SAT Math · Problem Solving & Data Analysis
Ratios, proportions, and units
Setting up ratios and converting between units.
What's tested in this subtopic
Items ask you to set up a proportion from a description, scale a recipe, convert between units (often with a chain of two or three conversions), or compare two ratios. Unit conversion items are deliberately set up so you cannot do them in your head; they reward careful unit-tracking.
Tactics that actually move your score
Use dimensional analysis: write the unit you have, multiply by a fraction whose denominator has that unit and whose numerator has the unit you want, and continue until you reach the target unit. The arithmetic is usually trivial — the score comes from the setup. The single biggest leverage point on most subtopics isn't learning more math — it's recognizing the test's preferred surface forms quickly enough that you don't burn 30 seconds re-reading the question. The first time you see a particular phrasing it might take you a full minute. The tenth time you see it, you should be reaching for your method before you've finished the sentence. Repetition is what builds that recognition. Fifteen problems in a row of the same shape is more useful than fifty mixed.
Practice questions (14)
- Easy A class has boys and girls in the ratio 9:3. If there are 120 students in the class, how many are boys?
- Easy A class has boys and girls in the ratio 9:2. If there are 33 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 5:3. If there are 24 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 2:3. If there are 25 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 4:7. If there are 121 students in the class, how many are boys?
- Hard A class has boys and girls in the ratio 9:6. If there are 150 students in the class, how many are boys?
- Easy A class has boys and girls in the ratio 7:6. If there are 156 students in the class, how many are boys?
- Easy A class has boys and girls in the ratio 8:7. If there are 105 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 7:7. If there are 126 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 5:5. If there are 70 students in the class, how many are boys?
- Medium A class has boys and girls in the ratio 4:9. If there are 39 students in the class, how many are boys?
- Hard A class has boys and girls in the ratio 5:3. If there are 72 students in the class, how many are boys?
- Easy A class has boys and girls in the ratio 6:3. If there are 63 students in the class, how many are boys?
- Easy A class has boys and girls in the ratio 8:8. If there are 96 students in the class, how many are boys?
How to drill
Work through the questions above untimed. After each one, read the worked solution from start to finish — even when you got it right. Note which solution method you used, and which method we used; if they differ, ask yourself which would have been faster on test day. Speed in SAT math comes from shortening your method-selection step, not from doing arithmetic faster. Most fast students are doing the same arithmetic everyone else is — they're just spending less time deciding what to do.
Once you can clear the easy and medium items in this subtopic at 90% accuracy, attempt a timed mini-set of ten hard items at 75 seconds each. If you finish in time and score 7+ correct, you've effectively mastered the subtopic for test purposes and can move on.