SAT · Problem Solving & Data Analysis · Ratios, proportions, and units
Question sat-q-00119
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The question
A class has boys and girls in the ratio 7:6. If there are 156 students in the class, how many are boys?
- 12
- 156
- 84
- 72
Show answer & worked solution
Answer: 84
Worked solution. The ratio means there are 13 parts in total, with 7 parts boys. Each part is 156 / 13 = 12. So boys = 7 × 12 = 84.
Why each wrong choice is wrong. Swapping boys and girls is the obvious trap. Another distractor is the size of one 'part', which would be the answer if the ratio were 1:12 instead of 7:6.
Test-day tactic. Convert ratios into total parts first, divide the total by parts to get one unit, then multiply.
About this question type
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.
You will see a question shaped like this one on roughly every other official SAT form, typically at an early position in the section, where missing them carries an outsize penalty because the curve assumes everyone in your band gets them right. Treat any miss in this subtopic as a signal to drill the subtopic page before you do another full practice test.