GRE percentage problems rank among the most frequently tested arithmetic concepts on the quantitative reasoning section. This guide covers every type you will encounter -- basic conversions, compound changes, data interpretation -- with formulas, shortcuts, worked examples, and interactive practice questions.
Percentages make up roughly 25% of GRE quant, so solid fundamentals pay off across dozens of questions. A percentage is a number expressed as a fraction of 100: 45% means 45/100, or 0.45, or 9/20.
"Percent" means "per hundred." When 30% of students passed, that means 30 out of every 100. On the GRE, percentages appear as explicit numbers (25%), fractions (1/4), or decimals (0.25). Moving fluidly between all three forms is essential -- the GRE often presents data in one format and expects computation in another.
Percentage to decimal: divide by 100 (move the decimal two places left). So 75% = 0.75, 8% = 0.08. Reverse: multiply by 100. For fractions, divide numerator by denominator and multiply by 100: 3/8 = 37.5%. Percentage to fraction: place over 100 and simplify, so 60% = 3/5. Memorizing common conversions saves significant exam time.
| Fraction | Decimal | Percentage |
|---|---|---|
| 1/2 | 0.5 | 50% |
| 1/3 | 0.333 | 33.3% |
| 2/3 | 0.667 | 66.7% |
| 1/4 | 0.25 | 25% |
| 3/4 | 0.75 | 75% |
| 1/5 | 0.2 | 20% |
| 1/8 | 0.125 | 12.5% |
| 1/6 | 0.167 | 16.7% |
| 1/10 | 0.1 | 10% |
The translation method converts English into math: replace "what" with x, "is" with =, "of" with multiplication, and convert percentages to decimals. "What is 35% of 240?" becomes x = 0.35 x 240. "90 is what percent of 360?" becomes 90 = (x/100) x 360. Practice until this mapping is automatic.
Step-by-Step: Translation Method
What is 35% of 240?
Enter an original value and a new value to instantly calculate the percent change.
Select a common fraction to see its decimal and percentage equivalents instantly.
Percent change is the most frequently tested percentage problem type on the GRE. Whether a question involves a salary raise, stock drop, or population shift, the same formula applies. Mastering it handles both straightforward calculations and the tricky variations the GRE favors.
Percent Change = (New - Original) / Original x 100. Positive = increase, negative = decrease. The critical detail: always divide by the original. A stock rising from $40 to $50 is (50 - 40) / 40 x 100 = 25%. Dividing by 50 gives 20% -- wrong. This is the single most common error on GRE percent change questions.
| Problem Type | Formula | When to Use |
|---|---|---|
| Basic Percentage | Part = (Percent / 100) x Whole | Finding a percentage of a given number |
| Finding the Percent | (Part / Whole) x 100 | Determining what percent one number is of another |
| Percent Change | (New - Original) / Original x 100 | Calculating percent increase or decrease |
| Successive Changes | Original x Multiplier1 x Multiplier2 | Multiple percentage changes in sequence |
| Percent More Than | A = (1 + Percent/100) x B | When A is a certain percent more than B |
| Profit Percentage | (Selling Price - Cost) / Cost x 100 | Profit and loss word problems |
| Discount | Original x (1 - Discount/100) | Sale price after a percentage discount |
The GRE exploits one mistake relentlessly: dividing by the wrong base. "Price increased from $80 to $100" -- many students compute 20/100 = 20% instead of 20/80 = 25%. Always identify the original value first. If a problem says "increased to" or "decreased to," the original is the value before the change.
"A is 25% of B" means A = 0.25 x B. "A is 25% more than B" means A = 1.25 x B. If B = 200, those give 50 vs. 250. Similarly, "30% less than B" means A = 0.70 x B. For "less than," subtract from 100%; for "more than," add to 100%.
Step-by-Step: Percent Increase
A company's revenue increased from $80,000 to $96,000. What is the percent increase?
Compound percentage problems trip up even confident test-takers. They involve applying multiple percentage changes sequentially, and simply adding or subtracting percentages is almost always wrong.
Classic trap: +20% then -20% does not return to the original. $100 + 20% = $120, then $120 - 20% = $96. Net: a 4% loss. The second percentage operates on a different base. This applies universally -- a 50% increase then 50% decrease does not cancel out, and two consecutive 10% raises do not equal 20%.
Convert each change to a multiplier: +20% = 1.20, -15% = 0.85, +5% = 1.05. Multiply together for the combined effect. Example: +40% then -25% = 1.40 x 0.75 = 1.05, a net 5% increase. Faster and less error-prone than step-by-step calculation.
Recurring contexts: discount-then-tax, compounded investment returns, and population changes over successive periods. Watch for successive discounts: 20% off then 10% off is not 30% off. Multipliers 0.80 x 0.90 = 0.72, a 28% total discount. That 2-point gap often separates two answer choices.
Step-by-Step: Successive Changes
A store marks up an item by 40%, then offers a 25% discount during a sale. If the original cost was $50, what is the final price?
Mental math shortcuts save 15 to 30 seconds per question -- that adds up to several extra minutes per section. The "pick 100" strategy alone lets you solve most unknown-value percentage questions in under 60 seconds.
Find 10% by moving the decimal one place left: 10% of 350 = 35. Derive others: 5% = half of 10%, 20% = double 10%, 1% = 10% / 10. For estimation, 37% of 240: 10% (24) x 3 = 72, plus 5% (12), plus 2% (4.8) = 88.8 -- close enough to identify the correct choice.
When a problem gives no starting value, pick 100. Any percentage of 100 equals itself: "+30% then -20%" gives 130, then 104 -- a net 4% increase. Especially powerful for quantitative comparison. Key rule: no specific starting value = use 100.
You only need to determine which quantity is larger -- not exact values. Comparing "15% of 812" vs. "120"? Estimate 15% of 800 = 120, then fine-tune upward. Round to friendly numbers: 23% of 487 is roughly 23% of 500 = 115. Practice estimation -- many students waste time computing exact values when estimates suffice.
Data interpretation sets present information in tables, bar graphs, pie charts, or line graphs and ask you to compute percentages or percent changes. The math is the same -- the added challenge is extracting correct numbers from visual data.
Apply (Part / Whole) x 100. The challenge is identifying the correct "part" and "whole" from the data. Read every label, axis title, and footnote before calculating -- a common mistake is misreading graph scales or confusing cumulative totals with individual values.
Apply the standard formula: (Later Value - Earlier Value) / Earlier Value x 100. Be precise about which periods you are comparing -- "from 2022 to 2024" differs from "from 2023 to 2024." Questions asking for the greatest or least percent change require computing it for each option.
Some questions require extracting values, combining them, then computing a percentage. Break these into discrete steps and write down intermediate values. Estimation helps -- round to convenient numbers. Answer choices are typically spaced far enough that reasonable rounding identifies the correct one.
Step-by-Step: Reading the Chart
A bar graph shows Company A earned $450 million and Company B earned $300 million in 2024. What percentage of the combined revenue did Company A earn?
The hardest GRE percentage problems combine percentages with ratios, algebra, or multi-group comparisons. These appear more in the second quant section and separate 160+ scorers from the rest.
Track which number is the "whole" for each group. You cannot average 75% and 50% to get 62.5% when groups differ in size. With 100 students (60 female, 40 male): (60 x 0.75) + (40 x 0.50) = 45 + 20 = 65%. Use "pick 100" whenever the problem gives percentages without actual numbers.
"After a 15% tax, an item costs $92." Translate: 1.15 x Original = 92, so Original = $80. Multi-step version: "After a 20% discount and 10% tax, the price is $108." Setup: Original x 0.80 x 1.10 = 108, giving Original = $122.73. The multiplier method combines naturally with algebra.
| Problem Type | Frequency | Difficulty | Best Strategy |
|---|---|---|---|
| Basic calculations | High | Easy | Translation method |
| Percent change | High | Medium | Percent change formula |
| Data interpretation % | High | Medium | Estimation + formula |
| Successive/compound changes | Medium | Medium-Hard | Multiplier method |
| Relative comparisons | Medium | Hard | Identify each group's whole |
| Percentage with algebra | Low-Medium | Hard | Convert to decimals, solve algebraically |
| Profit/loss/discount | Low-Medium | Medium | Cost-based percentage formulas |
Step-by-Step: Weighted Group Percentages
In a class of 80 students, 60% are female. If 75% of the female students and 50% of the male students passed an exam, what percent of the entire class passed?