GMAT Entrance Exam Math Preparation Course Online - 2023

This video explains data sufficiency, showing when statements alone or together determine sufficiency and using examples like b plus q equals 50 to decide value of b.

Explore data sufficiency by distinguishing whether B equals four from finding B's value, and test each statement’s sufficiency. Learn to combine statements, identify contradictions, and eliminate options accordingly.

Explore a GMAT data-sufficiency problem by testing |P+1|<3 and |P-1|<3, selecting values across zones to assess each statement's sufficiency and determine the correct option.

Evaluate data sufficiency for P squared greater than Q squared using statements P greater than Q and P plus one greater than ten, showing neither alone nor together suffice.

Analyze two statements about P and Q with modulus inequalities and the highest common factor. Determine when each statement is insufficient and how combining them yields a final yes.

Explore data-sufficiency techniques for GMAT math by evaluating two statements about class size and maximum weight to decide whether the average weight exceeds 10 kilograms.

Master data sufficiency for a GMAT coin division problem. Evaluate statements about five and four people to decide if total coins can be divided between X and Y without leftovers.

Apply data-sufficiency reasoning to a ratio problem, showing statement one yields multiple Y to P values, while statement two fixes Y to P at 1 to 4, revealing sufficiency conclusion.

This lecture shows determining the units digit via data sufficiency, comparing two x statements, and concludes the second statement alone fixes the last digit at zero.

Solve a data sufficiency problem by showing that X^2=4 yields the mean of (X+1)^2 and (X-1)^2 as five, and X^3=8 fixes X to 2, so both statements suffice.

Solve a GMAT math data-sufficiency problem about a three-digit number whose digits are in arithmetic or geometric progression. Combining two statements yields the only valid number, 210.

Practice data sufficiency reasoning on GMAT profit and loss questions by analyzing two statements about cost price, profit, loss, and overall profit or loss to determine sufficiency.

Learn four quick techniques for GMAT math: approximation, eliminating answer choices, substitutions, and sequencing to save time and improve accuracy.

Learn to estimate answers in GMAT math by using logical elimination, weighted averages, and quick approximations for unequal group sizes, pass/fail rates, and square-root problems.

Master the elimination technique for GMAT math by testing options with values and using the middle-value strategy to identify the greatest result in loan and instalment problems.

Apply elimination technique 2 to speed up GMAT math questions by checking options, using reverse thinking, and solving distance, time, and speed problems efficiently.

Apply substitution to solve (x+1)/x = 2 and simplify (x^100+1)/x^100, then combine four workers' rates to finish 60 units in 4 days.

Use substitution technique 2 by assuming a base value of 100 to simplify percent problems, like discount, profit, loss, and changes from MRP to cost price.

Solve algebraic equations and verify solutions by substitution, practice evaluating quadratics and linear inequalities, and learn option-based reasoning for GMAT math quizzes.

Explore sequencing techniques to infer answers from patterns, such as finding the average of the first 500 odd numbers and counting squares and rectangles on an eight by eight chessboard.

Count rectangles on n by n chessboard equals sum of cubes 1 to n, yielding 1296 for 8 by 8; use subtraction to count numbers, 605 between 257 and 863.

Explore last-digit cycles of powers and remainders modulo four to quickly determine the unique digit in GMAT sequencing problems.

Classify numbers into real and imaginary, with real numbers comprising all numbers except imaginary numbers and imaginary numbers represented using i. Distinguish rational numbers, irrational numbers, and integers, then describe decimals and fractions, including proper, improper, mixed fractions, and recurring or non-recurring decimals.

Explore integer classifications: even and odd numbers, zero and one as neither prime nor composite, natural and whole numbers, primes versus composites, twin primes, and perfect numbers with examples.

Explore the fibonacci sequence and learn to apply the bodmas rule—brackets, division and multiplication, and addition and subtraction—to solve expressions step by step.

Explore decimals and place value, from digits after the decimal to millions, billions, and trillions, learn place value and face value, and master rounding to hundreds, tens, units, and thousands.

Convert decimals to fractions by clearing the decimal part with multiplication, and convert repeating decimals using bar notation to obtain fractions such as 365/999.

Learn to add and subtract fractions with a common denominator, illustrated by 3/5, 7/15, and 9/10, and master multiplying and dividing with cancellation and reciprocals.

Learn to convert proper fractions to mixed fractions and back, perform addition and subtraction of mixed fractions by combining integers and fractions, and understand factors and multiples.

Compute the least common multiple and highest common factor using listing multiples and prime factorization. Practice with examples 4, 6, 8 and 32, 54, 96 to illustrate lcm and gcd.

Learn to compute the hcf and lcm of numbers and to find the sum and number of factors using prime factorization, illustrated with 480.

Master trailing zeros in factorials by counting factors of five with continuous division and explore the maximum power of six in 100!, via twos and threes, concluding with 6^48.

Apply divisibility rules to determine whether numbers are divisible by 2, 3, 4, 5, 7, 8, 9, 10, 11, and 12 using last-digit checks and digit-sum tests, and alternating-sum technique.

Learn the technique to solve mixed fractions by treating them as addition, separating the whole and fractional parts, and aligning denominators for quick arithmetic.

Explore ratios and proportions, distinguishing ratios from fractions as two-part relationships. Learn why combining class ratios isn’t additive and how to interpret boy-to-girl ratios.

Divide a twenty-four thousand total into shares for A, B, and C as six, eight, ten thousand dollars, then combine ratios by equalizing Y values to derive X:Z and X:W.

Understand proportion as a relation between price and chocolates, using 50 cents for 10 and 70 cents for 14, and apply the product of extremes equals the product of means.

Explore the three types of proportion: main (mean) proportion, third proportion, and fourth proportion, and identify direct and inverse proportional relationships with examples.

Define percentage and compute it as obtained divided by total multiplied by 100. Use percentages for comparison and calculate overall percentage from multiple scores.

Compute percentage change using (new minus original) divided by original value, multiplied by 100, to assess improvement. Convert percentages to fractions by dividing by 100, as shown with examples.

Practice with percent calculations using stepwise decomposition, converting percentages to tens, multiplying base values, and combining results to compute percentages like 20% of 600, 39%, and 250% of 300.

Develop skills to compute consecutive percentage changes and discounts on prices, from 10% to 50%, using examples like 4000, 3000, and 8000 MRPs to find final prices and overall change.

Explore practical percentage change problems with initial and final values, including successive increases and decreases, reverse calculations, and real-world examples like price and population changes.

Learn the core profit and loss concepts, including cost price, selling price, and mark price, and apply profit, loss, and discount percentage formulas.

Graph the relationship between market price, selling price, and cost price to solve 20% discount and 20% profit problems using a 600 mark price.

Calculate the overall profit or loss percentage from two mobiles bought at the same price, one with a 30 percent profit and the other with a 20 percent loss.

Learn to determine the original car price from successive discounts of 30% and 40%, using algebra to relate final price to the initial price.

Explain the difference between simple interest and compound interest, and show how principal, rate, time, and compounding frequency determine interest and the total amount.

Explore how to compute averages for linear data using the first plus last divided by two rule, with examples of consecutive numbers and distinguishing linear from nonlinear data.

Understand nonlinear data with no order and compute average as sum over count; apply weighted averages to combine subgroup means, with 250 boys, 120 girls, and 30 teachers, yielding 14.4.

Explore solving average problems by combining totals and recognizing repeated values; compute individual scores from overall and subgroup averages, illustrated with cricket scores and class averages.

Learn to work with mixtures by equalizing vessel quantities using common multiples, then combine to determine the final milk-to-water ratio.

Compute mixing ratios for two vessels by scaling volumes to a common multiple, then determine resin, water, and salt portions to obtain the final mixture ratio.

The lecture explains a milk-to-water mixture in a 4:1 ratio, with 64 liters of milk and 16 liters of water, and concludes to add 40 liters to reach 1:4.

Learn how time, speed, and distance relate, and how to compute time from distance and relative speed using average speed and relative speed concepts with real examples.

Apply rate and relative speed to a two-train meeting problem: after four hours at 60 mph the second train starts, they meet 5.5 hours after, 440 miles from station B.

analyze a trip from X to Y and back at 40, 50, and 60 mph; compute total distance and time, then report the average speed as 1800/37 mph.

Compute the distance between house and office by analyzing travel at 20 m/s and 30 m/s, and derive the normal speed and time from time deviations.

Use proportion reasoning in quality control to scale seven bulbs per 400 to a production of 20,000, yielding 350 bulbs inspected.

Explore how earnings scale directly with attendance through a proportional relationship, solving for the amount earned at 20 attendees using cross-multiplication to arrive at 300.

calculate the profit for eight attendees by applying 43% costs to the 120 dollars earned, yielding 68.4 dollars.

Compute Earth's orbital speed by dividing the annual distance traveled (about 580,000 thousand miles) by the total hours in a year (365×24), yielding roughly 66,210 mph.

Calculate the atomic weight of an unknown element by applying a 20% reduction from calcium’s 40 amu, yielding 32 amu.

Define lines, rays, and line segments; explore parallel and perpendicular relationships, vertical opposite angles, supplementary and complementary angles, and transversal effects on equal angles and proportional segments.

Explore triangle basics: understand that a triangle's angles sum to 180 degrees, side lengths relate to opposite angles, and the triangle inequality governs third side ranges; examine exterior angles.

Explore triangle area formulas, including computing area from three sides using semiperimeter, base and height, and inradius, then derive the equilateral triangle area as sqrt(3)/4 a^2.

Apply the pythagorean theorem, with c squared equals a squared plus b squared, and identify the hypotenuse opposite the 90-degree angle. Recognize 3-4-5 triplets and similar or congruent triangles.

Explore triangle types: scalene, right, obtuse, isosceles, and equilateral, and key centers such as incenter, circumcenter, centroid, and orthocenter, plus the midpoint theorem and related areas.

Explore how special triangles simplify side calculations in the 30-60-90 and 45-45-90 configurations. Apply the equilateral triangle setup and the Pythagorean theorem to derive hypotenuse and side ratios.

Explore quadrilaterals—parallelograms, squares, rectangles, rhombuses, and trapezius—and learn their relations, diagonals bisecting and area formulas like base times height.

Learn how polygons extend from quadrilaterals to octagons, compute interior angle sums as (n-2)180, exterior angle sums as 360, and find diagonals with n(n-3)/2.

Explore circle basics, including radius, diameter, center, chords, segments, arcs, sectors, and tangents. Learn major and minor arcs and sectors, and derive arc length and sector area from central angles.

Explore circle properties: semicircle angles are 90 degrees; any triangle is right-angled; angles in same segment are equal; central angles double inscribed angles; cyclic quadrilaterals opposite angles sum to 180.

Explore three-dimensional geometry with cuboids and cubes, learn lateral and total surface areas, volume, and longest rod that fits inside a figure, and apply these ideas to cylinders and hemispheres.

Explore how cylinder surfaces break into lateral and total area, compute volumes from base area and height, and relate cones, spheres, prisms, and pyramids to their surface areas and volumes.

Master coordinate geometry basics, including distance between points, slope, and midpoint calculations, plus x- and y-intercepts and line equations.

Explore algebraic expressions and equations, including variables and constants, with examples like 3x + 4y + 3, and learn how single terms, binomials, and trinomials are formed.

Learn how to factorize a quadratic equation to find its roots. Understand the discriminant and how the sum and product of the roots relate to a, b, c.

Master exponents and powers through key rules such as a^m a^n, (a^m)^n, and a^0 = 1, plus binomial and trinomial expansions like (x+y)^2, (x+y)^3, and (x+y+z)^2.

Explore functions and algebraic expressions, including evaluating a function and solving linear equations using elimination; recognize when lines intersect, are parallel, or coincide to determine unique, zero, or infinite solutions.