Formula Library
Browse and search through 32 formulas, tricks, and mnemonics
Showing 32 of 32 formulas
Quantitative Aptitude • Algebra
(a-b)² Formula
(a-b)² = a² - 2ab + b²
The square of difference of two numbers equals the sum of their squares minus twice their product.
Quantitative Aptitude • Algebra
(a+b)² Formula
(a+b)² = a² + 2ab + b²
The square of sum of two numbers equals the sum of their squares plus twice their product.
Quantitative Aptitude • Algebra
(a+b+c)² Formula
(a+b+c)² = a² + b² + c² + 2ab + 2bc + 2ca
Expansion of square of three terms.
Quantitative Aptitude • Algebra
a² - b² Formula
a² - b² = (a+b)(a-b)
Difference of squares can be factored as product of sum and difference.
Quantitative Aptitude • Algebra
a³ - b³ Formula
a³ - b³ = (a-b)(a² + ab + b²)
Difference of cubes can be factored.
Quantitative Aptitude • Algebra
a³ + b³ Formula
a³ + b³ = (a+b)(a² - ab + b²)
Sum of cubes can be factored.
Reasoning • Coding-Decoding
Alphabet Coding - Shift Method
Each letter shifts by same position. A→D means shift by 3 for all letters.
Simple substitution cipher where each letter is replaced by another at fixed position.
Reasoning • Analogy
Analogy Pattern Recognition
A is to B as C is to D: A:B :: C:D
Finding similar relationships between different pairs.
Quantitative Aptitude • Arithmetic
Average Formula
Average = Sum of all values / Number of values
Mean or average of a set of numbers.
Quantitative Aptitude • Trigonometry
Basic Trigonometric Ratios
sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent
SOH CAH TOA mnemonic for sine, cosine, tangent.
Quantitative Aptitude • Geometry
Circle Area Formula
Area = πr²
Area of a circle with radius r.
Quantitative Aptitude • Time & Work
Combined Work Formula
1/Total Time = 1/Time_A + 1/Time_B
When two people work together, rates add up.
English • Error Spotting
Common Grammar Errors
Check: Subject-verb agreement, tense consistency, pronoun reference, article usage.
Identify grammatical mistakes in sentences.
Quantitative Aptitude • Arithmetic
Compound Interest Formula
A = P(1 + r/100)^n
Amount after compound interest for principal P at rate r% for n periods.
Reasoning • Series
Number Series - Arithmetic Progression
Series: a, a+d, a+2d, a+3d... where d is common difference. nth term = a + (n-1)d
Numbers increase or decrease by constant difference.
Reasoning • Series
Number Series - Geometric Progression
Series: a, ar, ar², ar³... where r is common ratio. nth term = ar^(n-1)
Numbers multiply or divide by constant ratio.
Quantitative Aptitude • Arithmetic
Percentage Increase/Decrease
Percentage = (Difference / Original) × 100
To find what percent one number is of another.
Quantitative Aptitude • Geometry
Pythagorean Theorem
a² + b² = c²
In a right triangle, sum of squares of two sides equals square of hypotenuse.
Quantitative Aptitude • Arithmetic
Ratio and Proportion
If a:b = c:d, then ad = bc
In proportion, product of extremes equals product of means.
English • Comprehension
Reading Comprehension Strategy
1. Read passage quickly (main idea). 2. Read questions. 3. Find relevant sentence. 4. Choose answer.
Systematic approach to solving comprehension passages.
Quantitative Aptitude • Speed & Distance
Relative Speed Formula
Relative Speed (same direction) = |S1 - S2|. Opposite direction = S1 + S2
Speed of one object relative to another depends on direction.
Quantitative Aptitude • Arithmetic
Simple Interest Formula
SI = (P × R × T) / 100
Simple Interest = Principal × Rate × Time / 100
Quantitative Aptitude • Speed & Distance
Speed-Distance-Time Formula
Speed = Distance / Time
Speed is distance covered per unit time.
English • Grammar
Subject-Verb Agreement
Singular subject + singular verb. Plural subject + plural verb.
Verb must agree with subject in number and person.
Reasoning • Logical Reasoning
Syllogism Basics
All A are B. All B are C. Therefore, All A are C.
Universal statement about relationships between three groups.
English • Vocabulary
Synonyms and Antonyms
Synonyms = similar meaning. Antonyms = opposite meaning.
Using context to identify word relationships.
English • Grammar
Tense Usage - Past, Present, Future
Simple: base action. Continuous: -ing form. Perfect: have/has/had + past participle
Three time frames, each with simple, continuous, and perfect forms.
Quantitative Aptitude • Geometry
Triangle Area Formula
Area = 1/2 × base × height
Area of any triangle is half the product of base and perpendicular height.
Quantitative Aptitude • Trigonometry
Trigonometric Values (0°-90°)
sin²θ + cos²θ = 1
Fundamental trigonometric identity. Standard angles: 0°, 30°, 45°, 60°, 90°
Reasoning • Logical Reasoning
Venn Diagram Logic
Use overlapping circles to represent relationships between sets.
Visual representation of logical relationships.
English • Vocabulary
Word Roots - Latin Prefixes
Common prefixes: un-, re-, pre-, dis-, mis-, over-, under-, de-, in-
Understanding prefixes helps decode unknown words.
Quantitative Aptitude • Time & Work
Work Rate Formula
Work = Rate × Time, or Rate = 1/Time
If a person completes work in T days, rate = 1/T of work per day.