GMAT Percentages: Complete Guide with Worked Examples
Quick Takeaways
- Multiplier method: A 20% increase = multiply by 1.20. A 15% decrease = multiply by 0.85.
- Successive percents: Never add them. Apply each multiplier in sequence.
- Language trap: '150% of x' = 1.5x. '150% more than x' = 2.5x. These are very different.
- Wrong-base trap: Always ask 'percent of what?' — the denominator determines your base.
- Compound interest shortcut: Use sequential multipliers rather than the full formula for 2–3 periods.
Why Percentages Are Central to GMAT Quant
Percentages appear on the GMAT more frequently than almost any other arithmetic concept because they are the primary language of business: profit margins, growth rates, market share, interest rates, and discount pricing are all expressed as percentages. The GMAT is designed to test whether you can reason about these concepts accurately under time pressure — which means percentage questions are not going away, and they will not be simple.
The good news is that every GMAT percentage question — from basic percent change to multi-step compound interest — is built from three or four underlying concepts. Master those concepts and the traps that surround them, and percentage questions become among the more reliable Quant points available.
Percentage Formula Reference
| Concept | Formula | Multiplier Shortcut | Common Trap |
|---|---|---|---|
| Percent increase | % increase = (New − Old) / Old × 100 | New = Old × (1 + r) | Using New as the denominator instead of Old |
| Percent decrease | % decrease = (Old − New) / Old × 100 | New = Old × (1 − r) | Applying the percent to the new (lower) value when comparing back |
| Successive percents | Final = Original × M₁ × M₂ × ... (each change is a separate multiplier) | Chain multipliers: 1.2 × 0.8 = 0.96 (a net 4% decrease) | Adding the percentages directly: +20% and −20% ≠ 0% |
| Simple interest | Interest = P × R × T | Total = P(1 + RT) | Confusing simple with compound when the question says 'compounded annually' |
| Compound interest | A = P(1 + r/n)^(nt) | For annual compounding: chain multipliers by year (1 + r)^t | Using simple interest formula when the question specifies compounding |
Percent Increase and Decrease: The Core Formula
The percent change formula has one critical requirement: the denominator must always be the original (starting) value, not the new value. This is the source of the wrong-base trap — the GMAT frequently constructs scenarios where the new value is more salient, making it tempting to use as the base.
The multiplier shortcut is faster and less error-prone than the standard formula for most GMAT scenarios. Instead of calculating the change and then adding or subtracting it, apply a single multiplier to the original value. A 30% increase: multiply by 1.30. A 25% decrease: multiply by 0.75. A 15% increase followed by a 10% decrease: multiply by 1.15 × 0.90 = 1.035 (a net 3.5% increase). This chain-multiplier approach makes multi-step percentage problems straightforward.
Multiplier quick reference: A p% increase → multiply by (1 + p/100). A p% decrease → multiply by (1 − p/100). Example: 40% decrease → 0.60. 8% increase → 1.08. These two patterns cover every percent change question.
Successive Percents: Why You Cannot Add Them
Successive percent changes — multiple percentage adjustments applied one after another — are among the most reliable sources of wrong answers on GMAT Quant. The error is always the same: adding the percentages together as if they operate on the same base. They do not. Each percentage change applies to the value as it exists after the previous change, which means the bases are different.
A 20% increase followed by a 20% decrease does not return you to the starting value. The multipliers are 1.20 × 0.80 = 0.96 — a net 4% decrease. The 20% decrease applies to a higher value than the original, so it removes more in absolute terms than the 20% increase added. This asymmetry is what the GMAT exploits.
The successive percent rule: Never add or subtract consecutive percentages. Always convert each change to a multiplier and chain-multiply. This is the single most valuable habit for GMAT percentage questions.
Simple vs Compound Interest
Interest questions appear regularly in GMAT Quant and directly test whether you understand the difference between two fundamentally different calculations. Simple interest applies a fixed rate to the original principal every period. Compound interest applies the rate to the growing total — which includes previously earned interest.
- Simple interest: Interest = P × R × T, where P is principal, R is the annual rate (as a decimal), and T is years. Total value = P(1 + RT). Interest accumulates linearly — the same dollar amount every period.
- Compound interest (annual): Total = P × (1 + r)^t. Think of this as chain-multiplying by (1 + r) once per year. This is successive percent change applied repeatedly. Interest compounds exponentially — each year's interest earns interest in subsequent years.
- Compound interest (non-annual): Total = P × (1 + r/n)^(nt), where n is compounding periods per year. For GMAT purposes, you rarely need this exact formula — estimation and multiplier chains cover most compound interest scenarios within the 2-minute time limit.
The Three Percentage Traps That Catch Most Students
Analysis of GMAT percentage errors across thousands of practice sessions reveals that three specific traps account for the vast majority of incorrect answers. Knowing them by name makes them easier to recognise and avoid.
- The wrong-base trap. Always identify the denominator before calculating. 'What percent of X is Y?' — X is the base. 'By what percent did the value increase?' — the original value is the base. If an item's price rises from $80 to $100, the percentage increase is 20/80 = 25%, not 20/100 = 20%. The GMAT places 20% in the answer choices.
- The 'of vs more than' language trap. '150% of x' means 1.5x. '150% more than x' means x + 1.5x = 2.5x. The difference is x — the entire original value. This phrasing appears frequently in revenue and population comparison problems. Read the sentence twice and circle the exact phrasing before calculating.
- The successive percent addition trap. As described above, consecutive percentage changes cannot be added together. +25% and −20% is not +5% — it is 1.25 × 0.80 = 1.00, a net 0% change. The GMAT constructs these scenarios specifically because 5% is the intuitive answer.
Error tracking by trap type: OpenPrep's error log tags percentage errors into three distinct sub-types — Wrong Base, Successive Addition, and 'Of vs More Than' — so reviewing after a percentage practice set immediately shows which trap is your weak point, rather than leaving you to infer it from a list of wrong answers.
Four Fully Worked Examples
Each example targets one of the four most heavily tested percentage scenarios on GMAT Focus Edition: successive changes, the language trap, percentage-of-a-rate problems, and compound interest. Try each question before reading the solution.
Example 1: Successive percent changes — the multiplier approach
Question: A stock price increases by 25% in Year 1 and then decreases by 20% in Year 2. What is the net percentage change over the two years?
Solution: Multiplier for +25% = 1.25. Multiplier for −20% = 0.80. Combined: 1.25 × 0.80 = 1.00. Net change = 0%. The stock returns exactly to its original price. The trap: +25% − 20% = +5%. This is wrong because the 20% decrease applies to the higher post-gain price, removing more in dollar terms than the 25% gain added on the original lower price.
Example 2: 'Of' vs 'more than' — the language trap
Question: Company A's revenue is 150% more than Company B's. If Company B earns $200,000, what does Company A earn?
Solution: '150% more than' = B + 150% of B = $200,000 + $300,000 = $500,000. If the question had said '150% of Company B', the answer would be 1.5 × $200,000 = $300,000 — a $200,000 difference on the same numbers. Circle the phrasing: 'more than' always means you add the percentage amount on top of the original.
Example 3: Percentage change between two rates
Question: A bank raises its annual interest rate from 4% to 5%. By what percentage has the interest rate increased?
Solution: Percent change = (New − Old) ÷ Old × 100 = (5 − 4) ÷ 4 × 100 = 25%. The trap answer is 1% — the raw arithmetic difference between the two rates. That would be the answer if the question asked for the change in percentage points, not the percentage change in the rate itself. The GMAT specifies 'percent change' to require the formula.
Example 4: Compound interest — multiplier chain vs formula
Question: $1,000 is invested at 10% annual compound interest. What is the total value after 3 years?
Solution using chain multipliers (fastest for ≤3 periods): Year 1: $1,000 × 1.10 = $1,100. Year 2: $1,100 × 1.10 = $1,210. Year 3: $1,210 × 1.10 = $1,331. For 4+ compounding periods, the formula A = P(1 + r)^t is more efficient: $1,000 × (1.10)^3 = $1,000 × 1.331 = $1,331. Both methods produce the same result — use chain multipliers when mental math is fast enough, the formula when periods are numerous or non-annual compounding is involved.