUM
Question 28
Five identical printers produce 1,200 pages in 10 minutes. How many pages will 8 printers produce in 10 minutes?
Which choice is correct?
A) 1,600
B) 1,800
C) 1,920
D) 2,400
Show full solution
Correct answer: C) 1,920
For the same time, output is proportional to the number of printers. Multiply 1,200 by 8/5 to get 1,920 pages.
SAT trap: The time is unchanged, so only the printer count creates the scale factor.
DIRECT PROPORTIONS
MEDIUM
Question 29
A car uses 11 gallons of fuel to travel 330 miles. At the same fuel efficiency, how many gallons are needed to travel 495 miles?
Which choice is correct?
A) 14.5
B) 15
C) 16.5
D) 18
Show full solution
Correct answer: C) 16.5
The car travels 330/11 = 30 miles per gallon. It needs 495/30 = 16.5 gallons.
SAT trap: To find fuel needed, divide distance by miles per gallon.
DIRECT PROPORTIONS
HARD
Question 30
Fourteen volunteers pack 630 kits in 3 hours. At the same individual rate, how many kits can 20 volunteers pack in 3 hours?
Which choice is correct?
A) 810
B) 840
C) 900
D) 960
Show full solution
Correct answer: C) 900
With time fixed, the number of kits is proportional to volunteers. Compute 630(20/14) = 900.
SAT trap: Do not multiply by both the volunteer ratio and the time because the time does not change.
How Do Percent, Scale, and Similarity Proportions Work?
These questions use part-to-whole relationships, percent equations, scale drawings, similar figures, shadows, and geometric scale factors.
PERCENT AND SCALE PROPORTIONS
EASY
Question 31
18 is 30% of what number?
Which choice is correct?
A) 54
B) 60
C) 72
D) 90
Show full solution
Correct answer: B) 60
Set 18/x = 30/100. Cross-multiply: 30x = 1,800, so x = 60.
SAT trap: The unknown whole belongs under the part in a percent proportion.
PERCENT AND SCALE PROPORTIONS
EASY
Question 32
What number is 45% of 80?
Which choice is correct?
A) 32
B) 36
C) 40
D) 45
Show full solution
Correct answer: B) 36
Set x/80 = 45/100 or calculate 0.45(80) = 36.
SAT trap: Convert 45% to 0.45, not 45, when multiplying.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 33
A jacket costs $64 after a 20% discount. What was the original price?
Which choice is correct?
A) $72
B) $76.80
C) $80
D) $84
Show full solution
Correct answer: C) $80
After a 20% discount, the sale price is 80% of the original. Set 64/x = 80/100, giving x = 80.
SAT trap: The sale price represents 80% of the original, not 20%.
PERCENT AND SCALE PROPORTIONS
EASY
Question 34
A town’s new population is 125% of its previous population of 24,000. What is the new population?
Which choice is correct?
A) 27,000
B) 28,800
C) 30,000
D) 31,250
Show full solution
Correct answer: C) 30,000
Multiply 24,000 by 1.25 to get 30,000.
SAT trap: A value of 125% means the new amount is 1.25 times the original.
PERCENT AND SCALE PROPORTIONS
EASY
Question 35
In a group of 75 students, 40% participate in a club. How many students participate?
Which choice is correct?
A) 25
B) 30
C) 35
D) 40
Show full solution
Correct answer: B) 30
Set x/75 = 40/100 or compute 0.40(75) = 30.
SAT trap: The part must be smaller than the whole when the percentage is below 100%.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 36
A solution is 30% concentrate. How many liters of concentrate are in 18 liters of solution?
Which choice is correct?
A) 4.5
B) 5.4
C) 6
D) 7.2
Show full solution
Correct answer: B) 5.4
Multiply the total volume by the concentration: 0.30(18) = 5.4 liters.
SAT trap: Use the total solution as the whole in the percent proportion.
PERCENT AND SCALE PROPORTIONS
EASY
Question 37
Two similar triangles have corresponding sides 6 and 9. If another side of the smaller triangle is 10, what is the corresponding side of the larger triangle?
Which choice is correct?
A) 12
B) 14
C) 15
D) 18
Show full solution
Correct answer: C) 15
The scale factor from smaller to larger is 9/6 = 3/2. Multiply 10 by 3/2 to get 15.
SAT trap: Use corresponding sides in the same order.
PERCENT AND SCALE PROPORTIONS
EASY
Question 38
The corresponding lengths of two similar rectangles are in the ratio 4:7. If the smaller width is 12, what is the larger width?
Which choice is correct?
A) 18
B) 20
C) 21
D) 24
Show full solution
Correct answer: C) 21
Set 4/7 = 12/x. Cross-multiply: 4x = 84, so x = 21.
SAT trap: The larger rectangle must have the larger corresponding dimension.
PERCENT AND SCALE PROPORTIONS
EASY
Question 39
A model uses a scale of 1:50. If a wall is 8 centimeters long on the model, how long is the actual wall?
Which choice is correct?
A) 200 cm
B) 300 cm
C) 400 cm
D) 450 cm
Show full solution
Correct answer: C) 400 cm
Multiply the model length by 50: 8(50) = 400 centimeters.
SAT trap: A 1:50 scale means one model unit represents 50 actual units.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 40
Two similar figures have a linear scale factor of 3. If the smaller figure has an area of 20 square units, what is the area of the larger figure?
Which choice is correct?
A) 60
B) 120
C) 180
D) 540
Show full solution
Correct answer: C) 180
Area scales by the square of the linear factor. Multiply 20 by 3² = 9 to get 180.
SAT trap: Area does not scale by the same factor as length.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 41
The areas of two similar figures are in the ratio 4:9. If the smaller area is 32 square units, what is the larger area?
Which choice is correct?
A) 54
B) 64
C) 72
D) 81
Show full solution
Correct answer: C) 72
Set 4/9 = 32/x. Cross-multiply: 4x = 288, so x = 72.
SAT trap: When the ratio already compares areas, do not square it again.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 42
Two similar solids have a linear scale factor of 2. If the smaller solid has a volume of 35 cubic units, what is the larger volume?
Which choice is correct?
A) 70
B) 140
C) 210
D) 280
Show full solution
Correct answer: D) 280
Volume scales by the cube of the linear factor. Multiply 35 by 2³ = 8 to get 280.
SAT trap: Volume uses the cube of the scale factor.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 43
A circle with diameter 14 has a circumference of 44. Using the same value of π, what is the circumference of a circle with diameter 21?
Which choice is correct?
A) 55
B) 60
C) 66
D) 72
Show full solution
Correct answer: C) 66
Circumference is proportional to diameter. Set 44/14 = x/21, giving x = 66.
SAT trap: Circumference changes directly with diameter, not with diameter squared.
PERCENT AND SCALE PROPORTIONS
MEDIUM
Question 44
A 6-foot pole casts an 8-foot shadow. At the same time, a tree casts a 28-foot shadow. How tall is the tree?
Which choice is correct?
A) 18 ft
B) 20 ft
C) 21 ft
D) 24 ft
Show full solution
Correct answer: C) 21 ft
Set height/shadow equal: 6/8 = x/28. Cross-multiply to get 8x = 168, so x = 21.
SAT trap: Match height with height and shadow with shadow.
PERCENT AND SCALE PROPORTIONS
EASY
Question 45
48 is what percent of 160?
Which choice is correct?
A) 24%
B) 30%
C) 32%
D) 40%
Show full solution
Correct answer: B) 30%
Set 48/160 = p/100. Since 48/160 = 0.30, p = 30.
SAT trap: Multiply the decimal ratio by 100 to convert it to a percentage.
Practice More SAT Problem-Solving and Data Analysis
Build accuracy with percentages, unit rates, proportions, scale drawings, and data-based SAT Math question sets.
How Does the SAT Test Inverse Proportions?
Inverse proportions appear when a fixed amount of work, distance, food, area, or production is shared across changing rates, workers, machines, or time periods.
INVERSE PROPORTIONS
EASY
Question 46
Six workers complete a job in 10 days. At the same individual rate, how many days will 12 workers need?
Which choice is correct?
A) 4
B) 5
C) 6
D) 8
Show full solution
Correct answer: B) 5
The total work is 6(10) = 60 worker-days. Divide by 12 workers to get 5 days.
SAT trap: More workers mean fewer days, so the relationship is inverse.
INVERSE PROPORTIONS
MEDIUM
Question 47
Four identical pumps empty a tank in 15 hours. How long will 10 identical pumps take?
Which choice is correct?
A) 5 hours
B) 6 hours
C) 7.5 hours
D) 9 hours
Show full solution
Correct answer: B) 6 hours
Pump-hours remain constant: 4(15) = 60. Then 60/10 = 6 hours.
SAT trap: Do not use a direct proportion when one quantity increases as the other decreases.
INVERSE PROPORTIONS
EASY
Question 48
A trip takes 4 hours at 60 miles per hour. How long will the same trip take at 80 miles per hour?
Which choice is correct?
A) 2.5 hours
B) 3 hours
C) 3.5 hours
D) 4.5 hours
Show full solution
Correct answer: B) 3 hours
The distance is 60(4) = 240 miles. At 80 miles per hour, time = 240/80 = 3 hours.
SAT trap: For a fixed distance, speed and time are inversely proportional.
INVERSE PROPORTIONS
MEDIUM
Question 49
Eight machines complete an order in 9 hours. How many hours will 12 identical machines need?
Which choice is correct?
A) 5
B) 6
C) 7
D) 8
Show full solution
Correct answer: B) 6
The order requires 8(9) = 72 machine-hours. Divide by 12 machines to get 6 hours.
SAT trap: Keep the total amount of work fixed.
INVERSE PROPORTIONS
MEDIUM
Question 50
Five identical faucets fill a tank in 24 minutes. How long will 8 faucets take?
Which choice is correct?
A) 12 minutes
B) 15 minutes
C) 18 minutes
D) 20 minutes
Show full solution
Correct answer: B) 15 minutes
The tank requires 5(24) = 120 faucet-minutes. Divide by 8 to get 15 minutes.
SAT trap: Adding faucets reduces the required time.
INVERSE PROPORTIONS
MEDIUM
Question 51
A 20-tooth gear turns at 60 revolutions per minute. If rotational speed is inversely proportional to the number of teeth, how fast will a 30-tooth gear turn?
Which choice is correct?
A) 36 rpm
B) 40 rpm
C) 45 rpm
D) 50 rpm
Show full solution
Correct answer: B) 40 rpm
The product of teeth and speed is constant: 20(60) = 30x. Thus x = 40 rpm.
SAT trap: More teeth correspond to a lower rotational speed in this model.
INVERSE PROPORTIONS
EASY
Question 52
Food for 18 people lasts 20 days. How many days will the same amount of food last for 24 people?
Which choice is correct?
A) 12
B) 15
C) 16
D) 18
Show full solution
Correct answer: B) 15
The food supply represents 18(20) = 360 person-days. Divide by 24 to get 15 days.
SAT trap: The total amount of food stays fixed while the number of people changes.
INVERSE PROPORTIONS
MEDIUM
Question 53
Three identical printers complete a job in 50 minutes. How long will five identical printers take?
Which choice is correct?
A) 25 minutes
B) 30 minutes
C) 35 minutes
D) 40 minutes
Show full solution
Correct answer: B) 30 minutes
The job requires 3(50) = 150 printer-minutes. Divide by 5 to get 30 minutes.
SAT trap: Use inverse proportion only because every printer is assumed to work at the same rate.
INVERSE PROPORTIONS
MEDIUM
Question 54
Sixteen students can complete a project in 3 hours. At the same individual rate, how long will 12 students need?
Which choice is correct?
A) 3.5 hours
B) 4 hours
C) 4.5 hours
D) 5 hours
Show full solution
Correct answer: B) 4 hours
The project requires 16(3) = 48 student-hours. Divide by 12 to get 4 hours.
SAT trap: Fewer students require more time for the same project.
INVERSE PROPORTIONS
MEDIUM
Question 55
A rectangle has a fixed area of 96 square units. If its length changes from 12 to 16, what is its new width?
Which choice is correct?
A) 5
B) 6
C) 7
D) 8
Show full solution
Correct answer: B) 6
For fixed area, length and width are inversely proportional. The new width is 96/16 = 6.
SAT trap: A fixed product creates an inverse relationship.
What Do Hard SAT Proportion Questions Look Like?
Hard questions may include variables in multiple expressions, mixtures, area scaling, exchange rates, survey projections, or more than one changing factor.
HARD MIXED PROPORTIONS
HARD
Question 56
Solve (x + 3)/(x – 1) = 2 for x.
Which choice is correct?
A) 3
B) 4
C) 5
D) 6
Show full solution
Correct answer: C) 5
Multiply both sides by x – 1: x + 3 = 2x – 2. Add 2 and subtract x to get x = 5.
SAT trap: The denominator cannot equal zero, but x = 5 is valid.
HARD MIXED PROPORTIONS
HARD
Question 57
Solve 4/(x + 2) = 6/(2x + 1) for x.
Which choice is correct?
A) 2
B) 3
C) 4
D) 5
Show full solution
Correct answer: C) 4
Cross-multiply: 4(2x + 1) = 6(x + 2). Then 8x + 4 = 6x + 12, so 2x = 8 and x = 4.
SAT trap: Distribute on both sides after cross-multiplying.
HARD MIXED PROPORTIONS
HARD
Question 58
Solve (2x + 5)/7 = (x – 1)/3 for x.
Which choice is correct?
A) 18
B) 20
C) 22
D) 24
Show full solution
Correct answer: C) 22
Cross-multiply: 3(2x + 5) = 7(x – 1). Then 6x + 15 = 7x – 7, so x = 22.
SAT trap: A negative sign inside parentheses affects the complete term.
HARD MIXED PROPORTIONS
HARD
Question 59
Solve 3/(x – 2) = 5/(x + 4) for x.
Which choice is correct?
A) 9
B) 10
C) 11
D) 12
Show full solution
Correct answer: C) 11
Cross-multiply: 3(x + 4) = 5(x – 2). Then 3x + 12 = 5x – 10, so 22 = 2x and x = 11.
SAT trap: Check that the solution does not make either denominator zero.
HARD MIXED PROPORTIONS
HARD
Question 60
How many liters of a 30% solution should be mixed with a 50% solution to make 20 liters of a 40% solution?
Which choice is correct?
A) 6 liters
B) 8 liters
C) 10 liters
D) 12 liters
Show full solution
Correct answer: C) 10 liters
Let x be liters of 30% solution. Then 0.30x + 0.50(20 – x) = 0.40(20). Solving gives x = 10.
SAT trap: The two mixture amounts must add to the total of 20 liters.
HARD MIXED PROPORTIONS
HARD
Question 61
The perimeters of two similar figures are in the ratio 5:8. If the smaller figure has an area of 75 square units, what is the area of the larger figure?
Which choice is correct?
A) 120
B) 160
C) 192
D) 240
Show full solution
Correct answer: C) 192
The linear scale factor is 8/5, so the area factor is (8/5)² = 64/25. Multiply 75 by 64/25 to get 192.
SAT trap: Perimeter gives a linear ratio, but area requires squaring that ratio.
HARD MIXED PROPORTIONS
HARD
Question 62
A recipe uses 3.5 cups of flour for 8 servings. How many cups are needed for 30 servings?
Which choice is correct?
A) 11.25
B) 12.5
C) 13.125
D) 14
Show full solution
Correct answer: C) 13.125
Set 3.5/8 = x/30. Then x = 3.5(30)/8 = 13.125 cups.
SAT trap: Do not round until the final calculation is complete.
HARD MIXED PROPORTIONS
MEDIUM
Question 63
An exchange rate is $1 for 0.80 euro. How many dollars are needed to receive 240 euros?
Which choice is correct?
A) $192
B) $240
C) $280
D) $300
Show full solution
Correct answer: D) $300
Set 1/0.80 = x/240. Then x = 240/0.80 = 300 dollars.
SAT trap: Because one dollar buys less than one euro, receiving 240 euros requires more than 240 dollars.
HARD MIXED PROPORTIONS
MEDIUM
Question 64
In a survey, 42 of 120 students prefer a certain option. At the same proportion, how many of 1,000 students would be expected to prefer it?
Which choice is correct?
A) 300
B) 325
C) 350
D) 420
Show full solution
Correct answer: C) 350
Set 42/120 = x/1000. Since 42/120 = 0.35, x = 350.
SAT trap: Use the sample proportion, not the difference between the sample counts.
HARD MIXED PROPORTIONS
HARD
Question 65
Four machines working for 5 hours produce 600 parts. At the same individual rate, how many parts will 10 machines produce in 8 hours?
Which choice is correct?
A) 1,800
B) 2,000
C) 2,400
D) 3,000
Show full solution
Correct answer: C) 2,400
The rate is 600/[4(5)] = 30 parts per machine-hour. Then 10(8)(30) = 2,400 parts.
SAT trap: Both the number of machines and the operating time change.
What Do Student-Produced Response Proportion Questions Look Like?
Student-produced response questions require you to enter the numerical answer without choosing from four options. Simplify the final value before entering it.
STUDENT-PRODUCED RESPONSE
EASY
Question 66
Solve x/18 = 7/9 for x.
Enter your answer.
Show full solution
Correct answer: 14
Multiply both sides by 18: x = 18(7/9) = 14.
SAT trap: Grid in the numerical value only.
STUDENT-PRODUCED RESPONSE
EASY
Question 67
Solve 5/12 = y/36 for y.
Enter your answer.
Show full solution
Correct answer: 15
The denominator is multiplied by 3, so multiply the numerator by 3. Thus y = 15.
SAT trap: Use the same scale factor in both parts of the fraction.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 68
Two similar triangles have corresponding sides 9 and 15. If another side of the first triangle is x and the corresponding side of the second is 25, what is x?
Enter your answer.
Show full solution
Correct answer: 15
Set 9/15 = x/25. Cross-multiply: 15x = 225, so x = 15.
SAT trap: Keep the first triangle’s sides together in the same ratio positions.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 69
Eight workers complete a job in 6 hours. At the same individual rate, how many hours will 12 workers need?
Enter your answer.
Show full solution
Correct answer: 4
The job requires 8(6) = 48 worker-hours. Divide by 12 workers to get 4 hours.
SAT trap: This is an inverse proportion because the total work is fixed.
STUDENT-PRODUCED RESPONSE
MEDIUM
Question 70
35% of a number is 84. What is the number?
Enter your answer.
Show full solution
Correct answer: 240
Set 84/x = 35/100. Cross-multiply: 35x = 8,400, so x = 240.
SAT trap: The number 84 is the part, not the whole.
What Mistakes Cost Students Points on SAT Proportions?
Most errors come from an incorrect setup rather than difficult arithmetic. Use the table below as a quick correction checklist.
| Mistake | Why It Happens | Correction |
|---|---|---|
| Reversing one ratio | Corresponding quantities are not aligned | Write units beside every numerator and denominator |
| Using addition instead of scaling | The student looks at differences rather than factors | Ask what number multiplies one quantity to reach the other |
| Treating inverse variation as direct | The total work or distance is overlooked | Check whether the product should remain constant |
| Using the wrong geometric factor | Length, area, and volume scales are confused | Use k for length, k² for area, and k³ for volume |
| Rounding too early | A decimal unit rate is shortened before the final step | Keep exact fractions or full decimals until the end |
How Should Students Study SAT Proportions in 2 Weeks?
| Days | Focus | Practice Goal |
|---|---|---|
| Days 1-2 | Equivalent ratios and cross-multiplication | Solve Q1-Q10 without a calculator |
| Days 3-4 | Variables and direct proportions | Complete Q11-Q22 and label all units |
| Days 5-6 | Maps, recipes, prices, and production | Complete Q23-Q30 under timed conditions |
| Days 7-9 | Percent, scale, area, and volume | Complete Q31-Q45 and create a scale-factor note |
| Days 10-11 | Inverse proportions | Complete Q46-Q55 and identify the fixed product |
| Days 12-13 | Hard mixed and student-produced response | Complete Q56-Q70 and review every trap note |
| Day 14 | Mixed review | Redo missed questions without viewing solutions |
He is a Digital SAT mentor with 10+ years of experience, working primarily with SAT students all Over worldwide. Their students have consistently progressed toward 1520+ scores by improving timing, accuracy, and trap-answer control through official-style practice, detailed mistake analysis, and clear weekly action plans.
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