Percents on the GMAT
61 flashcards covering Percents on the GMAT for the GMAT Quantitative section.
Percents are a way to express a portion of a whole as a fraction out of 100, making it easier to compare values or calculate changes. For instance, if something costs $100 and is discounted by 20%, you're paying $80. On the GMAT, percents are essential because they underpin many quantitative problems, such as those involving profits, losses, interest, and growth rates, helping you analyze business scenarios accurately and efficiently.
In the GMAT Quantitative section, percents appear in problem-solving and data sufficiency questions, often testing your ability to compute percentages, find increases or decreases, or work with ratios. Common traps include confusing percentage points with actual percentages, misapplying formulas, or overlooking hidden details in word problems. Focus on mastering quick conversions, like turning 25% into 0.25, and practicing real-world applications to spot errors early.
Always double-check your work by estimating the answer first.
Terms (61)
- 01
Percent
A percent is a fraction or ratio expressed per hundred, using the symbol %, and is used to compare quantities relative to 100.
- 02
Percentage
Percentage refers to the result of calculating a percent of a given quantity, often used in contexts like increases, decreases, or proportions.
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Base in percent problems
The base is the original quantity to which a percentage is applied, serving as the starting point for calculations like percent of or percent change.
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Rate in percent problems
The rate is the percentage value itself, indicating how much of the base is being considered, such as 20% meaning 20 per 100.
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Converting percent to decimal
To convert a percent to a decimal, divide the percentage by 100, which shifts the decimal point two places to the left.
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Converting percent to fraction
To convert a percent to a fraction, write the percentage over 100 and simplify, such as 25% becoming 25/100 or 1/4.
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Converting decimal to percent
To convert a decimal to a percent, multiply the decimal by 100 and add the percent symbol, like 0.75 becoming 75%.
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Converting fraction to percent
To convert a fraction to a percent, divide the numerator by the denominator and multiply by 100, then add the percent symbol.
- 09
Finding a percent of a number
To find a percent of a number, convert the percent to a decimal and multiply it by the number, such as 20% of 50 being 0.20 times 50.
- 10
What percent is A of B
To find what percent A is of B, divide A by B, multiply by 100, and add the percent symbol, giving the ratio as a percentage.
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Percentage increase
Percentage increase measures the growth from an original value to a new value, calculated as (increase divided by original) times 100%.
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Percentage decrease
Percentage decrease measures the reduction from an original value to a new value, calculated as (decrease divided by original) times 100%.
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Percent change formula
The percent change formula is [(new value - original value) divided by original value] times 100%, used for both increases and decreases.
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Successive percentages
Successive percentages involve applying multiple percentage changes in sequence, where the overall effect is not simply the sum but a compounded result.
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Simple interest
Simple interest is calculated only on the principal amount, using the formula interest = principal times rate times time, where rate is a percentage.
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Compound interest
Compound interest is calculated on the initial principal and also on the accumulated interest, using the formula A = P(1 + r/n)^(nt), where r is the annual rate as a decimal.
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Annual percentage rate (APR)
APR is the annual rate charged for borrowing or earning interest, expressed as a percentage, which helps compare different financial options.
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Discount percentage
Discount percentage is the reduction in price expressed as a percent of the original price, calculated as (discount amount divided by original price) times 100%.
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Markup percentage
Markup percentage is the amount added to the cost price to determine the selling price, calculated as (markup amount divided by cost price) times 100%.
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Profit percentage
Profit percentage is the gain from a transaction relative to the cost price, calculated as (profit divided by cost price) times 100%.
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Loss percentage
Loss percentage is the amount lost relative to the cost price, calculated as (loss divided by cost price) times 100%.
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Percentage points
Percentage points measure the absolute difference between two percentages, such as a change from 5% to 7% being 2 percentage points, not 40%.
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Mixtures and percentages
Mixtures involve combining solutions with different concentrations, where percentages represent the proportion of a substance in each, and the result is a weighted average.
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Alligation method
The alligation method is a shortcut for finding the ratio in which two or more ingredients at different percentages must be mixed to produce a mixture at a given percentage.
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Weighted average with percentages
Weighted average with percentages calculates the mean by giving different weights to values based on their percentages, often used in mixtures or data sets.
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Percent error
Percent error measures the accuracy of a measurement by comparing the difference between the estimated and actual values, calculated as [(estimated - actual) divided by actual] times 100%.
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Reverse percentages
Reverse percentages involve finding the original amount before a percentage change, such as working backwards from a final value after a discount.
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Percentage of a percentage
Percentage of a percentage is calculated by multiplying the decimals, such as 10% of 20% being 0.10 times 20, resulting in 2% of the original base.
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Increasing a quantity by a percent
To increase a quantity by a percent, multiply the quantity by (1 + the decimal form of the percent), such as increasing 100 by 20% to get 120.
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Decreasing a quantity by a percent
To decrease a quantity by a percent, multiply the quantity by (1 - the decimal form of the percent), such as decreasing 100 by 20% to get 80.
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Common trap: Percent vs. percentage points
A common trap is confusing percent change with percentage points; for example, an increase from 10% to 15% is 5 percentage points or a 50% increase, not the same thing.
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Common trap: Order of successive percentages
Successive percentages must be applied in the correct order, as the result differs; for instance, a 10% increase followed by a 10% decrease does not return to the original.
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Strategy for percent problems
A key strategy is to convert percentages to decimals or fractions early to simplify calculations and avoid errors in multi-step problems.
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Percent in ratios
Percents can express ratios, such as a 2:3 ratio being equivalent to 40% to 60% when the total is 100%, by dividing each part by the total and multiplying by 100.
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Percentiles in data
A percentile indicates the value below which a given percentage of observations fall, such as the 75th percentile meaning 75% of data is below that value.
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Sales tax as a percent
Sales tax is an additional percentage added to the purchase price, calculated by multiplying the price by the tax rate as a decimal.
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Commission as a percent
Commission is a percentage of sales paid to a salesperson, calculated by multiplying the sales amount by the commission rate.
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Interest rate conversion
Interest rates are often given as annual percentages but must be converted to decimals for formulas, such as 5% becoming 0.05.
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Effective annual rate
The effective annual rate accounts for compounding periods, calculated as (1 + r/n)^n - 1, where r is the nominal annual rate as a decimal.
- 40
Break-even point with percentages
The break-even point is when revenue equals costs, often involving percentages for profit margins to determine the required sales volume.
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Margin vs. markup
Margin is the profit as a percentage of selling price, while markup is as a percentage of cost price, and they are calculated differently in business contexts.
- 42
Example: 20% increase of 50
A 20% increase of 50 means multiplying 50 by 0.20 to get 10, then adding to the original for 60, illustrating basic percent application.
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Example: Successive 10% and 20% increase
Starting with 100, a 10% increase gives 110, then a 20% increase on 110 gives 132, showing the compounded effect of successive percentages.
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Example: Discount of 15% on 200
A 15% discount on 200 is calculated as 0.15 times 200 equals 30, so the final price is 170, demonstrating percent reduction.
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Example: Simple interest on 1000 at 5% for 2 years
Simple interest is 1000 times 0.05 times 2 equals 100, so the total is 1100, illustrating the formula in action.
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Example: Compound interest on 1000 at 5% annually for 2 years
Compound interest is 1000 times (1 + 0.05)^2 equals 1102.50, showing how interest accumulates on interest.
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Example: Mixture of 10% and 20% solutions
To get 10 liters of 15% solution, mix 5 liters of 10% and 5 liters of 20%, using alligation to balance the concentrations.
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Example: Profit percentage on 200 cost for 250 sale
Profit is 50, so profit percentage is (50 divided by 200) times 100% equals 25%, illustrating calculation from cost.
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Advanced: Percent change in averages
Percent change in averages requires weighting changes by their contributions, as a simple average percent change can mislead in weighted scenarios.
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Advanced: Percentiles in distributions
In a data set, percentiles divide the data into 100 equal parts, and calculating them involves ranking and interpolation for precise values.
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Advanced: Reverse engineering percentages
To find the original price before a 20% discount that resulted in 80, divide 80 by (1 - 0.20) to get 100, reversing the percent change.
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Advanced: Cascading discounts
Cascading discounts apply multiple percentages sequentially, where the overall discount is less than the sum, calculated step by step.
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Advanced: Percentage in probability
Percentages express probabilities as parts per hundred, such as a 25% chance meaning 1 in 4, but must be converted for calculations.
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Advanced: Elasticity with percentages
Price elasticity measures the percentage change in quantity demanded relative to percentage change in price, indicating responsiveness in economics.
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Common trap: Assuming additive percentages
Percentages are not always additive; for example, two successive 50% increases on 100 result in 225, not 200, due to compounding.
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Strategy: Using proportions for percentages
Set up proportions to solve percentage problems, such as part/whole = percent/100, to find unknown values systematically.
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Percent in work rates
Work rates can be expressed as percentages of a job completed per unit time, allowing for calculations of combined efforts.
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Percent in data interpretation
In charts and graphs, percentages represent proportions of totals, requiring careful reading to avoid misinterpreting scales.
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Formula: Percentage increase and decrease
The formula for net percentage change after successive increases or decreases is more complex, often requiring algebraic expansion.
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Example: Weighted average of percentages
For two groups with 40% and 60% averages weighted 2:1, the overall average is (240% + 160%) divided by 3, equaling about 46.67%.
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Advanced: Percent error in estimates
Percent error helps evaluate the accuracy of estimates in problems, calculated relative to the true value for comparison.