GRE General Test Quantitative Reasoning Ultimate
Cheat Sheet
Course Code: GRE_QUANT_2026
Topic: Comprehensive Formula Bank , High-Yield Math Shortcuts& Example
Exam questions
Academic Year: 2026/2027
1. THE MOST FORGETTABLE & ADVANCED FORMULAS (HIGH-YIELD
ADDITIONS)
• Three-Set Venn Diagram Formula (Overlapping Sets):
Total = Group A + Group B + Group C - (Both A&B + Both B&C + Both
A&C) + (All Three A&B&C) + Neither
• Sum of an Arithmetic Sequence:
Sum = n × [(First Term + Last Term) / 2]
(Where n = number of terms, found by: n = [(Last Term - First Term) /
Common Difference] + 1)
• Combinations with Repetition Allowed:
Unique Combinations = (n + k - 1)! / [k!(n - 1)!]
(Used when picking k items from n categories, and you can pick the same
category multiple times)
• Standard Deviation (SD) Core Properties:
o If a constant \(k\) is added or subtracted to every term in a set, the
Standard Deviation remains unchanged.
o If every term in a set is multiplied or divided by a positive constant
\(k\), the Standard Deviation is also multiplied or divided by \(k\).
, • The Quadratic Formula & Discriminant:
For \(ax^2 + bx + c = 0\), the roots are found by: \(x = [-b \pm \sqrt{b^2 -
4ac}] / 2a\)
o If Discriminant (\(b^2 - 4ac\)) > 0: Two distinct real roots.
o If Discriminant (\(b^2 - 4ac\)) = 0: Exactly one real root.
o If Discriminant (\(b^2 - 4ac\)) < 0: No real roots.
2. ARITHMETIC & NUMBER PROPERTIES (THE FOUNDATION)
Core Formulas & Visual Mappings
• Percent Change Formula:
Percent Change = [(New Value - Original Value) / Original Value] × 100%
o High-Yield Tip: Always divide by the Original (Old) Value, never the
new one!
• Simple Interest:
I=P×r×t
(Where P = principal, r = annual interest rate as a decimal, and t = time in
years)
• Compound Interest:
A = P × (1 + r/n)^(n × t)
(Where A = total balance, n = number of times compounded per year)
Rules of Odds and Evens
• Even ± Even = Even
• Odd ± Odd = Even
• Even ± Odd = Odd
• Even × Any Integer = Even
• Odd × Odd = Odd
Absolute Divisibility Rules
• Divisible by 3: The sum of the digits must be a multiple of 3.
, • Divisible by 4: The last two digits formed as a 2-digit number must be a
multiple of 4.
• Divisible by 9: The sum of the digits must be a multiple of 9.
3. ALGEBRA & COORDINATE GEOMETRY (THE STRATEGY)
The Big Three Algebraic Identities (Must Memorize)
1. Difference of Squares: a² - b² = (a - b)(a + b)
2. Square of a Sum: (a + b)² = a² + 2ab + b²
3. Square of a Difference: (a - b)² = a² - 2ab + b²
Coordinate Systems & Linear Behavior
• Slope Formula:
m = (y₂ - y₁) / (x₂ - x₁) = Rise / Run
• Slope-Intercept Form:
y = mx + b
(Where m = slope, b = y-intercept)
• Distance on a Coordinate Plane:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
4. ESSENTIAL GEOMETRY (THE ROADMAP)
Polygons & Angles
• Sum of Interior Angles:
Sum = (n - 2) × 180°
(Where n = number of sides)
• Individual Interior Angle (Regular Polygon):
Angle = [(n - 2) × 180°] / n
Triangles & Quadrilaterals
• Area of a Triangle:
Area = 1/2 × Base × Height
Cheat Sheet
Course Code: GRE_QUANT_2026
Topic: Comprehensive Formula Bank , High-Yield Math Shortcuts& Example
Exam questions
Academic Year: 2026/2027
1. THE MOST FORGETTABLE & ADVANCED FORMULAS (HIGH-YIELD
ADDITIONS)
• Three-Set Venn Diagram Formula (Overlapping Sets):
Total = Group A + Group B + Group C - (Both A&B + Both B&C + Both
A&C) + (All Three A&B&C) + Neither
• Sum of an Arithmetic Sequence:
Sum = n × [(First Term + Last Term) / 2]
(Where n = number of terms, found by: n = [(Last Term - First Term) /
Common Difference] + 1)
• Combinations with Repetition Allowed:
Unique Combinations = (n + k - 1)! / [k!(n - 1)!]
(Used when picking k items from n categories, and you can pick the same
category multiple times)
• Standard Deviation (SD) Core Properties:
o If a constant \(k\) is added or subtracted to every term in a set, the
Standard Deviation remains unchanged.
o If every term in a set is multiplied or divided by a positive constant
\(k\), the Standard Deviation is also multiplied or divided by \(k\).
, • The Quadratic Formula & Discriminant:
For \(ax^2 + bx + c = 0\), the roots are found by: \(x = [-b \pm \sqrt{b^2 -
4ac}] / 2a\)
o If Discriminant (\(b^2 - 4ac\)) > 0: Two distinct real roots.
o If Discriminant (\(b^2 - 4ac\)) = 0: Exactly one real root.
o If Discriminant (\(b^2 - 4ac\)) < 0: No real roots.
2. ARITHMETIC & NUMBER PROPERTIES (THE FOUNDATION)
Core Formulas & Visual Mappings
• Percent Change Formula:
Percent Change = [(New Value - Original Value) / Original Value] × 100%
o High-Yield Tip: Always divide by the Original (Old) Value, never the
new one!
• Simple Interest:
I=P×r×t
(Where P = principal, r = annual interest rate as a decimal, and t = time in
years)
• Compound Interest:
A = P × (1 + r/n)^(n × t)
(Where A = total balance, n = number of times compounded per year)
Rules of Odds and Evens
• Even ± Even = Even
• Odd ± Odd = Even
• Even ± Odd = Odd
• Even × Any Integer = Even
• Odd × Odd = Odd
Absolute Divisibility Rules
• Divisible by 3: The sum of the digits must be a multiple of 3.
, • Divisible by 4: The last two digits formed as a 2-digit number must be a
multiple of 4.
• Divisible by 9: The sum of the digits must be a multiple of 9.
3. ALGEBRA & COORDINATE GEOMETRY (THE STRATEGY)
The Big Three Algebraic Identities (Must Memorize)
1. Difference of Squares: a² - b² = (a - b)(a + b)
2. Square of a Sum: (a + b)² = a² + 2ab + b²
3. Square of a Difference: (a - b)² = a² - 2ab + b²
Coordinate Systems & Linear Behavior
• Slope Formula:
m = (y₂ - y₁) / (x₂ - x₁) = Rise / Run
• Slope-Intercept Form:
y = mx + b
(Where m = slope, b = y-intercept)
• Distance on a Coordinate Plane:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
4. ESSENTIAL GEOMETRY (THE ROADMAP)
Polygons & Angles
• Sum of Interior Angles:
Sum = (n - 2) × 180°
(Where n = number of sides)
• Individual Interior Angle (Regular Polygon):
Angle = [(n - 2) × 180°] / n
Triangles & Quadrilaterals
• Area of a Triangle:
Area = 1/2 × Base × Height
