GMAT® Math | Official Guide 2017 | Problem Solving

Apply a simple template to convert fractions and decimals to percents, and to compute percent change by dividing the difference by the original number and multiplying by a hundred.

Convert between currencies using unit conversion rules, cancel units, and apply rates such as 0.8 euro per dollar and 1.2 dollars per euro to compute totals.

Simplify complex expressions by delaying math, then add or subtract fractions using the least common multiple (lcm) to expand to a common denominator.

Apply age-problem reasoning by formulating an equality: in this example, 34 + x equals 16 + 2x, yielding x = 18 (choice C).

Learn to convert mph and gallons per hour into miles per gallon by dividing the two rates, canceling units, and using approximate benchmarks to compute mpg.

Learn to plug in convenient numbers to solve algebraic must questions and eliminate answer choices, using boxes and paperclips to illustrate how most questions can be tackled.

Apply a plug-in approach to prove the total distance is more than 50 percent, yielding 55 percent as the correct answer.

Practice sketching coordinates on the x-y plane, plot points, and identify a parabola’s axis of symmetry and vertex to reason about symmetry and GMAT problem solving choices.

Break down complex GMAT percent problems by isolating parts, compute ten percent of five thousand, use division by a hundred and reciprocal multiplication, and obtain 495 for the correct choice.

Convert decimals to fractions; sixth root of 64 divided by a million equals sixth root of 64 divided by sixth root of a million, giving 2 over 10.

Determine probability by dividing the 100 desired numbers (200–299) by the 250 total options, using the gaps-and-items method for consecutive integers, and simplify to 2/5.

Learn to solve percent problems by treating seven percent of the excess over 1000 as x, then x equals 1250 and total equals 2250.

Set x as the number of twenty five cent coins and use 16 total coins and 235 cents to form 160 + 15x = 235, giving x = 5.

Learn the average‑and‑median question type by sorting numbers and recognizing constant difference sets, where the average equals the median (as in consecutive numbers like 1–5).

Convert percent to fractions, simplify before multiplying, and solve for x when 60 percent of x equals 300; x equals 500 (choice d).

Explore quadrilateral properties to solve perimeter problems. Show that the perimeters of a deltoid, parallelogram, and rectangle equal twice the sum of their sides, with an example solving for x.

Determine how many 2-by-2 squares fit into an 8-by-10 rectangle by counting how many fit across 8 and along 10, yielding 20 squares and a total value of 240 bucks.

Use benchmarks to simplify multiplication of ugly numbers by breaking one factor into near round numbers, for example 893×79 = 893×78 + 893, then add 893.

Define x as the smaller quantity and relate hardcover nonfiction, paperback nonfiction, and paperback fiction with 20 more and twice as many constraints. Solve the 140 equation to find x.

Learn to solve a GMAT average problem by equating the sum and count, break 18 into 10 and 8, and find the missing term, 21.

learn to plug in numbers to solve absolute value inequalities and algebra questions, test positive and negative values, and identify possible y-values.

Learn the GMAT trick: if k^2 = m^2, then k = ± m, and use plug-in numbers to quickly eliminate options for must-know problems.

Master ratio and portion problems by treating ratio quantities as units, solving for x with a total of 780, and using unit digit shortcuts to verify answers.

Identify right-triangle side ratios and recognize the 6-8-10 pattern, then apply the percent-increase formula to compare 14 to 10. Convert the difference into a percent to conclude 40 percent.

Solve x/2 + x/3 + x/10 + 6 = x by using the least common multiple of denominators to 30, then solve for x to get 90.

Learn to solve weighted average questions by visualizing two groups, placing the smaller average on the top left, and dividing the range in inverse proportion to quantities.

Convert decimals to fractions to simplify problems, as 1 - 1.25 equals -1/4, and moving terms changes signs, turning division into multiplication in GMAT problem 27.

Explore efficient strategies for solving decimal problems in GMAT math by converting decimals to simple fractions, manipulating decimal places, and using a common denominator to sum decimal terms.

Learn how increasing each side by a factor of two scales volume by eight in similar three-dimensional shapes, and apply linear ratios to compute volume ratios for cubes and cones.

Practice solving complex GMAT fractions by using a tree diagram to compute a fifth of a half of 40, recognizing percent of a percent and the role of multiplication.

Apply elimination by adding or subtracting two equations to reduce variables, use factoring to simplify, and multiply equations to eliminate a variable for quick GMAT problem solving.

Show how x:y = 4:1 and y:z = 2:1 can combine into x:z using a three-column table; multiply by the connecting factor to keep integers rather than fractions.

learn to read a graph by selecting a single extreme datum and turning it into a complete verbal sentence; use the data, such as 2.2 and -0.5, to find differences.

Master last-step pc calculations by translating verbal cues into algebra, using substitutions for words like percent and of, and simplifying before you multiply.

Multiply both sides by three to clear the denominator, turning the ratio into six to one. Recognize that two divided by a third equals six.

Calculate total refunds by taking 0.5% of 20000 units to get 100 items, then multiply by 2500 dollars per item for a total of 250,000.

Break an unfamiliar polygon into rectangles and triangles to compute area, using opposite rectangle sides and known dimensions to sum parts for the final solution.

Apply the weighted average method to two groups—a four-person group at 78 and a single unknown score—to obtain an overall average of 80, yielding the unknown as 88.

Apply the triangle angle sum and right-triangle complementarity to find the acute angles, deduce they are 40 and 50 degrees, and express their ratio as 4 to 5.

Learn to solve prime greater than 3 remainder questions by using must questions and plugging in convenient numbers; eliminate choices to confirm option b.

Learn to convert mixed fractions to improper fractions, multiply by the reciprocal for division, and use the BOTA method to add or subtract fractions in GMAT problem solving.

Demonstrate how AB and BA, two-digit numbers with reverse digits, yield AB+BA divisible by 11 and AB-BA equals 9(a-b), while using plug-in techniques to eliminate choices.

Assess problem solving questions by performing up to twelve simple counts, and apply up to five distinct calculations if needed; proceed when you estimate under two minutes per question.

Learn a plug-in numbers strategy to solve GMAT problem solving questions by substituting simple values, eliminating options, and deriving the box count from total oranges and per-box capacity.

Tackle must questions by plugging in convenient numbers to eliminate roman numerals and simplify inequalities, using color coding to track reasoning; conclude roman numeral 2 is correct, option b.

Master problem solving on the GMAT official guide by recognizing (x+2)(x-2) equals x^2-4, checking equivalent forms through divisions, and selecting the correct choice (D); memorize the quadratic formula.

Analyze how a larger range and more data points far from the average raise standard deviation, illustrated with company data, and grasp the variance–standard deviation relationship.

Use divisibility by eight to simplify 1174 intervals, examining last three digits and the thousand part. Test with a comfy number like 16 to count revolutions and land on e.

Plot points in the xy-plane, test answer choices by quadrant reasoning, and plug in numbers to see where xy is negative and where asymptotes occur.

Learn to subtract fractions by using the least common multiple to find a common denominator and solve for x. Verify the capacity is 9/4 by plugging in.

Solve a quadratic by factoring: find two numbers whose product is -15000 and sum is 250, yielding roots -300 and 50; recognize it as algebra, not geometry.

Learn to convert decimals to simple fractions and divide fractions by multiplying by the reciprocal, a method applied to solving GMAT-style problems.

Plug in convenient numbers for variables, such as x=2 with 10 bushels per tree and 350 total, to form x/35 and identify the non-eliminated correct choice in a GMAT problem.

Define an even number as divisible by two with no remainder, and note that 2n is always even for any integer n; test choices with zero to confirm option C.

Learn to solve a GMAT problem solving item by estimating with benchmarks using denominators 8 and 9, and apply the gamma method to find an answer just under one.

Interpret 'per' as a division line, cancel units, and use benchmarks to estimate miles per gallon calculations like 12,000 divided by 25 for GMAT problem solving.

Explore how absolute value measures distance from zero and can reach zero. Practice plugging in convenient numbers and testing positive and negative values to select the correct option.

Demonstrates solving square-root problems by factoring under the radical into perfect squares for estimation, and extracting integers from the root as a product of two factors.

Determine k from the point (2, 17) on the line y = kx + 3, then compute y for x = 4 using y = 7x + 3, yielding 31.

Explain how to translate nested percent statements into a total: 90% cleared for planting, with 40% for soybeans and 50% for wheat, leaving 720 for corn, then determine X.

The population starts at three and doubles each month, so after n months it equals three times two to the n.

Solve the linear equation 3x+4y=200 with y a multiple of five by plugging in convenient numbers, applying must questions, and eliminating options via coprime reasoning.

Solve the GMAT® math problem quickly by simplifying radicals and checking whether expressions yield integers, using primes, even exponents, and elimination of answer choices.

Apply ratio analysis and plug-in numbers to test whether totals like 80, 96, 160, or 192 can equal 16x for four workers, identifying feasible options and the non-feasible one.

Compute combined rates by converting fractions and adding them (1/6, 1/9), then apply work over rate to find the total time for filling one tank.

Plug in coordinates to test line equations with parameter k; show (0,2) lies on the line for any k, while (1,1) requires k=3; interpret graph intersections to find the solution.

Solve x^2 < 2 by locating the positive and negative roots; x lies between them. Use must-question reasoning and convenient-number tests, starting with 0, to eliminate answer choices.

Use a convenient number to solve percents by plugging in 100, treat percent as multiplying by 100 over 100, and determine nine percent decrease in bicycles produced and sold.

Apply the gamma method to compare differences between fractions with unlike denominators, showing that closer to 1 1/2 yields smaller differences, and identify the correct choice as D.

Master GMAT problem solving techniques by simplifying fractions, ensuring denominators are nonzero, and using the plug-in values (like p=1 and p=-1) to quickly test options and eliminate incorrect answers.

Determine the range as max minus min, and show how adding x to a set with 3 and 14 yields a 12-range when x is 15 or 2.

Demonstrates solving a GMAT ratio problem by multiplying to avoid awkward divisions, then computes the 16-to-18 percent increase as 12.5 percent (an eighth).

Learn to translate percent statements into equations, divide by a hundred, and solve for x in a GMAT problem, showing how 115 percent of x and 60 are used.

Tackle invented operation questions by plugging in numbers in an orderly fashion, isolate t in terms of u, and raise the result to the power of two to solve.

Solve a percent decrease from 10 ounces after a 0.2-ounce drop by computing (0.2/10)*100 to get 2%, illustrating decimal handling and percent conversion in GMAT problem solving.

Learn to identify equivalent ratios among x, y, C, D, B, and A by swapping numerators and denominators. Systematically evaluate answer choices to determine the correct roman numeral, here C.

Explain how multiplying decimals by powers of ten moves the decimal point. The result has twelve decimal places, with the last digit being five, guiding the correct k value.

Factor the quadratic x^2+2x-24=0 as (x+6)(x-4), yielding roots -6 and 4, and assign them to a and b to determine the correct GMAT answer choice.

Apply percent tree thinking to tackle difficult percent-of-a-percent questions. Split the initial quantity into branches, note that 40 percent are independent (60 percent registered), and compute 10 percent of 60 percent as 6 percent to simplify the problem.

Apply circle properties, including inscribed angle opposite a diameter, to solve a right triangle using a 6-8-10 ratio. Derive arc length as half the circumference with radius five, yielding 5π.

Apply a 1 to 1 ratio by plugging in a small number to find volumes, then divide 1.20 by three to get 40 cents per glass.

Decompose polygons into rectangles and use opposite sides are equal to relate dimensions. Solve 1200 = 3W^2 with L = 3W to find W = 20 and L = 60.

Solve a GMAT math problem by pricing apples at 0.70 and bananas at 0.50, convert to integers, extract a common factor, and determine the total apples plus bananas.

Isolate y from the equation 3x + 7y = constant to reveal the slope, -3/7, confirming option b.

Learn the clone rate formula for work problems with identical machines, and how to simplify before multiplying to solve GMAT work questions quickly and accurately.

Learn to solve GMAT ratio problems by building a single ratio table and bringing first through fourth graders to a common level using the second and fourth as connectors.

Explore converting inches to kilometers using scientific notation and powers of ten, and learn practical estimation with benchmarks to simplify GMAT problem solving.

Apply the weighted average method for two equal groups with different averages. The missing score equals 2x-8, verifiable by a quick numerical check.

Master percent and algebra reasoning by converting percent to fractions (25% = 1/4, 37.5% = 3/8), simplifying before multiplying, and testing with convenient values for must questions.

Sketch data, build right triangles, and use the distance formula and Pythagoras’ theorem to find the radius and compute the circle area pi r^2.

Learn to compute percent change and percent increase using 100 plus the change, contrast with decreases, and apply to examples like 100 to 150 and 3 to 1.

Apply a percent-based cost model for removing a pollutant, using 100,000 times p divided by (100 minus p) for p = 90 and p = 80, then take the difference.

Factor the disguised quadratic with a = x y, obtain x and y from numbers with product -6 and sum -1; then plug in to eliminate roman numeral options.

apply the distance formula with distance in feet and speed 40, simplify before multiplying, and use benchmark estimates to approximate the final result around 520 when dividing by 11.

Approximate GMAT problem solving by converting roots to powers and using benchmarks to simplify large numbers. Adjust strategies when stuck, turning decimals into integers for cleaner estimates.

Compute the combined work rate of three printing presses by adding equations to cancel variables, then use work over rate to find the time needed for one job.

Sum volumes of spheres with radii 1, 2, and 3 via V = 4/3 pi r^3 to obtain 36 pi; large diameter is 2 times the cube root of 36.

Learn a fast trick for sums of symmetric consecutive integers by canceling negative and positive pairs, and apply the average times count formula to find totals in arithmetic sequences.

Shows strategies for absolute value problems by plugging comfy numbers (1, 2, -3) to define s, t, and r, then compute averages via substitution or answer-choice testing.

Solve multiple inequalities to determine the range of n that satisfies all conditions. Unify the conditions on a number line to find the integer solution n equals 11.

Apply a number line to double-overlap GMAT questions, relate total 5000 to X, Y, and Z, and find neither via 5000 − X − Y + Z.

Master percent and ratio problems in GMAT data by using a convenient whole, simplifying 5:6 ratios, and benchmarking to divide totals by 11 for accurate stock scenarios.

Master solving double overlap questions by using a number line instead of venn diagrams, placing 62 stockholders and 47 employees in a 100-unit whole to deduce a 9-unit overlap.

Divide both sides by y, since y is not zero, yielding 1 on the left. Solve for x to get x = 7/3; option c is correct.

Learn to find the least common multiple of 8 and 12 by checking multiples of 12 until 24, and note a quick prime-factor view using three twos and a three.

Explore how regular polygons decompose into isosceles triangles that share a common central vertex, using central angles 360/n and the sum 180(n-2); equilateral triangles have 60-degree angles.

Analyze how two thirds of 40 translates to at least 27 in favor and at most 13 against, guiding which GMAT problem choices are correct.

Shows that 20 factorial plus 17 is divisible by 17 because 20 factorial is a multiple of 17, and adding 17 preserves divisibility.

Solve a quadratic by isolating a variable, substituting into b = a − 4, and factoring to find two negatives with product 160 and sum -2.

To maximize a positive term minus twenty times a square, minimize the square by setting t to five, turning the square to zero and depth to five hundred.

Analyze a moving object using distance, rate, and time to determine how many more miles can be run before turning back within 15 minutes.

Identify and solve a compound interest question with two 8% increases; set up the compound interest formula, factor out X, and isolate X to satisfy doubling of the sum.

Estimate the sum of about 100 reciprocals with denominators near 200–300 by approximating each as about one third, showing why option a is correct.

Learn to solve must-questions by plugging in comfortable numbers, and derive the two-machine rate: B's time is xy/(y-x) hours to complete 800 nails of work.

Apply a fast ratio method by summing components to eight ratio units of the total, then divide by four to relate to the total and select the correct choice.

Use percentage benchmarks and mental math to estimate and solve percent problems, convert between fractions and decimals, and set up equations to find the unknown in a GMAT problem.

Explore how compound interest, with 8 percent interest compounded semiannually, grows a $10,000 principal to $10,816 after two six-month cycles, illustrating why it exceeds simple interest.

Convert decimals to simple fractions to simplify multiplication and enable cancellation, then use reciprocals to divide. Estimate with decimals like 0.0036 and 0.28 for quick GMAT problem solving.

Explore why the product of three consecutive integers is divisible by six, hence by three. Learn how to use must questions and plug‑in testing to eliminate answer choices.

Identify the median as the first employee in the 80s age group for 161 employees. The first two groups total 87, placing the median between 20 and 29; answer a.

Learn to solve a GMAT problem by testing feasible values of x and y given x+y=1, using factoring and substitution to verify which options are possible and which are not.

Determine the least N such that N factorial is divisible by 990, using coprime factors, and show why 11 must appear while 6 factorial is insufficient.

Compute P(M) and P(R) from their complements, then add them to obtain P(M or R) as 0.6 (3/5). Since M and R cannot occur together, the total probability equals 0.2 plus 0.4.

Calculate total cost with fixed setup and variable production, then compute revenue from 20,000 units at $8, and determine profit per tool as $4.50.

Organize the consecutive integers in increasing order and remember that for such sets the average equals the median. When Q is odd, the largest item is 120 plus (Q-1)/2.

Master the 30-60-90 triangle, its 1:√3:2 side ratios, and the step-by-step method to convert hypotenuse to legs with memory-powered practice for GMAT problem solving.

Break down unfamiliar hybrid shapes into a rectangle plus a half circle using the template. Compute 4 by 8 to get 32, add half-circle area 2π for 32 + 2π.

Learn a fast approach to a GMAT power and decimal problem, using ten powers, decimal place reasoning, and plug-in estimates to find the minimum to reach the eighth decimal place.

Compute the number of three-digit codes using combinations, subtract undesired outcomes, and compare two scenarios where the second digit is 0 or 1.

Learn to solve mixing problems with weighted averages by combining a 2% and a 12% solution to yield 5% in a total volume of 60, using inverse ratio division.

Master solving a GMAT problem by isolating a variable from the easier equation, substituting into the more complicated equation, and deriving a single equation that contains only what is asked.

Use the inclusion-exclusion formula to solve a triple overlap GMAT problem with England, France, Italy counts totaling 84 and overlaps 0, 6, 11, yielding 67 via a Venn diagram.

Estimate percent change by using a nearby comfy number 64 to replace 65, showing the change from 320 is slightly over 20 percent; apply 10 percent steps for quick reasoning.

Solve a GMAT problem using remainder concepts and basic algebra. The lecture analyzes 96 with remainder 9, converts 12/100 to 3/25, and finds y = 75 (choice B).

Master the GMAT order of operations, including simplifying inside parentheses and brackets, powers and roots, and using reciprocals to divide fractions.

Identify the 1:8 ratio, set up a total of 144 with x, solve for x, and determine oxygen weights; use the 8/9 of 144 method for a faster result.

Explore how zero product yields x equals zero or minus a half. Unify the solutions on a number line using same heights for or and different heights for and.

Learn to solve GMAT geometry quickly by spotting right isosceles (45-45-90) triangles, using root 2 to relate sides, and comparing perimeters of dissimilar shapes via identical triangles.

Explore a GMAT problem solving question that uses powers of ten, showing that multiplying by ten five times yields 10^5 = 100000, confirming option c.

Learn to solve a two-equation problem by subtracting to eliminate a variable, then determine least and greatest possible values for n using integer constraints and a plug-in elimination strategy.

Identify the median as the middle item in a positive set, and compute the mean from the sum divided by the count. Use convenient numbers and elimination for must questions.

Apply ratios and cube roots to relate volume to base area and height in a GMAT problem. Use comfortable numbers to eliminate choices and study cube root algebra.

Master GMAT problem solving by simplifying before multiplying, using benchmarks to estimate, and checking the units digit to prune answer choices. Apply these tactics to conversion and arithmetic questions.

Learn to rewrite adjusted numbers with x, convert the ratio problem into an algebraic equation, apply cross multiplication, and solve for x, yielding 15 as the current count.

Apply exponent rules to compare 25^n with 5^12 by rewriting 25^n as (5^2)^n = 5^(2n). Deduce 2n > 12, so n > 6; for integers, n ≥ 7.

Explore a GMAT problem solving method using fractions and percentages, setting a total of 160, deriving 27 women lawyers, and computing the probability as 27/100.

Demonstrates that increasing a quantity by a quarter multiplies it by five quarters, applies (5/4)^4 to simplify, and solves for x by dividing by 6/5.

Learn to determine the median by ordering a data set and selecting the sixth item in an 11-element span from 1990 to 2000, using benchmarks to guide a rough estimate.

Decode a novel divisibility symbol through inverse operations, and determine the largest k where 2^k divides 72 but 2^(k+1) does not.

Master the normal distribution with the GMAT focus: the mean as the 50th percentile, symmetry, and 34% and 14% within one and two standard deviations, yielding 84% and 98% cumulative.

Master solving a GMAT fraction problem by modeling three of four sandwiches among people, plugging in a convenient number to eliminate choices, and deriving the final fraction 7/15.

Back engineer the equation to remove a root by moving terms and squaring, or solve quadratics by factoring or the quadratic formula, extracting an integer from under radicals.

Learn the percent change formula, difference over the original times 100, and how to estimate with benchmarks when facing ugly numbers in GMAT problems.

Solve a probability question by selecting two non-defective pens from twelve, using chronological probabilities (9/12 then 8/11), simplifying before multiplying, and detailing each step.

Apply the weighted average method to quickly solve two-price problems by using inverse ratios to determine the quantity distribution and track how putting back fruit shifts totals.

Learn to compute percent change by converting percents to fractions, simplifying, and using a common denominator to find the difference over original amount, then express the result as a percent.

Explore properties of a rhombus within a parallelogram, including perpendicular diagonals, angle bisectors, and 30-60-90 subtriangles, revealing a 1:3 diagonal ratio.

Count the powers of three in 30 factorial by summing threes from multiples of 3 and higher powers like 9 and 27, totaling 14; hence k equals 14.

Solve this GMAT problem in real time and extract takeaways. Use power-to-power rules to rewrite expressions as squares, apply the quadratic formula, and test divisibility using coprime factors.

Apply area ratios to solve quickly: the ring area is three times the small circle, so the large circle area is four times small; infer radius and circumference ratios 1:2.

Derive a number that leaves remainder three when divided by four and by five, using X = 4m+3 and X = 5n+3; plug in m=5, n=4 to get X=23.

Model reading as work and use a one-variable equation to compare planned and actual reading rates (90 vs 74 pages per day) to finish the assignment.

Learn to isolate root expressions and solve equations by raising both sides to appropriate powers, handling cube roots and square roots for GMAT math problem solving.

Learn to compare expressions in GMAT math problems by plugging in convenient values, recognizing that squares are nonnegative, and using power trends for negative fractions.

Master GMAT math problem solving for percent changes and ratios by plugging in convenient numbers, interpreting 'percent less' correctly, and using quick ratio reasoning to compare incomes.

Use the combination formula n(n-1)/2 to count lines connecting 30 cities. The order of selection doesn't matter, so you divide by two to avoid double counting.

Scale ratios by a common factor, as shown when 2 becomes 8, and write x beside terms to add or subtract within the ratio.

Count x values for x = 3 p^2 with p prime and x < 100. Show p = 2,3,5 yield 12,27,75; seven exceeds 100.

Plug in options and count letter pairs to solve a GMAT problem. Five letters yield ten pairs, at least twelve; then apply x^2+x-24>=0 via factoring and the quadratic formula.

Sketch data on the x–y plane left to right, and compute slope as rise over run. Use parallel lines with equal slopes to deduce y = (2/3)x, identifying problem's solution.

maximize a quadratic height expression by identifying the vertex at t=3, giving a maximum height of 150, and compute height two seconds after as 86 via parabola symmetry.

Learn to solve single-variable inequalities by isolating x, applying addition or subtraction to all parts, and representing the solution on a number line with open and closed circles.

Use a ratio method by setting the smallest value to 1, deducing J = D/3 and P = 2D, then sum D+J+P = 10D/3 to identify C.

Apply pair counting to determine matchups among eight teams, treating games as unordered pairings, yielding twenty-eight distinct pairings.

Explore the invented theta operation used in GMAT solving, translate it verbally, and learn to plug values to deduce a = c when a theta c = 0.

Learn to handle percent increases by converting to fractions (115% = 23/20) and simplifying before calculation, then apply quick division to deduce per-person amounts.

Solve a deceptive work-rate problem by expressing the rate as a function of time and solving a quadratic using substitution and the quadratic formula.

Demonstrates how flipping the numerator and denominator in a fraction flips the inequality, and uses plugging in strategies to test must GMAT choices with representative values.

Combine two machines' rates, 1/4 and 1/3, using the bow tie method to get 7/12, then compute time as work over rate to obtain 12/7.

Explains solving a GMAT problem on shipping costs, comparing separate versus combined packages using x and y, and using must questions with plug-in values to eliminate options.

Apply the rule of 72 to estimate doubling time for compound interest, use benchmarks when numbers are ugly, and show that doubling occurs in about 9 years.

Learn how rounding to the nearest ten and nearest unit sets bounds on miles and gallons, then compute the maximum and minimum miles-per-gallon by using extreme distance and fuel values.

Master solving a must-question GMAT absolute-value problem by plugging in values and applying range reasoning to eliminate answer choices.

Solve a two-group weighted average with six days at 360 and four days at an unknown average, overall 400. The unknown average is 460.

Compute dollars per person by dividing 1.2×10^12 by 240 million, using exponent rules and decimal shifting to obtain 5,000 dollars per person.

Explore combinations and probability by counting paths from X to Y, considering intersections, multiplying options at each step, and noting that order of selections matters for the GMAT solution.

Apply the invented dot operation as the square root of a product, using order of operations and factoring under radical with examples like 5 dot 45 and 15 dot 60.

Recognize non-terminating and terminating decimals indicated by a bar, and use decimal shifts when multiplying by powers of ten in GMAT problem solving.

Learn to solve a GMAT ratio problem by combining the night-to-day and worker counts, multiplying ratios to 3:4 and 4:5, and compute total boxes loaded by day crews.

Apply prime factorization to turn 3150 into a perfect square by ensuring every prime factor appears an even number of times; multiply by 14 to achieve 2^2 3^2 5^2 7^2.

Use the floor operation, where [x] means the greatest integer less than or equal to x. Plug in 2.7, 3.4, and -1.6, then sum the results to get 3.

Learn to solve GMAT problem solving with arithmetic sequences and consecutive integers by using the sum equals average times number of items and the middle-term average.

Solve non arithmetic sequences by plugging numbers in an orderly, recursive fashion, treating each term as dependent on the two preceding terms to determine the answer.

Compute the probability of rain and no rain across three days by multiplying stage probabilities (no rain, no rain, then rain); convert to fractions to obtain 0.128, noting order matters.

Explore how to solve a GMAT problem on average speed using two methods: plug-in numbers and algebraic reasoning, applying distance over time and distance is rate times time.

Explore how the units digit of powers of three cycles every four, ending in 3, 9, 7, 1, and how combining a 7-ending and a 3-ending number yields 0.

Solve unfamiliar polygon area problems on the GMAT by breaking the shape into rectangles, using plug-in numbers to check progress, and solving the resulting quadratic to find the margin width.

Learn to convert fractions to terminating decimals by simplifying denominators to powers of two and five, then apply decimal placement to a GMAT problem.

Learn to sum even numbers from 100 to 300 using average times count, recognizing 101 terms and a total of 20200.

Learn prime factorization and primality checks using divisibility tests, square roots, and rules like divisibility by 11 to solve GMAT problem solving questions.

Explore how plugging in values reveals a pattern in a sequence a_n, showing that a_{n+1}=a_n^2 and a_{n+2}=a_{n+1}^2, then derive the power relationships to solve the problem.

Learn to solve GMAT math by plugging in convenient numbers to compare price over earnings ratios and compute the percent increase between them.

Learn to solve triple-overlap questions on the GMAT by applying the whole equals sum of groups and overlaps, using quick Venn-diagram reasoning and the core formula.

Develop techniques for handling negative powers by flipping numerator and denominator, converting to positive exponents, and evaluating expressions like a^(-2) as 1/a^2.

Explore how to compute profit or loss as a percent of cost by canceling the initial cost, using 100 as a plug-in, with 54 sold and 6 returned, yielding 13–14%.

Organize seven numbers in increasing order; the largest equals four times the smallest plus fourteen, the median is eighty-four, and with sixty-eight average, minimize the others to maximize the target.

Learn to solve a GMAT problem-solving sequence with non-constant differences by plugging in consecutive terms, compute a5 and a6 from the given relation, and find their difference is 17.

determines the least possible product for 20 numbers by taking minus ten to the 19th power and multiplying by ten, yielding minus ten to the twenty.

learn to calculate total arrangements with duplicates by dividing by factorials, then subtract adjacent-item cases by forming a single block and accounting for internal orders.

Plug in convenient numbers, starting with a total of 100 newspapers, to solve for R using revenue shares. Verify choices with ballpark checks and divisibility insights while applying cross-multiplication.

The lecture shows solving a difficult GMAT problem by converting all terms to powers of ten, using scientific notation, and applying the difference of squares to cancel terms and simplify.

Sketch the data on a coordinate system to identify point r’s y coordinate, then apply the triangle area formula to find y_r = 6.

Identify rate and speed problems by using a distance over rate over time approach, subtract speeds to obtain relative rate, then compute catch up and overtake distances.

Apply weighted average reasoning to two groups by using inverse ratios of quantities and their averages. Recognize that the proportional splits reflect unit ratios and enable quick solution.

Apply a must-question strategy by substituting 1/x for x, plug in x = 2, and simplify via the bow-tie method to (1+x)^2/(1-x^2) to identify the correct choice.

Show that two lines perpendicular to the same line are parallel, and that a third line creates equal small and large angles whose sum is 180 by exterior angle theorem.

Determine the line through (0,2) and (3,0) by testing coordinates in candidate equations. Derive the slope -2/3 and obtain the line in standard form 3y+2x=6.

Analyze AB and BA two-digit numbers, use their difference 9(a-b) = 27 to get a-b = 3, and note AB+BA = 11(a+b) to check divisibility for GMAT problem solving.

Recognize a coordinate setup with a circle tangent to the axes forming a square; from the diagonal to a leg, divide by root 2 to obtain k over root 2.

Explain solving a parallel resistance problem by using reciprocal sums, cross-multiplication, and isolating R to express it in terms of X and Y.

Apply probability rules to independent events by multiplying probabilities. Use the complement to exclude undesired outcomes, arriving at 3/64.

Solve a GMAT problem by plugging in numbers to verify a value, then use a common denominator to solve for x, confirming x equals -2.

Master negative exponents and base power rules to simplify expressions with 1/2, 1/4, and 16. Apply multiplying powers and adding exponents for the same base.

Master how to handle maybe questions in GMAT problem solving by using convenient numbers, checking roman numeral conditions, and analyzing rounding from actual sums to estimated sums.

Use prime factorization to determine how many times seven divides 147000, using 1000 as a convenient benchmark and identifying that seven appears with exponent two.

Solve two-group double overlap questions using a number line instead of Venn diagrams, recognizing maximum overlap equals the smaller group and applying this approach for easier solving.

Multiply by x to obtain 5x - 6 = x^2, so x^2 - 5x + 6 = 0. Factor into (x-2)(x-3)=0, giving x=2 or x=3; correct answer is C.

Learn to solve a GMAT mixture problem using the weighted average method, recognizing two groups with different quantities and averages, and applying inverse ratios to determine X’s share.

Solve a rational inequality by locating zeros of the numerator and denominator, testing points, and unifying interval solutions to find integer values below five.

Apply exponent rules, including managing negative powers, combining like bases, extracting common factors, and using least common multiple to simplify fractions, as shown in GMAT® math problem solving.