Quantitative Aptitude: Percentage Calculations

• Quantitative aptitude is a category that includes numerical and mathematical skills used to solve problems
• Topics include percentage calculations, data interpretation, number series, algebraic expressions, profit and loss, and others

Percentage Calculations

• Percentage means "per hundred" or "out of 100"
• The symbol for percent is %
• Percentages are used to express a fraction or ratio as a part of 100
• To convert a fraction to a percentage, multiply the fraction by 100
• To convert a percentage to a fraction, divide the percentage by 100
• To find a percentage of a number, multiply the number by the percentage (expressed as a decimal or fraction)
• Percentage increase is calculated as [(New Value - Old Value) / Old Value] * 100
• Percentage decrease is calculated as [(Old Value - New Value) / Old Value] * 100
• Percentage change is calculated as [(New Value - Old Value) / Old Value] * 100; it can be increase or decrease
• If a value is increased by x%, the new value is (1 + x/100) times the original value
• If a value is decreased by x%, the new value is (1 - x/100) times the original value
• Successive percentage changes: If a number is changed successively by x% and y%, the net change is (x + y + xy/100)%

Data Interpretation

• Data Interpretation (DI) involves analyzing and interpreting data presented in various formats
• Common formats include tables, bar graphs, line graphs, pie charts, and caselets
• The goal is to extract relevant information and draw conclusions from the data
• Tables present data in rows and columns, useful for comparing discrete values
• Bar graphs use bars of different lengths to represent data, suitable for comparing quantities across categories
• Line graphs display data as a series of points connected by lines, ideal for showing trends over time
• Pie charts represent data as sectors of a circle, showing proportions of different categories to the whole
• Caselets provide a textual description of a data set, requiring careful reading and analysis to extract relevant information
• Key skills include reading and understanding the data, performing calculations, identifying trends, and making inferences

Number Series

• A number series is a sequence of numbers that follow a specific pattern or rule
• The goal is to identify the pattern and find the missing or next number in the series
• Common patterns include arithmetic progressions (constant difference), geometric progressions (constant ratio)
• Other patterns include differences (or ratios) of differences, squares, cubes, prime numbers
• Arithmetic Progression (AP): Each term is obtained by adding a constant value (common difference) to the previous term
• Geometric Progression (GP): Each term is obtained by multiplying the previous term by a constant value (common ratio)
• Identifying the pattern is crucial for solving number series problems
• Look for differences, ratios, squares, cubes, or combinations of these in the series

Algebraic Expressions

• Algebra involves using letters (variables) to represent numbers and mathematical operations
• An algebraic expression is a combination of variables, constants, and operators (+, -, *, /)
• Simplifying algebraic expressions involves combining like terms and applying the order of operations (PEMDAS/BODMAS)
• Equations are statements that two algebraic expressions are equal
• Solving equations involves finding the value(s) of the variable(s) that make the equation true
• Linear equations are equations where the highest power of the variable is 1
• Quadratic equations are equations where the highest power of the variable is 2 (ax^2 + bx + c = 0)
• Factoring is the process of expressing an algebraic expression as a product of simpler expressions
• Expanding is the process of multiplying out terms in an algebraic expression
• Common algebraic identities include: (a + b)^2 = a^2 + 2ab + b^2; (a - b)^2 = a^2 - 2ab + b^2; (a + b)(a - b) = a^2 - b^2; (x+a)(x+b) = x^2 + x(a+b) + ab
• These identities are useful for simplifying and solving algebraic problems quickly

Profit and Loss

• Profit and Loss are terms used to determine the financial outcome of a transaction
• Cost Price (CP) is the price at which an article is purchased
• Selling Price (SP) is the price at which an article is sold
• Profit occurs when the Selling Price (SP) is greater than the Cost Price (CP)
• Loss occurs when the Selling Price (SP) is less than the Cost Price (CP)
• Profit = Selling Price (SP) - Cost Price (CP)
• Loss = Cost Price (CP) - Selling Price (SP)
• Profit Percentage = (Profit / Cost Price) * 100
• Loss Percentage = (Loss / Cost Price) * 100
• Marked Price (MP) is the price labeled on an article, often higher than the cost price
• Discount is a reduction on the Marked Price
• Discount = Marked Price (MP) - Selling Price (SP)
• Discount Percentage = (Discount / Marked Price) * 100
• Selling Price (SP) = Marked Price (MP) - Discount
• Successive discounts: If an article is sold at successive discounts of x% and y%, the net discount is (x + y - xy/100)%
• False weight, a seller uses faulty weighing machine to increase profit