GMAT math formulas: Essential knowledge for a high quantitative score

The Graduate Management Admission Test (GMAT) is a standardised test that assesses the mathematical and analytical skills of prospective business school candidates. One of the important sections of GMAT is the maths section, also known as the quantitative section, which measures your ability to understand, interpret, and analyse mathematical and data-related problems within a limited time frame.

To excel in the GMAT maths section and achieve a high quantitative score, it's essential to have a strong understanding of the fundamental mathematical concepts and formulas that are tested on the exam.

In this guide, we will cover the essential GMAT maths formulas that you should know.

Arithmetic formulas

1. Properties of integers:

• Even numbers: n is even if n = 2k, where k is an integer.
• Odd numbers: n is odd if n = 2k + 1, where k is an integer.
• Divisibility rules:
  • A number is divisible by 2 if its unit digit is even (ends in 0, 2, 4, 6, or 8).
  • A number is divisible by 3 if the sum of its digits is divisible by 3.
  • A number is divisible by 4 if its last two digits form a multiple of 4.
  • A number is divisible by 5 if its unit digit is 0 or 5.
  • A number is divisible by 6 if it is divisible by both 2 and 3.
  • A number is divisible by 9 if the sum of its digits is divisible by 9.
• Prime numbers: A prime number is a positive integer greater than 1 that has no positive integer divisors other than 1 and itself.

2. Percentages

• Percentage change: Percentage change = (New Value - Old Value) / Old Value * 100%
• Percentage increase: Percentage increase = (Increase/Original Value) * 100%
• Percentage decrease: Percentage decrease = (Decrease/Original Value) * 100%

3. Ratios and proportions

• Ratio: A ratio is a comparison of two quantities. The ratio of a to b is written as a:b or a/b.
• Proportion: A proportion is an equation that states two ratios are equal. In a proportion, the product of the means (ad) is equal to the product of the extremes (bc), where a/b = c/d.

4. Averages and weighted averages:

• Mean (Average): Mean = Sum of all values / Total number of values
• Median: The median is the middle value in a set of values when arranged in numerical order.
• Mode: The mode is the value that appears most frequently in a set of values.
• Weighted Average: Weighted Average = (Sum of (Value * Weight) for all values) / (Sum of Weights)

5. Interest

• Simple Interest: Simple Interest = (Principal * Rate * Time) / 100
• Compound Interest: Compound Interest = Principal * (1 + Rate/100)^Time - Principal
• Effective Interest Rate: Effective Interest Rate = (1 + Nominal Rate/Number of Compounding Periods)^Number of Compounding Periods - 1

Also Read: GMAT Exam Pattern

Algebra formulas

1. Linear equations

• Formula for solving linear equations with one variable: ax + b = 0 -> x = -b/a
• Formula for solving linear equations with two variables: ax + by = c, dx + ey = f -> x = (ce - bf) / (ae - bd), y = (af - cd) / (ae - bd)

2. Quadratic equations

• Quadratic Formula: For ax^2 + bx + c = 0, x = (-b ± √(b^2 - 4ac)) / (2a)

3. Inequalities

• Linear Inequalities: ax + b < c, ax + b > c, ax + b ≤ c, ax + b ≥ c -> x > (c - b) / a, x < (c - b) / a, x ≥ (c - b) / a, x ≤ (c - b) / a
• Quadratic Inequalities: ax^2 + bx + c < 0 
  or ax^2 + bx + c > 0, ax^2 + bx + c ≤ 0, ax^2 + bx + c ≥ 0 -> solving quadratic inequalities involves finding the values of x that satisfy the inequality and lie within the specified range.

4. Functions

• Domain: The domain of a function is the set of all possible input values (x-values) for which the function is defined.
• Range: The range of a function is the set of all possible output values (y-values) that the function can produce.
• Function notation: If y = f(x), then f(x) is the function notation for the function y.

Also Read: GMAT Books for Preparation

Geometry formulas

1. Perimeter and area of basic shapes

• Rectangle: Perimeter = 2 * (length + width), Area = length * width
• Square: Perimeter = 4 * side length, Area = side length^2
• Circle: Circumference = 2 * π * radius, Area = π * radius^2
• Triangle: Perimeter = sum of lengths of all sides, Area = 0.5 * base * height
• Trapezoid: Perimeter = sum of lengths of all sides, Area = 0.5 * (sum of bases) * height

2. Properties of triangles

• Pythagorean Theorem: In a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. a^2 + b^2 = c^2, where a and b are the lengths of the two shorter sides and c is the length of the hypotenuse.
• Triangle Sum Property: The sum of the measures of the angles in a triangle is always 180 degrees.
• Area of a Triangle: Area = 0.5 * base * height or Area = √(s * (s-a) * (s-b) * (s-c)), where s is the semi-perimeter of the triangle, and a, b, c are the lengths of the three sides.

Also Read: GMAT Study Plan

Statistics formulas

• Mean: The mean, or average, of a set of numbers is the sum of all the numbers divided by the total number of numbers in the set. Mean = (Sum of all numbers) / (Total number of numbers)
• Median: The median of a set of numbers is the middle value when the numbers are arranged in ascending or descending order. If there is an even number of numbers, the median is the average of the two middle values. Median = Middle value(s)
• Mode: The mode of a set of numbers is the value(s) that appears most frequently. Mode = Most frequent value(s)

Exponents and radicals formulas

1. Exponent rules

• Product of Powers: a^m * a^n = a^(m+n)
• Quotient of Powers: a^m / a^n = a^(m-n)
• Power of a Power: (a^m)^n = a^(m*n)
• Power of a Product: (ab)^m = a^m * b^m
• Power of a Quotient: (a/b)^m = a^m / b^m
• Negative Exponent: a^(-m) = 1 / a^m

2. Radical rules

• Square Root: √a * √a = a
• Cube Root: ∛a * ∛a * ∛a = a
• nth Root: √n√a = a^(1/n)

Probability formulas

• Probability: Probability of an event = Number of favourable outcomes / Total number of possible outcomes
• Complementary Probability: P(A') = 1 - P(A), where A' represents the complement of event A, and P(A) and P(A') represent the probabilities of event A and its complement, respectively.

Coordinate geometry formulas

• Distance Formula: The distance between two points (x1, y1) and (x2, y2) in a coordinate plane is given by: d = √[(x2 - x1)^2 + (y2 - y1)^2]
• Slope of a Line: The slope (m) of a line passing through two points (x1, y1) and (x2, y2) is given by: m = (y2 - y1) / (x2 - x1)
• Midpoint Formula: The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by: Midpoint = [((x1 + x2)/2), ((y1 + y2)/2)]

Arithmetic and geometric progression formulas

• Arithmetic Progression (AP): An arithmetic progression is a sequence of numbers in which the difference between any two consecutive terms is constant. The nth term of an arithmetic progression with the first term 'a' and the common difference 'd' is given by: An = a + (n - 1)d where n is the position of the term in the sequence.
• Geometric Progression (GP): A geometric progression is a sequence of numbers in which the ratio of any two consecutive terms is constant. The nth term of a geometric progression with the first term 'a' and the common ratio 'r' is given by: Gn = a * r^(n - 1) where n is the position of the term in the sequence.

Set theory formulas

• Union of Sets: The union of two sets A and B, denoted as A ∪ B, is the set of all elements that are in either A or B or in both.
• Intersection of Sets: The intersection of two sets A and B, denoted as A ∩ B, is the set of all elements that are in both A and B.
• Complement of a Set: The complement of a set A, denoted as A', is the set of all elements that are in the universal set but not in A.

Profit and loss formulas

• Cost Price (CP): The price at which an item is bought is known as the cost price.
• Selling Price (SP): The price at which an item is sold is known as the selling price.
• Profit (P): The amount earned after selling an item at a price higher than its cost price. P = SP - CP
• Loss (L): The amount incurred after selling an item at a price lower than its cost price. L = CP - SP
• Profit Percentage (PP): The percentage of profit earned on the cost price. PP = (Profit / CP) * 100
• Loss Percentage (LP): The percentage of loss incurred on the cost price. LP = (Loss / CP) * 100

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Conclusion

It is important to note that while memorising these formulas is essential, understanding their applications and being able to apply them in various problem-solving scenarios is equally important. Practising GMAT maths problems and using these formulas in real-world scenarios will help you improve your quantitative skills and achieve a high score on the GMAT maths section.

Frequently asked questions

How important is it to memorise GMAT maths formulas?

While it's important to be familiar with the essential GMAT maths formulas, it's equally important to understand how to apply them in different problem-solving scenarios. The GMAT is not solely about memorization, but also about critical thinking and logical reasoning. So, focus on developing a deep understanding of the concepts and their applications, rather than just memorising formulas.

Can I use my own calculator during the GMAT?

No, you cannot bring your own calculator to the GMAT test. The GMAT provides an on-screen calculator for certain sections of the test. However, it's important to note that the calculator is basic and only allows for basic arithmetic calculations.

How can I effectively prepare for GMAT maths?

To effectively prepare for GMAT maths, start by reviewing the fundamental mathematical concepts that are tested on the GMAT. Familiarise yourself with the essential GMAT maths formulas and practice solving a wide range of GMAT maths problems. Additionally, take practice tests and review your mistakes to identify areas where you need to improve.