Ratios and Proportions · Sub-skill drill
Similar Figures and Proportional Sides
When two figures are similar, the ratios of corresponding sides are equal. Set up a proportion using two pairs of corresponding sides — one pair where both lengths are known, and one pair where one length is the unknown. Cross-multiply to solve. The trickier SAT version of this asks about ratios of areas or volumes, which scale as the square or the cube of the side ratio respectively. Confusing the linear ratio with the area or volume ratio is the dominant wrong-answer pattern.
How this sub-skill is tested on the SAT
When two figures are similar, the ratios of corresponding sides are equal. Set up a proportion using two pairs of corresponding sides — one pair where both lengths are known, and one pair where one length is the unknown. Cross-multiply to solve. The trickier SAT version of this asks about ratios of areas or volumes, which scale as the square or the cube of the side ratio respectively. Confusing the linear ratio with the area or volume ratio is the dominant wrong-answer pattern.
This sub-skill sits inside the broader Ratios and Proportions topic, which is part of the College Board's Problem Solving & Data Analysis content domain. Problem Solving and Data Analysis is where the SAT pretends to be the real world. Every question in this domain is wrapped in context: a recipe, a survey, a clinical trial, a lab measurement, a marketing report. The math itself is rarely harder than middle-school arithmetic — ratios, proportions, percentages, unit conversions, means, medians, scatter plots, two-way tables, and basic probability. What trips students up is the reading. The College Board has spent two decades calibrating these prompts to reward students who slow down on the setup and punish students who rush to compute. ScoreRe
Practice questions in this drill set
Below are 6 practice questions targeting this exact sub-skill, ordered from easier to harder. Each question is tagged with its target score band so you can focus on questions that match the band you are working out of. Worked solutions are open by default — read each one even if you got the question right, because the way the solution is structured often reveals a faster path than the one you used.
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In a class, the ratio of seniors to juniors is 7:2. If there are 54 students total, how many are seniors?
- A 9
- B 11
- C 42
- D 12
Worked solution
Answer: C — 42
The ratio 7:2 means seniors make up 7/9 of the total. Multiply: (7/9) × 54 = 42 seniors. As a check, juniors are 12 and 42 + 12 = 54.
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In a class, the ratio of seniors to juniors is 4:9. If there are 117 students total, how many are seniors?
- A 36
- B 81
- C 13
- D 80
Worked solution
Answer: A — 36
The ratio 4:9 means seniors make up 4/13 of the total. Multiply: (4/13) × 117 = 36 seniors. As a check, juniors are 81 and 36 + 81 = 117.
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In a class, the ratio of seniors to juniors is 4:5. If there are 27 students total, how many are seniors?
- A 9
- B 15
- C 14
- D 12
Worked solution
Answer: D — 12
The ratio 4:5 means seniors make up 4/9 of the total. Multiply: (4/9) × 27 = 12 seniors. As a check, juniors are 15 and 12 + 15 = 27.
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In a class, the ratio of seniors to juniors is 2:5. If there are 35 students total, how many are seniors?
- A 24
- B 25
- C 7
- D 10
Worked solution
Answer: D — 10
The ratio 2:5 means seniors make up 2/7 of the total. Multiply: (2/7) × 35 = 10 seniors. As a check, juniors are 25 and 10 + 25 = 35.
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In a class, the ratio of seniors to juniors is 2:3. If there are 25 students total, how many are seniors?
- A 15
- B 14
- C 10
- D 5
Worked solution
Answer: C — 10
The ratio 2:3 means seniors make up 2/5 of the total. Multiply: (2/5) × 25 = 10 seniors. As a check, juniors are 15 and 10 + 15 = 25.
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In a class, the ratio of seniors to juniors is 7:8. If there are 150 students total, how many are seniors?
- A 70
- B 15
- C 79
- D 80
Worked solution
Answer: A — 70
The ratio 7:8 means seniors make up 7/15 of the total. Multiply: (7/15) × 150 = 70 seniors. As a check, juniors are 80 and 70 + 80 = 150.
Why this band assignment matters
Every question in this drill is tagged with a target score band — 400–500, 500–600, 600–700, or 700–800 — based on its difficulty and the patterns the College Board uses for questions at each level. If you are aiming to break out of a 580 plateau, the 600–700 questions in this drill are your highest-leverage practice. If you are chasing 750+, the 700–800 questions here are the ones that separate the top 10% of test takers from everyone else.
Use the band tags to filter your work. If you can confidently solve every 400–500 and 500–600 question without notes, move to the 600–700 set. If those land cleanly, the 700–800 set is your final boss. The worked solutions in this drill are written so that even the hardest questions become learnable patterns once you have seen the structure of the solve a few times.