GMAT arithmetic and percentages make up the largest chunk of the Quantitative Reasoning section — about 30-40% of all quant questions test these foundational concepts. The good news: the GMAT does not require complex computation. It rewards students who know the right shortcuts, especially the multiplier method for percent changes and fast fraction-to-percentage conversions.
The multiplier method is the single most important technique for GMAT arithmetic and percentages problems. Instead of calculating a percentage and then adding or subtracting it, convert the entire operation into one multiplication step. This approach eliminates the most common percentage error: adding sequential changes instead of multiplying them.
For a percentage increase of P%, multiply the original value by (1 + P/100). A 30% increase on $200 means $200 × 1.30 = $260. For a decrease of P%, multiply by (1 - P/100). A 15% decrease on $200 means $200 × 0.85 = $170. The multiplier is always one operation — no separate step needed to find the percentage and add or subtract it.
| Change Type | Formula | Example | Multiplier |
|---|---|---|---|
| Increase by P% | Multiply by (1 + P/100) | 30% increase on $200 | 1.30 → $260 |
| Decrease by P% | Multiply by (1 - P/100) | 15% decrease on $200 | 0.85 → $170 |
| Sequential increase | Multiply multipliers | 20% up then 10% up | 1.20 × 1.10 = 1.32 |
| Sequential decrease | Multiply multipliers | 20% off then 10% off | 0.80 × 0.90 = 0.72 |
| Increase then decrease | Multiply multipliers | 40% up then 40% down | 1.40 × 0.60 = 0.84 |
| Reverse a % increase | Divide by (1 + P/100) | Price after 25% increase is $150. Original? | $150 ÷ 1.25 = $120 |
When multiple percentage changes are applied in sequence, you must multiply the multipliers — never add the percentages. A 20% increase followed by a 10% decrease is not a net 10% increase. The correct calculation: 1.20 × 0.90 = 1.08, which is a net 8% increase. This is a classic GMAT trap.
Problem: A store increases the price of a jacket by 40%, then offers a 40% discount on the new price. Is the final price the same as the original?
No — the final price ($84) is 16% less than the original. Equal percentage increases and decreases never cancel out because they apply to different base values.
Fractions, decimals, and percentages are three ways of expressing the same value. On the GMAT, fractions are easier to compute with than decimals about 90% of the time. Your first instinct when you see a decimal or percentage should be to convert it to a fraction for faster calculation.
Percent literally means "over 100," so x% = x/100. To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100. To convert a decimal to a percent, multiply by 100 (slide the decimal point two places right). The key is choosing whichever form makes the computation simplest for the specific problem.
Memorizing these conversions eliminates calculation time entirely. When you see 37.5% in a problem, you should instantly recognize it as 3/8 without any computation.
| 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% |
| 3/8 | 0.375 | 37.5% |
| 5/8 | 0.625 | 62.5% |
| 7/8 | 0.875 | 87.5% |
| 1/6 | 0.167 | 16.7% |
| 1/10 | 0.1 | 10% |
On the GMAT, GMAT ratios and proportions questions test your ability to work with part-to-part and part-to-whole relationships. A fundamental point that many students miss: a ratio IS a fraction. The number 3:5 is identical to 3/5. This means every rule for fractions applies to ratios.
A ratio is a single fraction by itself (e.g., 3/5). A proportion is an equation that sets two ratios equal to each other (e.g., 3/5 = 12/20). This distinction matters because solving proportions uses cross-multiplication, while working with ratios often uses the multiplier approach — find what factor scales the ratio to the actual numbers.
Cross-multiply to solve any proportion: if a/b = c/d, then ad = bc. For multi-ratio problems (where you need to combine ratios like A:B = 2:3 and B:C = 4:5), find the common term and scale. Since B = 3 in the first ratio and B = 4 in the second, multiply the first ratio by 4 and the second by 3 to get A:B:C = 8:12:15.
Problem: In a class, the ratio of boys to girls is 3:5. If there are 24 boys, how many girls are in the class?
There are 40 girls. Faster approach: 24 ÷ 3 = 8 (the multiplier), so 5 × 8 = 40.
Profit, loss, and discount problems combine GMAT arithmetic formulas with real-world business scenarios. These questions are essentially percentage problems in disguise — and the same multiplier method applies. The key is always identifying the correct base value for each calculation.
Profit percentage is always calculated relative to the cost price (CP), not the selling price: Profit % = (SP - CP) / CP × 100. Similarly, Loss % = (CP - SP) / CP × 100. When you know the profit percentage and need the selling price, use the multiplier directly: SP = CP × (1 + Profit%/100).
| Concept | Formula | Example |
|---|---|---|
| Profit % | (SP - CP) / CP × 100 | Buy at $80, sell at $100 → 25% profit |
| Loss % | (CP - SP) / CP × 100 | Buy at $100, sell at $80 → 20% loss |
| Selling Price from Profit % | SP = CP × (1 + Profit%/100) | CP=$50, 30% profit → SP = $50 × 1.30 = $65 |
| Cost Price from Selling Price | CP = SP / (1 + Profit%/100) | SP=$65, 30% profit → CP = $65 / 1.30 = $50 |
| Successive Discounts | Multiply (1 - D₁/100)(1 - D₂/100) | 20% then 10% off → 0.80 × 0.90 = 0.72 (28% off) |
Successive discounts are a frequent GMAT trap. Two discounts of 20% and 10% are NOT a total 30% discount. Apply the multiplier method: 0.80 × 0.90 = 0.72, which means the customer pays 72% of the original — a 28% total discount, not 30%. The difference grows larger with bigger discount percentages.
Problem: A retailer buys a product for $60 and wants to sell it at a 25% profit. After slow sales, the retailer offers a 10% discount on the selling price. What is the actual profit percentage?
The actual profit is 12.5%, not 15% (25% - 10%). You cannot subtract percentages when they apply to different base values.
The GMAT is explicitly designed to allow shortcuts — estimation, testing real numbers, and benchmark calculations. If you find yourself doing long division or complex multiplication by hand, you are probably taking the wrong approach to the problem.
Start with 10% — find it by moving the decimal one place left. Then build other percentages: 5% is half of 10%, 1% is 10% divided by 10, and any other percentage is a combination. Need 12% of 350? Find 10% = 35, then 1% = 3.5, so 12% = 35 + 3.5 + 3.5 = 42. This is faster than multiplying 350 × 0.12.
Many GMAT problems are designed so that estimation gets you close enough to eliminate wrong answers. If the answer choices are 12%, 28%, 45%, and 72%, and your rough estimate is "somewhere around 30%," you can confidently choose 28% without precise calculation. The GMAT tests reasoning, not computation — the answer choices are usually spread far enough apart that estimation works.
Number properties are another powerful elimination tool. If the question asks for a percentage of an odd number and only one answer choice is odd, that is likely the answer. Look for these shortcuts before diving into calculation.
GMAT percentage problems are designed to exploit predictable student errors. Knowing these traps in advance is just as valuable as knowing the formulas.
The single most common GMAT percent change mistake is adding sequential percentages instead of multiplying multipliers. A 20% increase followed by a 20% decrease is NOT 0% — it is a 4% decrease (1.20 × 0.80 = 0.96). A 50% increase followed by a 50% decrease is a 25% decrease (1.50 × 0.50 = 0.75). The larger the percentages, the bigger the error from adding.
Problem: A city's population increased by 20% in 2024 and decreased by 20% in 2025. What is the net percentage change?
The population actually decreased by 4%. Whenever percentage increases and decreases are applied sequentially, multiply the multipliers — never add or subtract.
Another frequent error is confusing the base value. "20% less than X" means 0.80 × X, but "X is 20% less than Y" means X = 0.80 × Y, and "Y is what percent more than X" requires using X as the base. Always identify which number is the base before computing. The phrase "percent of" identifies the base — it is always the number that follows "of."
Apply the concepts above to these GMAT-style practice problems.
Enter an original value and up to two sequential percentage changes to see the final value and net percentage change.
Select a common fraction to see its decimal and percentage equivalent instantly.
Approximately 10 to 15 questions in the GMAT quantitative section focus on arithmetic, contributing to about 30-40% of the overall quant score. Combined with algebra, these foundational topics account for over 51% of all quantitative questions on the GMAT Focus Edition.
No. The GMAT does not allow calculators on the Quantitative Reasoning section. However, the questions are designed so that complex computation is unnecessary. Learning mental math shortcuts and estimation techniques is far more valuable than relying on precise calculation.
The multiplier method converts percentage changes into multiplication factors. For an increase, add the decimal to 1 (a 30% increase uses multiplier 1.3). For a decrease, subtract from 1 (a 15% decrease uses 0.85). For sequential changes, multiply the multipliers together instead of adding the percentages.
Memorize common conversions: 1/4 = 25%, 1/3 = 33.3%, 1/5 = 20%, 1/8 = 12.5%, 3/8 = 37.5%, 5/8 = 62.5%. For uncommon fractions, divide the numerator by the denominator and multiply by 100. Using fractions instead of decimals is faster 90% of the time on the GMAT.