GRE Percents, Ratios and Proportions

By Muntasir Jul 27, 2026 6 min read

TL;DR

Find a percent of a number by turning the percent into a decimal and multiplying: 20 percent of 150 is 0.20 times 150, or 30. These skills sit inside the Arithmetic content area of GRE Quantitative Reasoning. For a percent increase, multiply the original value by one plus the rate. For a percent decrease, multiply by one minus the rate. Successive percent changes do not add together: two 10 percent increases in a row raise a value by 21 percent, not 20 percent. Simplify a ratio by dividing both terms by their greatest common factor, and solve a proportion by cross-multiplying. Practice each skill with our free GRE drills, no signup required.

Percent, ratio and proportion questions appear across both Quantitative Reasoning sections on the GRE. ETS groups them inside the Arithmetic content area, one of four content areas covered in our GRE Quantitative Reasoning section guide, alongside Algebra, Geometry and Data Analysis. The ETS content overview lists percent and ratio directly inside Arithmetic, next to estimation, rate, absolute value, the number line, decimal representation and number sequences.

This guide covers percent-of and percent-change formulas, successive percent changes, ratio simplification, part-to-whole versus part-to-part comparisons, and proportion setups solved by cross-multiplication. For the fraction and decimal skills these calculations build on, see our guide to GRE integers, fractions, decimals and exponents.

How Percent and Ratio Fit Into GRE Arithmetic

The official ETS Math Review closes its Arithmetic chapter with ratio and percent, and solves percent problems two ways: convert the percent to a decimal, or set up and solve a proportion. Both methods land on the same answer, so choose whichever fits the numbers in front of you.

ETS does not name proportion as a separate topic inside its Arithmetic content list. The official list names only ratio and percent directly, and treats proportion as a solving technique for both, not a standalone topic. Proportion setups appear throughout the sections below instead of standing alone as a separate heading.

Percent-Of and Percent Change Calculations

Finding a Percent of a Number

Finding a percent of a number takes one step: turn the percent into a decimal, then multiply. Twenty percent of 150 equals 0.20 times 150, or 30. The same move works in reverse: if 30 people out of 150 applicants received an interview, the interview rate is 30 divided by 150, or 0.20, written as 20 percent.

Percent Increase and Percent Decrease

A percent increase multiplies the original value by one plus the rate written as a decimal. A percent decrease multiplies the original value by one minus the rate. A bookstore raises the price of a 40 dollar book by 15 percent: the new price equals 40 times 1.15, or 46 dollars.

The table below collects every formula in this section. Reach for the rate formulas, original times one plus or minus the rate, when a question gives you a starting value and a percentage and asks for the new value. Reach for the two-value percent change formula in the opposite case, when a question gives you the original value and the new value and asks for the percentage between them.

Goal	Formula	Example
Percent of a number	(percent / 100) x number	20% of 150 = 0.20 x 150 = 30
Percent increase	original x (1 + rate)	40 x 1.15 = 46
Percent decrease	original x (1 - rate)	8,000 x 0.85 = 6,800
Percent change from two values	(new - original) / original x 100	(6,800 - 8,000) / 8,000 x 100 = -15%

Successive Percent Changes

Two percent changes applied one after another do not add together, because the second change applies to the new amount, not the original amount. Multiply the two growth factors instead of adding the two rates.

Applying a 10 percent increase twice in a row raises a value by 21 percent overall, not 20 percent, because 1.10 times 1.10 equals 1.21. The table below works through this pattern and a mixed increase-then-decrease case.

Sequence	Combined factor	Net change
10% increase, then 10% increase	1.10 x 1.10 = 1.21	21% increase
20% increase, then 20% decrease	1.20 x 0.80 = 0.96	4% decrease
50% increase, then 50% decrease	1.50 x 0.50 = 0.75	25% decrease

An increase followed by an equal-percent decrease never returns to the original value, and the gap grows wider as the rate grows larger. Test this against the original value directly instead of trusting instinct.

Ratio Simplification and Part-to-Whole vs Part-to-Part

Simplifying a Ratio

A ratio compares two quantities through division, written with a colon or as a fraction. Simplify a ratio the same way you simplify a fraction: divide both terms by their greatest common factor. A ratio of 18 to 24 simplifies to 3 to 4, since both terms divide evenly by 6.

Part-to-Whole vs Part-to-Part

Read the exact wording of a comparison question before you set anything up. A part-to-part comparison measures one group against another group, while a part-to-whole comparison measures one group against the full total. The two forms carry different denominators, so mixing them up produces a wrong answer even when the arithmetic is correct.

A classroom holds 12 boys and 18 girls, for 30 students total. The ratio of boys to girls, a part-to-part comparison, is 12 to 18, or 2 to 3 once simplified. The fraction of students who are boys, a part-to-whole comparison, is 12 out of 30, or 2 out of 5. Both use the same two numbers, but answer different questions.

Setting Up and Solving Proportions

A proportion sets two ratios equal to each other: a over b equals c over d. Cross-multiply to solve for an unknown term: a times d equals b times c.

A recipe calls for 3 cups of flour for every 2 cups of sugar. How much flour is needed for 5 cups of sugar? Set up 3 over 2 equals x over 5, then cross-multiply: 2 times x equals 3 times 5, so 2x equals 15, and x equals 7.5 cups of flour.

Keep the same category of quantity in the same position in both fractions. Flour sits on top in both fractions above, and sugar sits on the bottom in both, so the cross-multiplication compares like with like.

Common Traps: Percent of a Percent and Reversed Ratios

These five errors account for most wrong answers in this topic. The table below names each one, shows the wrong move, and gives the fix.

Trap	Wrong move	Fix
Percent of a percent	Adding two discount rates together, such as treating a 30% discount plus a 10% discount as 40% off	Apply the rates one after another: 1.00 x 0.70 x 0.90 = 0.63, a 37% total discount
Wrong base for percent change	Dividing by the new value instead of the original value	Always divide the change by the original, starting value
Reversed ratio order	Writing girls to boys when the question asks for boys to girls	Match the ratio order to the exact order named in the question
Part-to-part read as part-to-whole	Treating a 2 to 3 ratio of boys to girls as 2 out of 3 students being boys	Add the ratio terms first to find the whole, then build the part-to-whole fraction
Unreduced ratio compared directly	Comparing 8 to 12 against 2 to 3 without simplifying first	Reduce every ratio to lowest terms before comparing two ratios

Practice Percent, Ratio and Proportion Questions

Reading the formulas is a start. Recognizing which formula a question needs, quickly, is the skill the test rewards, and repetition builds it.

We offer three difficulty levels of free percent drills, easy, medium and hard, plus three difficulty levels of free ratio and proportion drills, easy, medium and hard, each with instant explanations and no signup required. Percent and ratio setups reappear inside interest, mixture and rate word problems, covered in our guide to GRE algebra word problems. For full-length timed practice, visit our GRE exam page, and check practice results against the scoring scale with our free GRE score calculator.