Quantitative review
57 flashcards covering Quantitative review for the GMAT Quantitative section.
Quantitative review involves strengthening your foundational math skills, such as algebra, geometry, arithmetic, and data analysis. These concepts form the core of problem-solving in business and management contexts, helping you tackle real-world scenarios like calculating profits or interpreting statistics. For someone new to this, think of it as building a toolkit of logical reasoning and numerical techniques that go beyond rote memorization to foster critical thinking.
On the GMAT Quantitative section, these skills appear in two main question types: Problem Solving, which requires selecting the correct answer from multiple choices, and Data Sufficiency, which tests your ability to determine if given information is enough to solve a problem. Common traps include misinterpreting word problems or falling for answer choices that look plausible but are incorrect. Focus on mastering time management, recognizing patterns in questions, and applying formulas accurately to boost your score.
Practice with a mix of easy and hard problems to build confidence.
Terms (57)
- 01
Integer
An integer is a whole number that can be positive, negative, or zero, with no fractional or decimal parts, and it is fundamental for arithmetic operations on the GMAT.
- 02
Prime Number
A prime number is a natural number greater than 1 that has exactly two distinct positive divisors: 1 and itself, often appearing in GMAT problems involving factors.
- 03
Factors and Multiples
Factors are integers that divide evenly into another integer, while multiples are the results of multiplying that integer by other integers, commonly tested in number theory questions.
- 04
Fractions
A fraction represents a part of a whole, expressed as one integer divided by another, and operations like addition or simplification are key for GMAT algebra and word problems.
- 05
Decimals
Decimals are numbers based on powers of ten, used to represent fractions or perform calculations, and they frequently appear in percentage and ratio problems on the exam.
- 06
Percentages
A percentage expresses a number as a fraction of 100, used for calculations like increases, decreases, or interest, and is essential for interpreting real-world scenarios in GMAT questions.
- 07
Ratios and Proportions
A ratio compares two quantities, while a proportion equates two ratios, both crucial for solving mixture, scaling, and similarity problems on the GMAT.
- 08
Exponents
Exponents indicate how many times a base number is multiplied by itself, following rules like multiplying powers or raising to another power, which are common in algebraic expressions.
- 09
Roots
Roots, such as square or cube roots, are the inverse of exponents and represent values that, when raised to a power, yield the original number, often tested in simplification tasks.
- 10
Linear Equations
Linear equations are first-degree equations like ax + b = c, solved by isolating the variable, and they form the basis for many GMAT algebra problems involving straight lines.
- 11
Quadratic Equations
Quadratic equations are second-degree polynomials of the form ax² + bx + c = 0, solved using factoring, completing the square, or the quadratic formula, appearing in advanced word problems.
- 12
Inequalities
Inequalities compare expressions using symbols like < or >, and solving them involves similar steps to equations but considers sign changes when multiplying by negatives, key for optimization scenarios.
- 13
Absolute Value
Absolute value is the distance of a number from zero on the number line, always non-negative, and equations involving it require considering both positive and negative cases in GMAT problems.
- 14
Functions
A function relates inputs to outputs via a rule, such as f(x) = x + 2, and understanding domain, range, and composition is important for interpreting relationships in data analysis.
- 15
Sequences and Series
A sequence is an ordered list of numbers, and a series is the sum of a sequence; arithmetic and geometric types are tested for patterns and sums in GMAT quantitative reasoning.
- 16
Permutations
Permutations are arrangements of objects where order matters, calculated using formulas like nPr = n! / (n-r)!, and they are essential for counting problems involving selections.
- 17
Combinations
Combinations are selections of objects where order does not matter, computed with nCr = n! / (r!(n-r)!), and they appear in probability and grouping scenarios on the exam.
- 18
Probability
Probability measures the likelihood of an event, calculated as favorable outcomes divided by total possible outcomes, and is crucial for problems involving chance and uncertainty.
- 19
Mean
The mean is the average of a set of numbers, found by summing them and dividing by the count, and it's a basic statistical measure used in data interpretation questions.
- 20
Median
The median is the middle value in an ordered list of numbers, or the average of the two middle values if even, helping to identify central tendencies in skewed data sets.
- 21
Mode
The mode is the number that appears most frequently in a data set, useful for understanding the most common value in distributions encountered on the GMAT.
- 22
Range
The range is the difference between the largest and smallest values in a data set, providing a simple measure of spread that is often compared with other statistics.
- 23
Pythagorean Theorem
The Pythagorean Theorem states that in a right-angled triangle, the square of the hypotenuse equals the sum of the squares of the other two sides, fundamental for distance and geometry problems.
- 24
Area of a Triangle
The area of a triangle is calculated as (base × height) / 2, and variations like Heron's formula are used for problems involving shapes and spatial reasoning on the GMAT.
- 25
Circumference of a Circle
The circumference of a circle is the distance around it, given by C = 2πr, where r is the radius, and it's essential for perimeter and arc length calculations.
- 26
Area of a Circle
The area of a circle is computed as A = πr², where r is the radius, and this formula is frequently applied in geometry questions involving sectors or shaded regions.
- 27
Volume of a Rectangular Prism
The volume of a rectangular prism is length × width × height, used for three-dimensional problems like capacity or packing in GMAT word problems.
- 28
Slope of a Line
The slope of a line is the change in y-coordinates divided by the change in x-coordinates between two points, indicating steepness and used in coordinate geometry equations.
- 29
Distance Formula
The distance formula calculates the straight-line distance between two points (x1, y1) and (x2, y2) as √[(x2 - x1)² + (y2 - y1)²], vital for spatial problems.
- 30
Midpoint Formula
The midpoint formula finds the center point between two coordinates as ((x1 + x2)/2, (y1 + y2)/2), helpful for symmetry and averaging in graphs.
- 31
Rate Problems
Rate problems involve speed, distance, and time, solved using the formula distance = rate × time, and they often include scenarios like travel or work.
- 32
Work Rate
Work rate is the fraction of a job completed per unit time, and combined rates for multiple workers are calculated by adding reciprocals, common in efficiency problems.
- 33
Mixture Problems
Mixture problems involve combining solutions with different concentrations, solved by setting up equations for total amounts, like in alloy or solution blending.
- 34
Simple Interest
Simple interest is calculated as principal × rate × time, used for financial problems where interest is computed only on the initial amount, not compounded.
- 35
Compound Interest
Compound interest is interest calculated on the initial principal and also on accumulated interest, using formulas like A = P(1 + r/n)^(nt), for growth over time.
- 36
Profit and Loss
Profit is the selling price minus cost price, and loss is the cost price minus selling price, with percentages calculated relative to cost, appearing in business math.
- 37
Discounts
A discount reduces the original price by a certain percentage, and successive discounts are multiplied, not added, for accurate final price calculations.
- 38
Greatest Common Divisor (GCD)
The GCD is the largest number that divides two or more integers without a remainder, found using methods like Euclidean algorithm, for simplifying fractions.
- 39
Least Common Multiple (LCM)
The LCM is the smallest number that is a multiple of two or more integers, calculated to find common denominators in fraction operations.
- 40
Divisibility Rules
Divisibility rules are quick tests, like a number is divisible by 3 if the sum of its digits is divisible by 3, used to factor numbers efficiently.
- 41
Factoring
Factoring breaks down polynomials into products of simpler expressions, such as (x + a)(x + b), essential for solving equations and simplifying.
- 42
Systems of Equations
Systems of equations involve two or more equations solved simultaneously, often by substitution or elimination, for finding intersection points.
- 43
Polynomial
A polynomial is an expression with variables and coefficients, like 3x² + 2x + 1, and operations include addition, multiplication, and factoring.
- 44
Quadratic Formula
The quadratic formula solves ax² + bx + c = 0 as x = [-b ± √(b² - 4ac)] / (2a), determining roots and used when factoring is difficult.
- 45
Similar Triangles
Similar triangles have the same shape with proportional sides and equal angles, allowing for ratio-based calculations in scaled geometry problems.
- 46
Pythagorean Triples
Pythagorean triples are sets of three positive integers, like 3-4-5, that satisfy the Pythagorean Theorem, speeding up right triangle calculations.
- 47
Venn Diagrams
Venn diagrams visually represent sets and their overlaps, used to solve problems involving unions, intersections, and element counting.
- 48
Standard Deviation
Standard deviation measures the spread of data from the mean, calculated by finding the square root of the variance, indicating data variability.
- 49
Counting Principle
The counting principle states that for independent choices, the total outcomes are the product of choices at each step, fundamental for permutations and combinations.
- 50
Independent Events
Independent events are those where the outcome of one does not affect the other, and their joint probability is the product of individual probabilities.
- 51
Conditional Probability
Conditional probability is the likelihood of an event given that another has occurred, calculated as P(A|B) = P(A and B) / P(B), for dependent events.
- 52
Order of Operations
Order of operations, or PEMDAS (Parentheses, Exponents, Multiplication/Division, Addition/Subtraction), ensures expressions are evaluated correctly to avoid calculation errors.
- 53
Plugging in Numbers
Plugging in numbers involves substituting simple values for variables to test equations or inequalities, a strategy to simplify complex algebraic problems.
- 54
Backsolving
Backsolving means testing answer choices starting from the middle or easiest one to find which satisfies the problem, efficient for multiple-choice questions.
- 55
Estimating
Estimating involves approximating values to quickly eliminate unreasonable answers, useful in time-pressured calculations involving large numbers.
- 56
Overcounting
Overcounting occurs when counting methods include duplicates, requiring adjustments like division by symmetries to get the correct total.
- 57
Data Sufficiency
Data sufficiency questions ask if given statements provide enough information to answer a question, requiring evaluation of each statement's sufficiency separately.