GMAT Exam > GMAT Notes > Crash Course > Quick Revision: Quant Reasoning (Algebra)
Quick Revision: Quant Reasoning (Algebra)
Quadratic Equations
Inequalities and Absolute
Sequences
Coordinate Geometry
Linear Equations
Exponents
Functions
Fractions, Decimals, Percents (FDP)
The document Quick Revision: Quant Reasoning (Algebra) is a part of the GMAT Course Crash Course for GMAT.
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FAQs on Quick Revision: Quant Reasoning (Algebra)
| 1. What are the key methods for solving quadratic equations? |  |
Ans. Quadratic equations can be solved using several methods: factoring, completing the square, and applying the quadratic formula. Factoring involves expressing the equation in the form (ax + b)(cx + d) = 0. Completing the square transforms the equation into a perfect square trinomial. The quadratic formula, x = (-b ± √(b² - 4ac)) / 2a, provides solutions directly from the coefficients a, b, and c of the equation ax² + bx + c = 0.
| 2. How do you solve linear inequalities? | |
Ans. To solve linear inequalities, first isolate the variable on one side using similar steps as solving linear equations. When multiplying or dividing both sides by a negative number, the inequality sign must be reversed. The solution can be expressed in interval notation or graphically on a number line, indicating the range of values that satisfy the inequality.
| 3. What is the difference between functions and relations? | |
Ans. A function is a special type of relation where each input (or x-value) has exactly one output (or y-value). In contrast, a relation may have multiple outputs for a single input. For example, the equation y² = x represents a relation but not a function, as each x may correspond to two different y values (positive and negative).
| 4. How are fractions, decimals, and percents related? | |
Ans. Fractions, decimals, and percents are three different ways to express the same concept: part of a whole. A fraction represents a part as a numerator over a denominator (e.g., 1/2), a decimal represents the same part in base ten (0.5), and a percent expresses it as a part out of 100 (50%). They can be converted into one another using multiplication or division by 100.
| 5. What role do exponents play in algebra? | |
Ans. Exponents indicate how many times a number, known as the base, is multiplied by itself. In algebra, they are used to simplify expressions, solve equations, and express large numbers in a more manageable form. Understanding the laws of exponents, such as aᵐ × aⁿ = aᵐ⁺ⁿ and (aᵐ)ⁿ = aᵐⁿ, is essential for manipulating algebraic expressions effectively.
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Apr 18, 2026 Last updated
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