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Important Formulas: Percentages | Quantitative for GMAT PDF Download

A percentage is a way of expressing a number as a fraction of 100. 
The term "percent" comes from Latin: per centum, meaning "by the hundred." So, when we say 45%, we’re saying 45 out of every 100 parts.

Important Formulas: Percentages | Quantitative for GMAT

On the GMAT, percentages are commonly used to measure things like growth, reduction, interest rates, proportions, and rates of change.
Examples of Percentages are as following

  • 10% = 10/100 = 1/10 fraction
  • 25% = 25/100 = 1/4 fraction
  • 90% = 90/100 = 9/10 fraction
  • Percentages are dimensionless values, meaning they lack any specific units of measurement. 
  • Therefore, they are referred to as dimensionless numbers. When we state something like "50% of a number," it signifies 50 percent of the entire amount.
  • Percentages can also be expressed as decimals or fractions, such as 0.6% or 0.25%. In educational contexts, academic performance is often evaluated using percentages. 
  • For Example, suppose Ram obtains a score of 78% in his final exam. In that case, this percentage is calculated based on the total marks Ram achieved across all subjects relative to the total available marks.

Percentage Formula

  • To determine the percentage, we have to divide the value by the total value and then multiply the resultant by 100.
  • Percentage formula = (Value/Total value) × 100
  • For Example: 2/5 × 100 = 0.4 × 100 = 40 per cent

How to calculate the percentage of a number?

  • To calculate the percentage of a number, we need to use a different formula such as: 
    P% of Number = X, where X is the required percentage.
  • If we remove the % sign, then we need to express the above formulas as;
    (P/100) x Number = X
  • Example: Calculate 10% of 80.
    Sol: Let 10% of 80 = X
    10/100 * 80 = X
    X = 8

Question for Important Formulas: Percentages
Try yourself:
What is 15% of 200?
View Solution

Percentage Difference Formula

  • If we are given with two values and we need to find the percentage difference between these two values, then it can be done using the formula:
  • Important Formulas: Percentages | Quantitative for GMAT
  • For Example, if 20 and 30 are two different values, then the percentage difference between them will be
    % difference between 20 and 30 =Important Formulas: Percentages | Quantitative for GMAT
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Percentage Increase and Decrease

  • The percentage increase is equal to the subtraction of the original number from a new number, divided by the original number and multiplied by 100.
  • % increase = [(New number – Original number)/Original number] x 100
    where, increase in number = New number – Original number
  • Similarly, a percentage decrease is equal to the subtraction of a new number from the original number, divided by the original number and multiplied by 100. 
  • % decrease = [(Original number – New number)/Original number] x 100
    Where decrease in number = Original number – New number
    So basically if the answer is negative then there is a percentage decrease.
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Percentage Chart

Important Formulas: Percentages | Quantitative for GMAT

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Converting Fractions to Percentage

  • A fraction can be represented by a/b.
  • Multiplying and dividing the fraction by 100, we have
    Important Formulas: Percentages | Quantitative for GMAT

  • From the definition of percentage, we have; (1/100) = 1%
    Thus, equation (i) can be written as: (a/b) × 100%
  • Therefore, a fraction can be converted to a percentage simply by multiplying the given fraction by 100.

Example 1: If 16% of 40% of a number is 8, then find the number.

Sol: 
Let X be the required number.
Therefore, as per the given question, 
(16/100) × (40/100) × X = 8
So, X = (8 × 100 × 100) / (16 × 40)
= 125

Example 2: What percentage of 2/7 is 1/35?

Sol:
Let X% of 2/7 is 1/35.
∴ [(2/7) / 100] × X = 1/35
⇒ X = (1/35) × (7/2) × 100 
= 10%

Difference between Percentage and Percent

Important Formulas: Percentages | Quantitative for GMAT

Example 1: 70% of 30 is 21

Sol: 70 is the percentage.
30 is the base.
21 is the part.

Example 2: 25% of 200 is 50

Sol: 25 is the percent.
200 is the base.
50 is the part.

Question for Important Formulas: Percentages
Try yourself:What is the percentage increase if a value goes from 50 to 70?
View Solution

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FAQs on Important Formulas: Percentages - Quantitative for GMAT

1. What is the formula to calculate percentages?
Ans. The formula to calculate a percentage is: Percentage = (Part / Whole) × 100. For example, if you want to find out what percentage 25 is of 200, you would calculate (25 / 200) × 100 = 12.5%.
2. How do you convert a fraction to a percentage?
Ans. To convert a fraction to a percentage, you divide the numerator by the denominator and then multiply the result by 100. For example, to convert 3/4 to a percentage: (3 ÷ 4) × 100 = 75%.
3. How can I find the percentage increase or decrease?
Ans. To find the percentage increase or decrease, use the formula: Percentage Change = [(New Value - Old Value) / Old Value] × 100. For example, if the old value is 50 and the new value is 75, the percentage increase is [(75 - 50) / 50] × 100 = 50%.
4. What is the difference between a percentage and a fraction?
Ans. A percentage represents a part out of 100, while a fraction represents a part of a whole. For instance, 50% means 50 out of 100, which can also be expressed as the fraction 1/2.
5. How do I calculate the percentage of a number?
Ans. To calculate the percentage of a number, you multiply the number by the percentage (expressed as a decimal). For example, to find 20% of 50, you would calculate 50 × 0.20 = 10.
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