GRE Ratios and Proportions
Ratios are one of the most testable GRE topics because the numbers stay small and the setup does all the work. Get three ideas straight, parts vs. the whole, cross-multiplying, and combining ratios, and this becomes free points.
A ratio is parts, not totals
3:2 means three parts to two parts, five parts in all. To split a total by a ratio, divide the total by the number of parts to get the value of one part, then multiply. Splitting 30 in a 3:2 ratio: 30 / 5 = 6 per part, so 18 and 12. If a question asks for a fraction of the whole, convert first: in 3:2, the first share is 3/5 of the total, not 3/2.
Proportions: cross-multiply
A proportion is two equal ratios. Solve a/b = c/d by cross-multiplying to ad = bc. The only discipline that matters is consistency: keep the same unit on top in both fractions. For a scaling problem (3 pens cost $4, how much for 12 pens), set 3/4 = 12/x and cross-multiply to get x = 16. Ratios scale linearly, so doubling one side doubles the other.
Combining two ratios
When a question links A:B and B:C, scale both so the shared term matches, then read off the three-way ratio. If A:B = 2:3 and B:C = 4:5, make B a common 12: A:B = 8:12 and B:C = 12:15, so A:B:C = 8:12:15. This is the standard route for three-quantity ratio questions.
Rates are ratios too
Speed, price per unit, and work rates are all ratios, so the same tools apply. Distance = rate x time, and unit conversions are just proportions with the units cancelling. Line up the units, cancel, and the arithmetic falls out.
Frequently asked questions
A class has boys to girls in a 3:2 ratio and 30 students. How many boys?
Add the ratio parts: 3 + 2 = 5 parts for 30 students, so each part is 30 / 5 = 6. Boys are 3 parts: 3 x 6 = 18. The key move is turning the ratio into a 'per part' value using the total parts.
Does the ratio 3:2 mean the first thing is 3/2 of something?
No. 3:2 means 3 parts to 2 parts, so the first thing is 3/5 of the whole and the second is 2/5. Convert the ratio to fractions of the total before you compute a fraction of an amount.
How do I solve a proportion?
Set the two ratios equal and cross-multiply: a/b = c/d becomes ad = bc. Keep the same quantity on top in both fractions (miles with miles, hours with hours) or you will invert the relationship.
How do I combine A:B and B:C into A:B:C?
Scale each ratio so the shared term B matches. If A:B = 2:3 and B:C = 4:5, make B = 12 in both: A:B = 8:12 and B:C = 12:15, so A:B:C = 8:12:15.
Drill ratios with real GRE questions
Grezi turns ratios and proportions into interactive lessons and adaptive practice, with an AI tutor that shows you where the setup went wrong, not just the answer.
More GRE Quant: all topics, formula sheet.