Crack GMAT/GRE Math | Proven techniques to ace GMAT/GRE!

Master averages by applying the mean of observations divided by the total number of observations, with tips, tricks, and example-driven strategies for solving GMAT/GRE questions.

Use a symmetry trick with five consecutive numbers around a center to relate sum and average; the example yields the largest number as 15.

solve an averages problem: with a 10-month average of 32, total is 320; to raise to 36 over 11 months, the 11th month must be 76, totaling 396.

Explore fundamentals of averages and learn how a mistaken value in 50 observations distorts the average. Correct the total by replacing 23 with 48, yielding 1825 and a 36.5 average.

Explore ages problems with a timeline, deriving the present family average from an initial average age of 23 at marriage by adding five years and including the child.

Apply a quick averages and ratios technique by fixing a total, like 100 students, to compute total age and deduce the 40:60 boys-to-girls ratio.

Apply the ratio concept to split a total into A and B with A plus B. Solve for x to obtain numerical values, such as A=3x and B=7x.

Express incomes as A=2x and B=3x, apply a uniform 100-dollar increment to both, convert to a linear equation by equating 5:7, and solve for x to find the present income.

Solve a three-number problem using ratios and a sum constraint: form A+B+C=98, A:B=2:3, B:C=5:8; substitute to eliminate variables and find B, then A and C.

Solve a proportion problem with money distributed among W, X, Y, Z in the 5:2:4:3 ratio. Convert to actual values with a common factor and quickly compute each share.

practice solving a two-number problem where a = x and b = 2x, add seven to both, and solve 5x+35 = 6x+20 to find the larger number.

Tackle algebra problem where variables mix with numbers, using a substitution trick to set expressions equal to five x and two x. Practice helps solve under time limit, yielding 29.

Explore how percentages are defined as parts of a hundred, visualize with a pie chart, and apply discounts using 100 minus discount to find the new price.

Master profit and loss concepts by comparing cost price and selling price to determine profit or loss, and compute profit or loss percentages and discounts on cost price.

Master percentage and discount fundamentals to calculate after-tax income for two salaries and determine the percent difference, illustrating how to set up and solve related equations.

Compute the total cost for 5000 candies by charging $1 for the first 1000 and $0.98 for the remaining 4000, giving a total of $4920.

Use a base value of 100 to simplify percentage questions and reveal salary chains, such as one salary being 40% of another and another 25%, enabling quick solutions.

Demonstrates that a 10% decrease followed by a 10% increase does not restore the original value, yielding 0.99x; solving 0.99x = x - 10 gives x = 1000.

Use a 100 price and 100 consumption assumption; a 20% price rise with a 20% consumption drop reduces expenses from 10,000 to 9,600, a 4% decrease.

Master how to solve Venn diagram problems using a universal space and regions A, B, C, and D, with percentage reasoning for GMAT/GRE style questions.

Apply a two-set Venn diagram and inclusion-exclusion to find the class size: with 65% English, 60% math, 40% both, and 90 failing both, determine the total students.

Learn to solve percentage problems quickly using a two-by-two table of males and females with literate and illiterate categories, deriving female literacy from town totals and the overall literacy rate.

Crack a GMAT/GRE math problem on discounts and markup, using a 20% then 10% sale to reach a 10% profit, and apply a number-assumption trick to find the required markup.

Master time and distance by using the core equations for speed, time, and distance, and apply them to real problems with varying units like meters, kilometers, seconds, and minutes.

Compute speeds from distance and time for a basic GMAC problem, then compare car and bus speeds to yield a 1:2 speed ratio.

Compute the train’s average speed by adding distances from 50 mph for 2.5 h and 70 mph for 1.5 h, then divide by total time to get 57.5 mph.

Learn to solve a distance problem with speeds 3 and 6 mph via the unitary method, converting 30 minutes to half an hour, and applying time equals distance over speed.

solve a time and distance problem with two cars from A and B after 1 pm, meeting after 36 minutes by using speeds D/60 and D/90.

master solving a two-speed travel problem by splitting the trip into two legs, applying time = distance over speed, and solving for distance from the total time.

solve a two-part journey by equating times for the original speed and a reduced speed (one fifteenth less), where the second leg travels 10 miles less.

solve a speed and distance problem by equating times: X walks 2 mph for two hours (4 miles) before a 4 mph pursuer starts, yielding an 8-mile meeting distance.

Learn equal-time travel with two cars at 50 mph and 40 mph; equate (D+100)/50 = D/40 to find D = 400 and initial distance 900 miles.

Learn to solve tricky GMAT/GRE math problems quickly by applying the fundamental method, using distance and time relationships, and setting up linear equations to compare A, B, and C.

Master the work rate concept by analyzing one day's work for two workers and expressing contributions as fractions. Calculate the combined rate and the time to finish the job.

Convert individual times to daily contributions, sum to get the joint work rate, and compute total days; for example, Adam's 10-day and Bob's 15-day times yield a six-day completion.

Determine how long c would take to finish the job alone, given a completes in 10 days, b in 50 days, and a, b, c together finish in 4 days. The lecture sets up and solves the rate equation 1/10 + 1/50 + 1/x = 1/4.

Working together, A and B complete two-thirds of a job in 20 days. A finishes the remaining one-third in 20 days, so solo completion takes 60 days.

Solve a two workers' work-rate problem where A works alone for four days before B joins, using the union method to find the remaining work and total time.

Master work-rate modeling by formulating equations for X, Y, and Z. Learn to analyze six days of joint work and deduce X's solo time as 15 days.

Develop quick problem solving by forming three equations for A, B, and C from joint-work scenarios; apply a trick to find daily contributions, and determine remaining work.

Assign pipe rates—A fills 1/4, B 1/6, and C empties at -1/12 per hour—and find a net rate of 1/3 per hour, so the tank fills in 3 hours.

Model the fill and leak rates to solve a pipe problem, converting two hours twenty minutes to seven-thirds hours to reveal the leak drains the tank in fourteen hours.

Use option putting to solve a time-work problem: find that a needs 9 days and b 18 days, which together take 6 days since 1/9 + 1/18 = 1/6.

Distinguish simple interest from compound interest using principal, rate, and time, and follow practical examples with a $1,000 principal at 5% to show annual, half-yearly, and quarterly compounding.

Apply the simple interest formula i = p × r × t to relate principal, rate, and time; the example derives a 6 percent rate from the interest and amount.

Explore how simple interest stays the same every year, derive the principal from two-year and seven-year cases, and compute the five-year interest to ace gmat/gre math.

Analyzes two investments with 1500 principal over three years, using simple interest to link the 13.5 difference in interest to the rate difference, about 2.3 percent.

Apply a quick compound interest method: if money doubles in five years, determine when it becomes eight times the original using (1 + r)^t. Eight equals two cubed; fifteen years.

Learn how to compute future value with different compounding frequencies, using an $8,000 investment at 10% for one year, and see how semiannual and quarterly compounding affect the amount.

Master divisibility rules to quickly decide whether a number is divisible by 2, 3, 4, 5, 6, 8, 9, or 10 using last digits, last two digits, and digit sums.

Master finding the highest common factor and least common multiple with prime-factorization, for GMAT and GRE math, using the lowest and highest powers of each prime.

Master permutations and combinations for GMAT and GRE by learning when to apply permutations versus combinations, guided by factorial concepts and the formulas nPr and nCr.

Define probability as favorable outcomes over total outcomes, using the sample space concept. Apply to coin tosses, dice, and cards to count outcomes.

Set the book's total pages as x; after Monday the remaining is 5x/8 (three-eighths read). After Tuesday it's x/8 (four-fifths read); with 30 pages left, solve x.

Apply divisibility rules to GMAT/GRE style questions by summing digits and testing for divisibility by nine, two, six, four, and eight to quickly identify the correct option.

Use divisibility techniques with the lowest common multiple and multiples of 75, 50, 40, and 25 to determine the smallest number that divides 600.

Find the smallest multiple of seven that leaves remainder four when divided by 6, 9, 15, and 18 by using the least common multiple 90; the solution is 364.

Learn a quick trick for ratio problems: set A, B, C proportional to a common value k, derive them in terms of k, and compute A+B+C.

Demonstrates the counting method with boxes to form four-digit numbers from digits 1 to 4 without repetition, illustrating permutations and step-by-step strategies for GMAT/GRE math.

Count four-digit numbers formed from digits 0, 1, 2, and 3, avoiding leading zeros, by analyzing digit placement. Apply the zero trick to yield 18 as the answer.

Count four-digit numbers formed from digits 0–3 with repetition allowed, ensuring the first digit is nonzero. Use a case-based approach to handle zero and repetition, yielding 192 valid numbers.

Count two- and three-digit numbers formed from digits 1–6 with no repeats, divisible by five; the last digit must be 5, giving 20 valid three-digit numbers.

Learn how to solve a combinations problem by selecting five men from seven and two women from three, using seven choose five and three choose two.

Solve a combinatorics problem: from four boys and six girls, select four students with at least one girl using complementary counting (total minus no girls).

Apply the frequency of repeated letters to permutations, using n! divided by the factorials of each repeated count; illustrated with moon and Apple.

Treat the always-together letters as a single block, then count with factorials and internal permutations to obtain the total arrangements, illustrating group-based GMAT/GRE strategies.

Apply a gap method by first placing 19 science books to create 20 gaps. Then arrange 17 math books in nonadjacent gaps with combinations, yielding 1140.

Learn to solve dice probability by counting outcomes on one or two dice, using 36 total outcomes to find the probability that both numbers on two dice are even.

Draw two cards from a 52-card deck; calculate the probability of one heart and one spade by counting 13 hearts and 13 spades among 52*50 total outcomes, yielding 13/200.

Explore coin-based probability, distinguishing heads and tails, and compare counting and probabilistic methods. Solve for at most one head across multiple coins using favorable outcomes over total outcomes.

Apply the counting approach with combinations to a five-coin problem: total outcomes are 2^5 = 32, favorable outcomes are 5C2 or 5C3 heads, yielding 5/8.

Calculate the probability of drawing a nine or a heart from a 52-card deck by counting 16 favorable outcomes and 52 total, avoiding double counting the nine of hearts.

Calculate the probability of drawing two balls with none red from a bag containing two red, three green, and two blue balls. Use combinatorics to count favorable outcomes, yielding 10/21.

Explore algebra by examining numbers and variables, linear and quadratic equations, and find the roots and unknowns, identifying one, two, or no real solutions using the quadratic formula.

Master age problems with timeline methods, translate relationships like seven times a son's age into a solvable equation, and use simple algebra to find present ages.

Master linear equations and the elimination method to ace GMAT/GRE math, using the Linnet equation approach to solve two equations and detect traps while finding costs.

Solve a three-equation linear system by converting percentages to fractions, substituting to eliminate variables, and finding A, B, and C.

Solve a quadratic by completing the square and using the sum and product of the roots to find x, illustrating the root-based approach and option trick.

Learn to solve a quadratic using roots A and B, leveraging A+B and AB. Compare finding A and B with a conceptual approach and compute the final value, 65.

Identify critical points where the expression equals zero, plot them on number line, and determine intervals where it is negative or positive using factoring to find roots x=2 and x=5.

Factor x^2-16 to (x+4)(x-4) and identify critical points at -4 and 4 to determine where the expression is negative, noting endpoint and denominator caveats.

Introduce absolute value in a quadratic, solve x^2 - 12x + 35 = 0 for roots 5 and 7, and show that -5 and -7 also satisfy.

Discover an approach to problem 9 on GMAT/GRE math: isolate the variable, simplify the inequality, and determine the largest x by comparing to constants and powers.

Learn to approach algebra problems by rewriting equations and taking reciprocals to isolate variables. Add the equations to find the correct answer and apply these GMAT/GRE math techniques.

Master lock-and-key type GMAT/GRE math questions by spotting a common factor (X−1 or X+1) and rewriting expressions to compare powers, enabling quick solutions (e.g., X=5).

Apply the quadratic formula to find the roots, explore sums and products like a+b and a-b, and use the a^2-b^2 identity to verify the correct roots.

Solve a tricky quadratic problem by deriving relations between coefficients from the roots, use sum and product relationships to form a new equation, and verify by testing options.

Analyze how exponents behave with bases between 0 and 1, showing that higher powers enlarge the denominator and alter comparisons, illustrated by x^2 vs x^7 and related expressions.

Solve a rational inequality by drawing a number line, factoring numerator and denominator, and testing intervals to count integer solutions where the expression is less than or equal to zero.

Learn the lines and angles concept, including parallel line relationships, opposite and corresponding angles, and the 180-degree straight angle rule, with application to triangles and symmetry.

Master triangle concepts for GMAT/GRE, including triangle existence, angle sums and exterior angles, area formulas (base-height and Heron's), and types like equilateral, isosceles, and right triangles.

Master quadrilaterals by studying squares and rectangles, their equal sides, 90-degree angles, and diagonals. Learn to use diagonals to connect squares with equilateral triangles and solve related problems.

Learn circle concept: radius is the constant distance from center to any point on the circle, and a tangent touches at a point, perpendicular to the radius, forming right triangles.

Explore surface area and volumes for cube, cuboid, cylinder, cone, sphere, and hemisphere, focusing on essential formulas and intuition to solve exam questions.

Apply Pythagoras theorem to a right triangle with hypotenuse 10 and leg 6 to determine the other leg as 8, and compute the rectangle area as 48.

Apply area formulas for the square and rectangle. Set the rectangle’s area four square metres less than the square’s, given a 14 m length, and determine the side and perimeter.

Apply the Pythagorean theorem to the right triangle with hypotenuse 26 and legs AB and BC; use AB+BC=34 to find AB*BC=240, then area = 1/2 AB*BC = 120.

Explore solving a geometry problem by using the square's diagonal as the base of an equilateral triangle, diagramming the figure, applying Pythagoras, and deriving the area ratio.

learn to compare areas of a square and a triangle with equal perimeters by deriving a relationship between x and y, and determine which area is larger.

Compute a square with area 44 by using side length and perimeter relations, compare to a circle, and apply pi approximation 22/7 to estimate areas.

Tackle a GMAT/GRE geometry problem: a circle with diameter 100 meters has an inscribed square; use the square's diagonal as the circle's diameter to compute the square's side.

Apply ratio reasoning by assigning x to cuboid edges, convert dimensions to multiples, use the total surface area formula to solve for x, and determine the answer 48.

Compare volumes and surface areas of cylinders with equal height but different diameters, use the volume formula to relate radius changes to height, and identify which has greater volume.

Compare a cube and a sphere with equal surface areas to derive the dimension relationship from 6a^2 = 4πr^2 and determine the ratio of their volumes.

melt a solid cylinder with diameter 60 into a sphere while keeping volume constant, equating cylinder and sphere volumes to find the sphere's diameter.

Learn how to solve volume ratio problems by melting three cubes with sides in ratio 3:4:5 into a single cube, using constant volume and diagonal relations.

Solve for x in triangle xyz using angle bisector properties and the triangle angle sum; deduce x equals 60.

Use exterior angle property and linear pair reasoning to solve triangle problems; given a 120-degree exterior angle, deduce x equals 40 using angle-sum and straight-line approaches.

Demonstrate how diminishing a circle's radius by 10 percent lowers its area, illustrating the radius area relationship and the squared rule for GMAT/GRE math problems.