GRE Math - A comprehensive Course

Explore the classification of numbers by type, covering real, imaginary, and complex numbers; examine fractions (proper, improper, mixed), zero, and the distinction between prime and composite numbers.

Examine real numbers on the number line, including fractions and infinite decimals, define absolute value as distance from zero, and distinguish imaginary and complex numbers plus basic inequalities.

Explore rational numbers as fractions and irrational numbers as those not expressible as a/b, and learn converting terminating and recurring decimals to fractions using fully and partially recurring methods.

Classify integers as negative, zero, and positive, defining even and odd numbers. Identify that sums of even numbers stay even, and a product is even if a factor is even.

Explore natural numbers, define primes and composites, and identify distinguishing factors. Note primes follow the six plus one or six k minus one pattern, and learn key sum formulas.

Learn to express numbers as products of prime factors using prime bases. See examples like 72 = 2^3 × 3^2 and 11:52 expressed through primes, and apply the (exponent+1) formula to count factors.

Learn divisibility rules for 2, 3, 4, 5, 8, 9, 11, 25 and 125, using last digits and digit sums, and break numbers into parts to test 6, 24, 36.

Learn to find the least common multiple by using division and prime-factorization methods, and explore common remainder and common difference models for numbers like 24 and 36, with practical examples.

Learn how to find the highest common factor, or greatest common divisor, using long division and prime factorization, with examples like 24 and 36.

Learn to compare performance using percentages by normalizing scores to a common maximum and converting between fractions, decimals, and percentages.

Master the six essential percentage concepts by solving four core questions, applying the percentage increase/decrease formula, and distinguishing percentage points from percentages.

Explore ratio, proportion, and variation, including direct and inverse variation, with practical rules such as the component rule and the constancy of product in inverse variation.

Use a four-range number line to solve GRE practice questions by comparing x^2 and x across intervals: less than -1, -1 to 0, 0 to 1, and greater than 1.

Explore practice questions 3 and 4 on comparing real numbers X and Y across sign cases, proving when X > Y is guaranteed. Evaluate X^2, XY, and substitutions.

Practice questions 5 and 6 guide learners through evaluating a sum of consecutive integers from minus 49 to 51 and show cancellations, with quantity a compared to quantity b.

Explore practice questions 7 and 8 on converting partially recurring decimals to fractions, comparing values, and using decimal shifts and numerators and denominators in GRE math.

This session analyzes parity and averages with consecutive integers. It shows the average of four consecutive numbers equals six and tests which expressions involving a and b are always even.

Explore practice questions 11 and 12 that compare differences between the largest and smallest positive integers and determine the greatest three-digit multiples of 16 and 17 using remainders.

Practice questions 13 and 14 guide you through identifying distinct prime factors of numbers such as 30 and 60 and evaluating related expressions for possible values.

Explore practice questions on divisibility rules for nine and eleven, using digit sums and alternating sums to determine A and B and possible values, with worked examples.

Explore GRE math practice questions 17 and 18, including a fractional voting problem and a unit-digit remainder analysis for 47-based calculations, with number plugging strategies.

Explore the least common multiple and greatest common factor through practice questions 19 and 20, including the least common multiple of 8 and 12 and remainder-based multiples of 120.

Explore practice questions 21 and 22 to find numbers leaving remainders 3, 4, and 5 when divided by 4, 5, and 6, using model two and option based checks.

Explore practice questions 23 and 24, solving cost comparisons between pens and notebooks and analyzing per capita GDP ranges from GDP and population bounds.

Analyze percent-based income problems from GRE practice questions 25 and 26, compare 30% of X and 40% of Y, and conclude that the relationship cannot be determined.

Explore practice questions 27 and 28 from the gre math course, analyzing percent increases, equality of quantities, and a data interpretation scenario on student fail rates.

Practice percentage problems from GRE Math, including calculating savings when income rises and spending increases. Compute exam clearance rates using percent data, with a girls and boys breakdown.

Understand how percentage increases and decreases interact, including net changes from rising then falling prices, and compare successive discounts with a single discount in GRE math questions 31 and 32.

Solve percent increase/decrease problems in January and February, compare quantities A and B, then calculate earnings from a $1,000 fixed pay plus 2% commission on $75,400.

Explore practice questions 35 and 36, computing the class average for 50 students (30 boys, 20 girls) with scores 20–25 and 26–30, and convert miles to kilometers using gallons.

Learn to determine the weight per piece by finding the greatest common factor of 1400, 1750, and 2450, and minimize the sum for a product 36 using 4 and 9.

Explore practical ratio problems from the GRE Math - a comprehensive course practice questions 39 and 40, focusing on positive-integer multiples, common multiples, and proportional reasoning.

This lecture covers practice questions 41 and 42 on ratio problems, solving for John's score using product of extremes equals product of means, and distributing 1750 in ratio 5:7:13.

Explore practice questions on ratios and age problems, including determining total items in a 2:3:4 mix and solving a 4:1 age difference when the mother was 24 at birth.

Practice questions 45 and 46 on ratio and proportion train you to analyze income, expenditure, and savings using algebra, cross-multiplication, and product-of-extremes, then apply to a two-section class scenario.

Practice questions 47 and 48 explore inverse relationships in work problems, using a constant product and cross-multiplication, plus a digit-puzzle on digits a and b.

Analyze practice questions 49 and 50, divisibility by eight and remainders, comparing divisions by 16 and 24, and identify the two-digit number that is both a square and a cube, 64.

Explore algebraic expressions as combinations of variables and constants, identify polynomials by term count, determine the degree as the highest power, and learn identities such as (A+B)^2, (A-B)^2, and (A+B)^3.

Explains exponents by defining base and power and presents key rules: multiplying and dividing powers, power of a power, zero and negative exponents.

Define equations and distinguish expressions; identify linear equations as those with degree one. Learn solving one-variable linear equations and two-variable systems using substitution and elimination with examples.

Explore how to distinguish quadratic equations from linear ones and solve ax^2 + bx + c = 0 using the quadratic formula and factoring, yielding two roots.

Defines the function as a relation where each input maps to a single output. Illustrates domain and range with examples such as f(x)=2x+3 and g(x)=2x, including restricted domains.

Learn the four inequality symbols and essential rules, including transitivity, preserving direction under adding or multiplying by positive constants, and how even versus odd powers affect comparisons.

Explore profit, loss, and discount concepts by relating cost price, selling price, and market price, with rules: discounts on market price, profit or loss on cost price.

Learn the concepts of principal, time, and rate, and compare simple and compound interest with formulas, including half-yearly and quarterly compounding.

Master averages, mixtures, and alligation by computing simple and weighted averages, and applying the alligation method to determine the mixture price.

Understand work and time concepts by assuming uniform daily output and equal input among workers, and learn two approaches to compute combined work rates and wage sharing based on contribution.

Analyze time and work problems with two workers and a later joint effort, using direct work-rate and equation methods to find total work and days required.

Explore the speed time and distance relationship, starting with the core formula distance equals speed times time, and learn unit conversions and inverse and direct relationships.

Explore speed, time, and distance with average speed formulas, equal time and equal distance cases, and relative speed for objects moving in the same or opposite directions.

Explore speed, time, and distance through trains crossing bridges and boats navigating streams, covering relative motion and solving practical problems.

Learn coordinate geometry basics: locate points on axes, identify quadrants, and determine coordinates relative to the origin; calculate distance and slope, and analyze reflections, symmetry, and parallel or perpendicular lines.

Explore the basics of coordinate geometry, including quadratic graphs and parabola behavior, circle equations, and key graph transformations such as shifting up, down, left, and right.

this session works through algebra practice questions 1 and 2, solving linear equations, comparing expressions, and using factoring and expansion to determine which quantity is greater.

Practice algebra questions 3 and 4 by solving x minus two and its square to determine possible values of x plus two, with emphasis on common mistakes.

Explore algebra practice on solving equations with square roots, distinguish plus-or-minus versus single square roots, and analyze when sums enforce zero by each term equaling zero.

Explore algebra practice questions focused on exponents and powers, including even and odd exponent rules, sign analysis with negative numbers, and comparing expressions to determine which is larger.

Practice questions 9 and 10 explore comparing exponential expressions by rewriting with common bases, applying power rules, and factoring strategies to determine which quantity is greater.

Solve systems of two linear equations using substitution and elimination to find x and y, then compare square root expressions to determine which quantity is greater.

This lecture analyzes when a product is positive, showing that two positives or two negatives yield a positive result, and works through algebraic examples to determine possible values of variables.

Explore algebra practice questions 15 and 16 by solving quadratics, factoring, and identifying the range (-12, 7) where the expression is negative.

Tackle algebra practice questions 17 and 18, focusing on sequences and sums, including S_n differences and recurrence relations like b_n = b_{n-1} + n^2, with concrete examples.

Practice algebra with substitution to evaluate functions and solve equations in questions 19 and 20, using given mappings to compute and compare values.

Analyze algebra practice questions 21 and 22 by examining domain restrictions for outputs and positivity under a square root, and determine the slope for the line through (-3,-4) and (2,3).

Tackle algebra practice questions 23 and 24 by examining reflection across the x-axis and solving quadratics by factoring to find x-intercepts 3 and 4 and the y-intercept 12.

Apply distance formula to determine triangle side lengths and perimeter for questions 25 and 26, then locate parabola vertex of y = 2x^2 − 6x + 9 at (3/2, 9/2).

Explore algebra practice questions on GRE math, including age problems and family size puzzles, by translating statements into equations and solving for unknowns.

Solve algebra practice questions 31 and 32, focusing on wage hour problems with tiered pay and totals, and an age-relationship scenario that shows multiple X-value scenarios.

Explore algebra practice problems focusing on averages and linear equations, including a royalties scenario with fixed fees and per-copy earnings across different book sales.

Explore algebra practice questions 35 and 36 on calculating total cost, selling price, and 20 percent profit, plus a shopkeeper discount problem with a free item.

Learn to compute profit or loss percentage from cost price and selling price using a short-cut formula, with 50 vs 40 articles and a mangoes example.

Explore algebra-based simple interest problems with a $12,000 two-part principal at 4% and 3%, to compute two-year interest and learn doubling and quadrupling cases.

Algebra practice questions 41 and 42 explore compound versus simple interest at 20 percent per year, using a 20,000 principal and two-year examples, plus a difference shortcut.

Set the total work to 120 units, calculate each worker’s daily rate, and sum A, B, and C to determine the three-person completion time.

Analyze algebra practice questions 45 and 46 by modeling work with man-hours and daily hours, illustrating variation concepts and wage-sharing based on work completed.

Explore algebra practice questions 47 and 48 on distance, speed, and time, including cases with different speeds and the harmonic mean formula for equal distances.

Explore algebra practice questions about two travelers starting from the same point toward a destination, using relative speed, time, and distance equals speed times time to determine their meeting time.

Explore basic line concepts in geometry, including line types, line segments, parallel and intersecting lines, perpendicularity, and the idea of a transversal with proportional intercepts.

Learn angle types—acute, right, straight, and reflex—and how complementary and supplementary sums apply. Explore parallel lines producing vertical, corresponding, alternate interior and exterior, and same-side angles.

Explore the properties of polygons, including convex and concave types, the sums of interior and exterior angles, diagonals, and the defining features of regular polygons.

Learn basic properties of triangles: non-collinear points form a triangle, interior angles sum to 180 degrees, sides satisfy triangle inequality, and exterior angles equal the sum of opposite interior angles.

Learn to classify triangles by sides and angles—scalene, isosceles, equilateral, and right triangles—use Pythagoras and common triplets, and apply area formulas like Heron's and base-height.

Explore similarity and congruency of triangles by examining equal corresponding angles and proportional sides, perimeters, and areas; learn sss, sas, asa/aas, and the hypotenuse-leg (hl) congruence criterion.

Understand the basic proportionality theorem in triangles using parallel lines, establish similarity through corresponding angles, and apply midpoint and mid-segment theorems to relate segments and parallels.

Explore triangle concurrency points, including the orthocenter from altitudes and the incenter formed by internal angle bisectors, with right-triangle special cases and the incircle center.

Learn how medians meet at the centroid, yielding six equal-area triangles, and explore the circumscribed circle and circumcenter, with a right-triangle case where the median to the hypotenuse is half.

Explore quadrilaterals, including cyclic quadrilaterals and trapeziums, with area formulas for triangles, bases and heights, and Ptolemy's theorem relating diagonals and sides.

Explore quadrilaterals, including parallelograms, rhombuses, rectangles, and squares, outlining properties such as opposite sides and angles, diagonals bisecting each other, and area and diagonal relationships.

Explore circle concepts, including center, radius, chords, tangents, and secants. Learn about external and internal tangency, common tangents, tangent lengths, and the distance between centers.

Review circle concepts: inscribed angles in the same segment are equal and a diameter subtends a 90-degree angle. Explore arc length, sector area, central angles, and tangent-chord relationships.

Explore solids by examining prisms, including right prisms and cubes, and derive volume and surface area formulas using base area, height, and lateral faces. Then study cylinders and diagonals.

Explore solids like cones, cylinders, prisms, spheres, hemispheres, and pyramids, with volume and surface area formulas and the roles of height, slant height, and base.

Practice geometry questions on complementary and supplementary angles, straight-line reasoning, and angle relationships through worked examples and competition-style prompts.

Explore practical geometry techniques for angle relationships with parallel lines and transversals, applying corresponding and vertically opposite angles, and using triangle angle sums to compare quantities.

Explore parallel lines and transversal theorem in geometry practice questions 5 and 6, using AB=6 and BC=4 to compare BQ and UR, and octagon interior 135-degree and exterior 45-degree angles.

Analyze triangle relationships by identifying the largest side and opposite angle, apply isosceles cases, and determine possible internal angles from an external angle of 110 degrees.

Explore triangle inequality; with a 20 cm perimeter, any side must be less than 10 cm, and the angle bisector theorem shows BD:DC=9:8, so BD>DC.

This lecture covers geometry practice questions 13 and 14, including isosceles right triangle where area equals half the product of legs, yielding 36 square centimeters, and it compares by estimation.

Practice geometry questions 15 and 16 using Pythagoras theorem to identify right triangles and triplets like 3-4-5 and 5-12-13, then apply the median-to-hypotenuse property.

explains geometry practice questions on triangle centers and medians, using circumcenter and incenter angle rules and centroid properties to compare subtriangle areas and the overall triangle area.

Discover how equal angles imply similar triangles, match corresponding sides, and apply the ratio of perimeters to determine unknown lengths and areas in geometry problems.

Apply midsegment theorem to relate area and perimeter of new triangle formed by joining midpoints, and examine the ratio of circumcircle to incircle areas for a triangle with side eight.

Practice geometry with questions on triangles, including dividing a regular figure into six equal triangles, calculating their areas, converting square feet to square inches, and solving for unknown angles.

Explore geometry practice questions 25 and 26, focusing on maximizing rectangle area under a constant product by making sides equal and applying Pythagoras to find rectangle diagonals.

Geometry practice questions 27 and 28 teach composite areas by finding the union of two 2-foot paths in a 60 by 40 rectangle, subtracting overlap to get 196 square feet.

Solve geometry practice questions 29 and 30 by deriving the area ratio of a square to its circumscribed circle, linking the circle's diameter to the square's diagonal (side times sqrt(2)).

This geometry lecture covers practice questions 31 and 32, comparing circle circumference (pi 22/7) with square perimeter, circle vs square areas, and inscribing a circle in 3 by 2 rectangle.

Explore practical geometry problems on circle circumference and semicircle perimeter using 22/7 for pi, and apply the equal angles in the same segment to solve a triangle angle.

Compute the center-to-chord distance in a circle with radius 17 cm and 30 cm chord (8 cm), then convert 3.42 km to cm to find wheel rotations.

Solve geometry practice questions on circles and triangles, applying radius and diameter, Pythagoras in right triangles, 3-4-5 triplets, and calculating sector area minus triangular area for the shaded region.

Explore circle geometry concepts through practice questions 39 and 40, solving for angles using radii, tangent and secant relations, and the alternate segment theorem.

Solve circle geometry problems 41 and 42 by applying the tangent length formula with d=20 and r1=10, r2=6. Examine inscribed versus central angles and cyclic quadrilateral properties to determine angles.

Solve circle and triangle geometry problems, including angle chasing in isosceles triangles, radius and diameter relationships, and area calculations using Pythagoras and semicircles.

Analyze circle sector areas inside a rectangle using radius 14 and 90-degree and 270-degree sectors; compare room diagonals with a 12-by-10-by-9 setup and sqrt(325) vs 18.

Calculate cylinder volume using radius 21 inches and height 3 feet with pi 22/7, convert units for the tank, and determine percentage filled in geometry practice questions 47 and 48.

Solve geometry practice questions 49 and 50, examining how cutting a sphere into hemispheres changes total surface area and comparing cylinder and cone with the same radius and height.

The lecture explains graphical forms of data, including bar charts, line graphs, pie charts, angles, and scatter plots, and shows how to compare values and compute percentages from visuals.

Explore forms of numerical data, including discrete and continuous series, with inclusion and exclusion boundaries, and analyze cumulative and frequency distributions in practice.

Explore the arithmetic mean as a measure of central tendency, computing it from discrete data using frequencies and from continuous data using class midpoints, with practical examples.

Learn to compute the median by ordering data, handling odd and even sizes, and using discrete and continuous data with cumulative frequencies to identify the median class.

Discover how to identify the mode, the most frequent value, in discrete and continuous data using frequency tables and the mode formula for the model class.

Explore measures of dispersion, including range, quartiles (Q1, Q2, Q3), mean deviation, and standard deviation, and learn how they describe data spread and compute variance.

Understand sets by distinguishing finite and infinite collections, identifying elements and null sets, and applying union, intersection, and cardinality with practical diagram-based examples.

Use a venn diagram in the GRE math course to count students who play football or basketball with inclusion-exclusion, detailing only football, only basketball, both, and the total 46.

learn the concepts of permutations and combinations, distinguishing selections from arrangements, and apply factorial-based formulas (nCr and nPr) with examples from choosing items and arranging people.

Explore probability basics. Define probability as favorable outcomes over total outcomes, using six-sided dice examples; cover union, intersection, mutual exclusivity, and independence with the product rule.

Practice questions use tabular data to compute year-wise totals and compare percentage changes between 2021 and 2017. Learn quick calculation techniques to speed up GRE math problems.

Analyze five companies' total and male employee data to determine which has the highest female employees. Use approximate calculations to compare the male-to-female ratio and identify where it is least.

Learn to compute percentage increases and average annual growth rates using year-over-year data from 2016 to 2021. Apply the final minus initial over initial formula and interpret denominators.

Discuss practice questions seven and eight by analyzing 2016 exports and imports, calculate the difference, and examine changes in global foreign trade to identify maximum shifts.

Explore how fixed total exports with changing product shares affect calculated percentage increases, and why export values may be undetermined when totals are unknown.

Analyze a line graph of income and expenditure from 2016–2021, calculate annual and total savings, and estimate total savings as about 5.6% of total income.

Explore percentage increases, year-over-year growth, and sequential calculations on line graphs, with examples like students and fees, using forward-direction calculations for practice questions 13 and 14.

Learn to compute total sales from pie-chart percentages and compare unit sales using percentage versus percentage points, with the basic approach and the direct method.

Analyze a five-country pie chart by converting angles to export shares, compute the difference between two countries' exports using 1080 million, and express the result in million dollars and percent.

Analyze how to compute the percentage increase in Product A’s sales from 2019 to 2020 using pie-chart shares and total sales figures.

practice questions 21 and 22 analyze a five-family income and expenditure graph, reading income on the x-axis and expenditure on the y-axis and estimating total income and total expenditure approximately.

Practice questions 23 and 24 tackle two-set and three-language scenarios, determining how many students like at least one game and how many employees speak at least one language.

Learn to compute a class average using a basic method and a shortcut that balances deviations from a reference average, illustrated with boys and girls height data and ratios.

This session uses GRE practice questions 27 and 28 to explore weighted averages with jerseys and tables, then applies the method to a fuel efficiency trip.

Practice questions 29 and 30 explore the mean and the median of three numbers, using a relation where one value is five more than another, to compare mean and median.

Learn to compute the mean for both discrete data with values and frequencies, and continuous distributions using midpoints, as shown in practice questions 31 and 32.

Learn to compute the median of a continuous distribution using cumulative frequencies and the median class; identify the modal class and apply the mode formula.

Practice questions show how to find the median from a frequency distribution using cumulative frequency, and how to compute the range as max minus min from given data.

Learn to compute variance and standard deviation from data sets by finding the mean, computing squared deviations, averaging them, and taking the square root.

Calculate the mean deviation for the data set, yielding 4.8, and determine the quartile deviation using Q1 = 70 and Q3 = 74, yielding 2.

Apply combinatorial counting to nine people: compare selecting four or five, use factorial formulas and the shortcut to show 9C4 equals 9C5, including seating arrangements.

Explore practice questions 43 and 44 on permutations with repeated letters, applying factorials and division by repeated counts, and solve extreme-position arrangements for ten people.

This lecture presents practice questions 45 and 46, using the multiplication principle to count with five options per letter and three choices per course across twelve courses.

Explore probability with practice questions 47 and 48, computing combinations to find the chance of drawing three balls of different colors and of the same color from 12 balls.

Practice questions 49 and 50 cover two-dice probability, including sums like ten, and a committee problem selecting five from six men and five women to ensure at least one man.