These Digital SAT questions give you two quantities that scale together — a recipe, a map, a speed — and ask you to find a missing amount by setting up and solving a proportion.
A ratio question gives you a fixed relationship between two quantities — flour to sugar, distance to time, model to real object — and one full pair of values plus one incomplete pair. Your job is to write both pairs as equivalent fractions with matching units in matching positions, then cross-multiply.
Use three steps: name the two quantities and their units, set up the proportion so the same quantity sits in the same position (both numerators are the same category, both denominators are the same category), then solve by cross-multiplying. Skipping the “name” step is where most points are lost — it is very easy to flip a fraction upside down under time pressure.
Try this: a recipe calls for 3 cups of flour for every 2 cups of sugar. How many cups of sugar are needed for 12 cups of flour? Walk through it below, then try the quiz underneath.
A map uses a scale of 1 inch = 8 miles. Two cities are 3.5 inches apart on the map. How many miles apart are the cities?
If you set that up in one clean fraction and solved without a second guess, you have the core mechanic. Now let’s add the rate version, where “per” replaces the colon.
A rate is a ratio between two different units — miles per hour, dollars per pound, gallons per minute. To find a unit rate, divide: total amount ÷ total time (or total cost, or total distance). Once you have the unit rate, scaling to any other amount is one multiplication.
A classic rate question is a distance-rate-time setup: d = rt. Given any two of distance, rate, and time, solve for the third. Watch units closely — if the rate is in miles per hour but the question asks for minutes, convert before or after solving, but don’t forget to convert at all.
Practice pulling the unit rate out first, then scaling.
A train travels at a constant 54 miles per hour. At that rate, how many minutes does it take to travel 108 miles?
A stated ratio like 3:5 compares one part to another part. But many questions actually ask for a part compared to the whole — and the whole is the sum of all the parts, not one of the numbers you were given. This mismatch is one of the most common ratio errors.
If a jar has red and blue marbles in a ratio of 3:5, that means for every 3 red marbles there are 5 blue ones — 8 marbles total per group. The fraction of marbles that are red is 3/8, not 3/5. Always add the ratio terms to find the whole before you compute a part-to-whole fraction.
Before solving, decide which kind of comparison the question is actually asking for.
Decide what the question needs — the ratio as given, or a fraction of the total.
Now apply it to a full question. Find the total number of “parts” first, then scale.
In a school club, the ratio of freshmen to sophomores is 2:3. If the club has 45 members and every member is either a freshman or a sophomore, how many are freshmen?
Three variations show up often enough to prepare for by name. Scaling problems multiply every term of a ratio by the same factor — a scale drawing, a model car, a recipe doubled. Mixture problems combine two groups with different rates or concentrations and ask about the blended result. Combined-rate problems put two workers (or two pipes, two machines) on the same job and ask how long it takes together.
For combined rates, don’t average the times — add the rates (job per hour), then take the reciprocal of the sum. If Pump A alone takes 6 hours to fill a tank, its rate is 1/6 tank per hour. Add rates, then flip.
Pump A can fill a tank in 6 hours working alone. Pump B can fill the same tank in 3 hours working alone. Working together at their individual rates, how many hours will it take to fill the tank?
These three variations all reduce to the same skill: identify the unit rate, then scale or combine it correctly. The next section drills that instinct until it’s automatic.
Fluency matters here — the algebra is simple, so the test rewards speed and clean setup over cleverness. Work these cold, write an answer before revealing, and pay attention to which ones tempt you into the part-to-whole trap.
Simplify the ratio 18:24 to lowest terms.
A car uses 1 gallon of gas every 28 miles. How far can it go on 6.5 gallons?
In a bag of chips, the ratio of plain to BBQ is 7:3. What fraction of the chips are BBQ?
Two hoses fill a pool in 4 hours and 12 hours working alone. How long will it take together?
A scale model is built at a ratio of 1:50. If the model is 8 cm tall, how tall is the real object, in meters?
The ratio of cats to dogs at a shelter is 4:9, and there are 65 animals total. How many are dogs?
Once these feel quick, the natural next skill is percentages, which use the same part-to-whole thinking with a fixed denominator of 100.
Here are three Ratios, Rates, and Proportions questions from our problem sets, from easier to harder, in the same format as the Digital SAT. Answer each one to see the full explanation.
Five shorter questions to finish: two unit rates, a part-to-whole ratio, a combined rate, and a scale factor. Name the quantities before you set anything up.
A recipe for 4 servings uses 2.5 cups of rice. How many cups of rice are needed for 10 servings?
A car travels 165 miles on 5.5 gallons of gas. At that rate, how many gallons are needed to travel 300 miles?
The ratio of adults to children at an event is 3:8. If there are 176 people total, how many are adults?
Pipe A fills a tank in 5 hours working alone. Pipe B fills the same tank in 10 hours working alone. Working together, how long will it take to fill the tank?
A photo that is 4 inches by 6 inches is enlarged proportionally so that the longer side becomes 15 inches. What is the new length of the shorter side, in inches?
Related: Percentages · Distributions, center & spread · Probability · SAT Math overview