GMAT Quant: Master 20 Essential Formulas – Your Ultimate Cheat Sheet

GMAT Quant is a formidable section for many test-takers, often requiring not just logical reasoning but also a solid foundation in core mathematical principles. While the GMAT emphasizes problem-solving and critical thinking over rote memorization, a strong command of essential formulas can dramatically improve your speed and accuracy. Think of these formulas not as shortcuts, but as the fundamental building blocks that allow you to quickly construct solutions to complex problems. Having a ready-to-go mental cheat sheet for the most common formulas will free up valuable mental bandwidth during the exam, letting you focus on the intricate logic rather than recalling basic equations.

Why Mastering Common Formulas is Crucial for GMAT Quant

The GMAT Quant section is time-pressured. Each question demands not only the correct approach but also efficient execution. While you won’t be asked to simply plug numbers into a formula, understanding and knowing the formulas allows you to:

Solve Faster: Recognize patterns and apply the appropriate formula without hesitation, saving precious seconds.
Reduce Errors: Solidify your understanding of foundational concepts, leading to fewer computational mistakes.
Tackle Complex Problems: Many challenging GMAT problems are multi-step, requiring the application of several different formulas in sequence. Knowing them cold helps you break down the problem efficiently.
Build Confidence: A strong grasp of the basics boosts your confidence, allowing you to approach trickier questions with a clearer mind.

Instead of trying to derive these formulas under pressure, internalizing them empowers you to focus on the strategic elements of each question.

The Essential GMAT Quant Formula Cheat Sheet

Here are 20 essential formulas and key concepts categorized by topic that you should have at your fingertips for the GMAT Quant section. This isn’t just about memorization; it’s about understanding when and how to apply each one.

Arithmetic & Number Properties

1. Percentage Change:
   Percentage Change = ((New Value - Old Value) / Old Value) <em> 100%
   Use this to calculate increases or decreases relative to an initial value.

2. Average (Arithmetic Mean):
   Average = Sum of Terms / Number of Terms
   A fundamental concept, often used with weighted averages or finding missing values.

3. Sum of an Arithmetic Series:
   Sum = (n/2) </em> (First Term + Last Term)
   Where ‘n’ is the number of terms. Useful for quickly summing sequences like 1+2+3+…+100.

4. Work Formula:
   Work = Rate × Time
   For combined work, remember 1/T_total = 1/T1 + 1/T2 + ... where T is the time each entity takes to complete the work alone.

5. Distance Formula:
   Distance = Rate × Time
   A core formula for motion problems, often involving relative speeds or average speed calculations.

6. Divisibility Rules:
   Know the rules for 2, 3, 4, 5, 6, 8, 9, and 10.
   By 3: Sum of digits is divisible by 3.
   By 9: Sum of digits is divisible by 9.
   These are crucial for number properties questions.

Algebra

1. Quadratic Formula:
   x = [-b ± sqrt(b² - 4ac)] / 2a
   Used to solve quadratic equations of the form ax² + bx + c = 0.

2. Difference of Squares:
   a² - b² = (a - b)(a + b)
   An invaluable factoring technique that can simplify complex expressions rapidly.

3. Exponent Rules:
   x^a </em> x^b = x^(a+b)
x^a / x^b = x^(a-b)
(x^a)^b = x^(ab)
x^0 = 1 (for x ≠ 0)
   x^-a = 1/x^a
   Mastering these helps simplify expressions with powers and roots.

4. Simple Interest:
   Interest (I) = Principal (P) × Rate (R) × Time (T)
   Basic interest calculation, often appearing in word problems.

5. Compound Interest (Understanding):
   While the full formula A = P(1 + r/n)^(nt) is complex, GMAT usually tests the concept of compounding (interest earned on interest) or simpler step-by-step calculations. Understand that compounding leads to faster growth than simple interest.