GMAT® Math | Official Guide 2020

Analyze 404 GMAT Official Guide 2019 questions to identify types, subtypes, and techniques for problem solving and data sufficiency. Use raw data and graphs to form insights for adaptive testing.

Explore the popularity matrix that maps question types and takeaways across 404 GMAT questions. Use Ctrl+F to search for topics like prime numbers and focus on weak areas.

Analyze the bubble chart of GMAT math question types and percentiles, focusing on algebra, statistics, powers and roots, overlaps, combinations and probability, and integers; master top techniques to boost score.

Explore the internal distribution of GMAT math question subtypes from algebra and geometry to percents, statistics, and overlaps (double and triple), with quick methods for quadratics and inequalities.

Explore problem solving and data sufficiency in GMAT, highlighting top techniques, common question types, and hardest subtypes like triple overlap, with tips to plug in numbers and simplify must questions.

Learn the top data sufficiency techniques for GMAT, including common question types—algebra, geometry, and percents—and how statements can lead to two conclusions, with focus on hardest question types.

Learn how to assess data sufficiency questions by evaluating statement 1 and statement 2. Identify the immutable answer choices and how they apply on test day.

Learn to determine data sufficiency by forming two contradicting conclusions from given data using a flowchart. Apply convenient and petty numbers to assess sufficiency, including terminating versus non-terminating decimal scenarios.

Identify the true meaning of the data sufficiency answer choices, determine when each statement is sufficient, and rapidly eliminate wrong options to find the correct answer.

Master the ad/bce split flowchart to tackle data sufficiency questions, quickly assess whether statement 1 is sufficient, and identify the correct answer among a, b, c, d, or e.

Apply the data-sufficiency flowchart to decide sufficiency. Test statements by plugging numbers, and note that a terminating decimal arises when the denominator has only powers of 2 and 5.

apply data-sufficiency flowchart strategies to simplify the question and decide what is needed. statement 2 alone suffices by yielding a+2p=0.4 for 5a+10p; statement 1 is insufficient.

Master data sufficiency in geometry by stretching alpha vertex to test if alpha stays fixed; if it changes, data are insufficient; if delta and beta fix alpha, data are sufficient.

Assess data sufficiency by determining whether each statement alone suffices before considering both; use totals and tea counts, avoid contradicting given data, and learn to plug in numbers carefully.

Learn how to tackle GMAT data sufficiency questions by recognizing that the average rate equals total distance over total time, and that statements alone or together may be insufficient.

Assess data sufficiency by testing statements to determine if x has a single value. Distinguish linear and quadratic cases, solve fully, and avoid contradictions or unnecessary math.

Learn data sufficiency strategies for the GMAT, focusing on when statements suffice, two-conclusion testing, DS flowcharts, and tips for geometry questions.

Access the study materials attached to this lecture to support your GMAT math preparation.

Master the GMAT Official Guide 2020 diagnostic section 3.1 through problem solving and data sufficiency questions, using video solutions that reveal fast techniques, takeaways, and practice tips.

Master GMAT quantitative reasoning by applying takeaways and must-question strategies; solve problems faster using benchmarks across arithmetic sequences, double-overlap data, volume, combinations, probability, and ratios.

Explore essential study materials for GMAT math with this introductory lecture, where you’ll access attached prep resources to begin your Official Guide study journey.

Apply a must-question strategy to GMAT perimeter problems, plug in convenient numbers, and sum external segments; for the example, the perimeter equals 12.

Master pricing questions by multiplying items by value per item to obtain totals, then break numbers into benchmarks and compare to find the max–min difference.

Apply the sum of distances from the given average to quickly solve PS questions. With average 80, distances -8, -2, +3 sum to -7, so R = 87.

Master the 10% chunk shortcut to calculate percentages quickly on GMAT math, applying it to 15% of 500 and 20% of the additional 800, with simple fraction steps.

Analyze a GMAT math problem by calculating coupons used and remaining from stock: 1040 envelopes with 2 coupons each yield 2080 used, leaving 920 unused, with answer A.

Demonstrates a real-time GMAT geometry solution, using a coordinate sketch to identify a right isosceles triangle with R at (5,-5) and eliminate answers from the drawing.

Apply the percent change formula by computing the difference over the original, then multiply by 100 to convert to percent, using the template for any increase or decrease.

Learn to simplify GMAT fractions by canceling opposite terms, applying the order of operations to additions and subtractions, and using the least common denominator for a quicker approach.

Shows solving a GMAT problem using unit analysis and per, translating weekly and daily rates into dollars, applying unit cancellations and unit-digit reasoning to find the correct choice.

Use a ratio approach by setting the employee share as x and owners as 3x, so 16x equals 48,000; x is 3,000 and owners get 9,000.

Master unit conversions by treating per as division, canceling units, and applying currency rates to reach final totals, as shown in euros to dollars calculations.

Master GMAT ratio questions by recognizing a fast setup with labeled squares, and learn to reduce ratios and use the correct order, whether vertical or horizontal, to avoid traps.

Learn to solve a coordinate geometry problem by plugging the point (0, 2) into the line equation to find k, noting a point on a graph yields a valid expression.

Learn to solve ratio problems by using the greatest common divisor to create equal bouquet batches of white and red tulips, applying divisibility rules and integer constraints.

master how to calculate 125 percent of a number by converting to fractions, using benchmarks, and treating the word of as multiplication for quick, accurate results.

Identify medians by sorting the data; for a 9-item set, the median is the 5th item. Use the ordered sequence 12, 16, 18, 25, 27 to determine option C.

Master unit conversion in GMAT math by dividing miles per hour by gallons per hour to obtain miles per gallon, using the ear-method; result 4/3 miles per gallon.

Apply a quick distance-percent strategy for a GMAT problem by summing 50% to the return leg, plugging in 100 as the total distance, and deducing 55% as the correct answer.

Learn how to treat increases or decreases by fractions as multiplicative factors, using 1/4 and 1/3 as examples, and to simplify before multiplying for GMAT PS question 20.

Five consecutive integers have equal average and median when the difference is constant; odd sets yield the median as an element, while even sets yield a non-integer median.

Solve a coin-value puzzle by setting X as the number of 25-cent coins and using a single equation with 16 coins totaling 235 cents to find X = 5.

Demonstrate an elegant eggs profit solution using integer cents, factoring to compare selling and cost for dozens, highlighting that focus on multiples of 12 avoids per-egg math.

Derive the pi over four ratio for a circle inscribed in a square and solve the square’s perimeter from a 25 pi circumference; use the diameter formula pi x D.

Apply the 'which of the following' plug-in method using convenient numbers to find the greatest option, then eliminate choices with a must-question focus on answer choices.

Examine how eight consecutive integers in set X, when increased or decreased by four, form set Y with sixteen elements—eight more than X—emphasizing reading comprehension and pattern recognition.

Learn to estimate GMAT numbers using close-by benchmarks and guesstimation, as shown by rounding 60.2 to 60 and approximating 1.03 × 4.86 to about 5, yielding 12.

Translate the GMAT problem into a single linear equation by assigning X to a quantity, using 20 more and twice as many relationships, and solve 4X=80 to get X=20.

Extract information while reading and apply midpoint reasoning to GMAT® Official Guide 2020 problem. Use a distance variable x and a 4-mile segment to solve Abdul and Carlos's house distance.

Apply the external angle theorem and triangle angle sum to deduce x equals 90. Use the drawing to estimate angles when not scaled and connect given data to the goal.

Apply rate times time equals work to solve a rate problem, recognizing that time is directly proportional to work and that units can be attached or detached to compute distance.

Solve a GMAT official guide 2020 problem about pine and oak doors with a 25% discount. Convert percents to fractions for quick arithmetic, yielding a total of 560.

Explore a GMAT PS problem from official guide: determine crate counts for Winesap, Macintosh, and Rome with total 25, using the least-value method and plugging in the smallest answer choices.

Analyze a GMAT official guide 2020 problem about two bike costs, 250 and 375, with a 450 selling price, illustrating possible profit pairs for P1 and P2.

Deliver quick geometry tactics for GMAT questions, emphasizing drawing reliability, isosceles triangle properties, angle relationships, and the polygon angle-sum rule.

Master the mathematical approach for GMAT must questions: use K^2 = M^2 to get K = ± M, then eliminate choices by plugging in convenient numbers (0, ±1, ±2).

Learn to solve ratio and proportion questions by assigning a ratio unit, treating totals as 13X = 780, and using benchmarks plus unit-digit checks to find M equals 180.

Identify common pythagorean triples, such as 6:8:10 and 13:12, to solve right-triangle problems. Compute percent change as the increase divided by the original value, e.g., 4/10 = 40%.

Check each answer choice quickly by testing whether 4^x equals y+3 and x is a positive integer. Memorize common powers of 4 to guide elimination using the powers table.

Convert decimals to fractions to simplify equations, using 1.25 as 5/4 to get -1/4. Move terms across sides, turning division into multiplication and sign changes, to identify the correct choice.

Master fast fraction division using the ear method and reciprocal multiplication, simplify before multiplying, and solve for x from the quotient 9/2, yielding x = 3.

Learn how an inscribed sphere fits inside a cube, showing the edge equals twice the radius, and apply must questions by plugging in a convenient unit of 1 for geometry.

shows how to solve a gmat pricing problem by calculating tiered charges: first 75 units at $8, next 20 units at $0.065, and multiplying decimals to total $9.3.

Learn to solve two-equation, two-variable problems by elimination—adding or subtracting equations—and by multiplying equations to eliminate a variable; use factoring such as 3(x+y)=12 to deduce x+y=4.

By using a single table and connecting Y, convert X:Y 4:1 and Y:Z 2:1 to X:Z 8:1, choosing multiplication by 2 over division to maintain integers.

Analyze how a GMAT question uses diminishing increments like 1/4, 1/9, 1/16 to show the cumulative sum stays below 2, and memorize these fractions, decimals, and percents.

Compute the total refund value by multiplying the number of units (20,000) by the per-item value ($2,500), comparing 0.5% and 0.3% and simplifying before multiplying.

Understand that when all items in a set increase by the same percentage, the average increases by that same percentage; use benchmarks and 10% chunks for efficient GMAT PS reasoning.

Break down the problem by translating hours and rates into a single equation, simplify by canceling zeros, and solve for x to verify the correct option.

Explain triangle angle sums of 180 and how right triangles have acute angles that complement to 90. Solve 2y+10=90 to get y=40 and the 40:50 (4:5) ratio, option D.

Explore how AB and BA as reverse two-digit numbers yield 11(A+B), so AB+BA is divisible by 11 and AB-BA equals 9(A−B). Use plugging to eliminate for must questions.

Identify efficient counting strategies in GMAT questions, using up to twelve simple counts or four to five calculations, rather than chasing tricks.

Plug in comfortable numbers for s, r, and n to eliminate answer choices, then apply the boxes formula s/r and unfilled boxes s/r − n to find the solution.

Identify must-be-true questions, plug in numbers to eliminate answer choices, and simplify inequalities; this lecture uses Roman numerals I–III and color-coding to find the correct option, B.

Learn to solve a GMAT coordinate geometry question by recognizing must questions, plugging in convenient numbers to eliminate options, and applying the midpoint formula to deduce Q(-r, -s).

Master fast percent problem solving by turning 'of' into multiplication, using ballparking, and simplifying decimals before dividing; apply to unit cost, production run, and 4200-unit solution.

Compute the number of units by dividing the equipment cost of $9,900 (990,000 cents) by the profit per unit of 55 cents, simplifying first to 18,000 units.

Plug in convenient numbers to solve a GMAT fraction problem, use least common multiple to merge denominators, find X as 9/4, then test n=1 to confirm answer D.

Factor the quadratic to find two numbers with product -15,000 and sum -250, yielding w = 50; this GMAT problem is algebra, not geometry, emphasizing the question’s essence.

Master GMAT percent questions by comparing simple and compound interest, using ballparking, split-rate per cycle for semiannual compounding, and quick last-digit checks to verify results.

See a real-time solution to a PS GMAT problem using the Pythagorean theorem, converting roots to 4√2, and quick estimation to select the correct answer with two takeaways.

Learn to solve must questions by plugging in convenient values, such as x=2 for trees with 10 bushels each from 350, then use elimination to identify correct GMAT® PS choice.

Translate the fraction X/(X+16) to 4/5, apply cross multiplication to get 5X=4X+64, and determine the denominator equals 80, illustrating a GMAT practice strategy.

Find the greatest daily units by assuming the other day had 30 units at $2, then allocate the remaining $120 at $2 and $2.5 per unit to reach 56 units.

Master the method for identifying the greatest value by squaring terms, handling roots and powers, using benchmarks, and eliminating unsuitable answer choices in GMAT questions.

Solve a two-object distance-rate-time problem with moving objects traveling in opposite directions by equating 40T plus 20(T+3) to 240 miles, yielding T=3 and 2 pm.

Use a percent tree to solve a GMAT problem: 90% of total, with 40% and 50% allocations and 720 for corn, yielding X = 8000 (choice D).

Apply exponential growth reasoning by modeling a population that doubles each month, starting at 3, yielding 3(2^10) after ten months and identifying the correct choice D.

Learn a time-saving GMAT strategy by spotting symmetry, extracting a common factor, and using benchmarks to simplify ugly fractions to solve question 80 quickly.

Tackle must-question GMAT problems by plugging in convenient numbers, using y as a multiple of 5 and 3x+4y=200, and eliminating options through co-prime factor reasoning.

Apply a fast root-simplification method and exponent rules to determine when expressions yield integers. Use prime-factor parity and the checks for I and III to confidently pick option E.

Compute a and b's rates from work over time, then sum to a combined rate. Use time equals work divided by this rate to solve the tank problem.

Plug in values to determine k, and show that the point (0,2) lies on all lines; the intersection of y=2 and x+3y=6 remains true regardless of k.

Master solving inequalities with even roots by noting x lies between -sqrt(2) and sqrt(2). Use must vs maybe questions, plug in zero, and eliminate choices to identify the correct option.

Master a fast strategy for question 86, PS in the GMAT official guide 2020 by breaking down pages and days, using benchmarks, and deciding to skip especially time-consuming data-heavy items.

Solve a tricky percents problem by plugging in 100, apply the must-question approach, and compare 42% and 33% of 100 to identify a 9 decrease in annual produced and sold.

Learn fast problem solving for remainders and divisibility by plugging in convenient numbers, recognizing must questions, and using factors to show three consecutive integers are divisible by 6.

Demonstrate subtracting fractions with unlike denominators using the gamma method, and compare differences with a half benchmark to select the smallest result.

Solve a rational equation with p nonzero by simplifying and multiplying through. Use the gamma method to obtain r = 2p^2 - 1, and apply must questions, plugging in values.

Learn how to compute range as max minus min and determine x values that yield a 12-range, shown by comparing 3, 14, and potential x candidates to select option D.

Translate the prompt into x equals two thirds of x plus 108, then x equals 324, so the answer is E, illustrating equation setup for GMAT PS questions.

Convert percent language into an equation: 460 is 115% of x, so x = 400, and the lecture highlights why the correct choice is B.

Multiply both sides by 8 to preserve the ratio, turning 16 to 18; calculate the percent increase as 2 over 16 equals 12.5%, identifying the correct choice.

Learn to solve invented operations on GMAT questions by plugging in numbers orderly, isolating roots, and raising to a power of two to express t in terms of u.

Use a 5-12-13 right triangle to find a circle's radius as 6.5 from the diameter 13. Compute the area as pi r^2. Apply inscribed angle and Pythagorean takeaways to solve.

Split the quadrilateral into two right triangles by connecting B and D, then use the pythagorean theorem and known triples to find AB as 2√6.

GMAT math problem compares two ways to reduce a 40 by 30 ft lawn to three-quarters of its area and computes perimeters to find the fence difference.

Master midsegment properties: a line parallel to a side and bisecting another yields CF equals 15 and similar smaller triangles. Compute the equilateral triangle area as 225 sqrt3.

Solve scale and ratio problems by converting inches to feet, calculating rectangle area, and counting 6x6 inch tiles in square feet, using similar shapes and no wasted area.

Apply must-question strategies to GMAT math, testing convenient and near-equal m and p with m^2+p^2<100 and m+p<100 to identify option D.

Master ratio manipulation by using the idea that switching numerator and denominator is allowed to relate x/y to a/b, and evaluate answer choices for mathematical equivalence.

learn how to multiply decimals by ignoring decimal points, count decimal places, and use powers of 10 to convert a product to an integer, with examples.

Factor x^2+2x-24 by identifying two numbers with product -24 and sum 2, namely 6 and -4, yielding roots -6 and 4 and the correct answer is B.

Solve percent-tree questions by breaking the total into branches and using 40% independent voters and 10% of 60% of n, simplifying before multiplying.

Apply circle properties: inscribed angle opposite a diameter is a right angle; use the 6-8-10 triangle to get hypotenuse; compute arc length as half the circumference, radius 5, 5 pi.

Explain how to use the weighted average axis to solve two-group GMAT data questions, with 2x and x quantities and 17 and 20 averages, and apply elimination criteria.

Solve this remainder problem by tallying 17 trips of 4 jugs to 68, then divide by 7 to see the last carton needs 2 jugs.

Break the polygon into rectangles to relate width and length, using area 4800 and rectangle area 1200 to form 1200 = 3w^2, giving w = 20 and l = 60.

Master the clones work-rate formula for GMAT work questions with identical rates, using simplification before multiplication to find how many machines produce 3x units in 4 days.

Analyze invented operation questions in GMAT math, determine must-be-true outcomes when symbols like @ equal subtraction or division, and use plug-in numbers to eliminate options with Roman numeral logic.

Master algebraic reasoning in the GMAT official guide 2020, question 112, by converting percents to fractions, simplifying, and using a must-question approach to deduce 12n/m equals 18.

Clarify percent change by multiplying by (100 plus the percent) over 100, and distinguish it from the increase or decrease, highlighting the whole for GMAT official guide 2020 PS.

Apply invented operation cost formula 100,000 times P divided by (100 minus P) to compare pollutant removal for P = 90 and P = 80, yielding 500,000 difference (option a).

Recast xy as A and solve A^2 - A - 6 = 0 to find possible xy values. Then test options by strategic roman numeral plug-ins to quickly eliminate choices.

Learn to approximate problem solving questions on the GMAT by using benchmarks, converting roots to powers, and simplifying products with sqrt(a b) = sqrt(a) sqrt(b).

Calculate the combined work rate of three printing presses. Use the gamma method to isolate a rate by subtracting equations and confirm with the time-work relation.

Sum volumes of spheres with radii 1, 2, and 3 to obtain R^3 = 36; the diameter is 2 times the cubic root of 36, giving answer E.

Apply a trick for sums of consecutive integers by canceling negatives and positives, then use sum equals average times number of items, with the average as the middle value.

Tackle absolute value questions by plugging in comfortable numbers and assigning s, t, and r as absolute values. Compare substitution and testing choices to identify the correct option, E.

Solve multiple inequalities for a single variable by interpreting 'at least' as greater than or equal to, then unify conditions on a number line to obtain n = 11.

Identify a double overlap problem and solve with a number line that marks the whole, groups, and overlap to determine the neither, using 5,000 minus x minus y plus z.

Solve double overlap questions on a number line by placing 62 and 47 on a 100-unit scale, compute overlap as 9, and identify stockholders not employees as 53.

apply the percent change formula: difference divided by the original, times 100, with the whole identified after 'of'. use answer-choice elimination to confirm the correct option, here d.

Identify five distinct calculations of day-to-day changes, compute each difference over the original as a percent, and compare magnitudes to select the greatest change, using simplification and benchmarks when needed.

Apply factorial divisibility and common-factor extraction from the GMAT official guide 2020 to see that 20!+17 is divisible by 17, identifying option C.

Explore maximizing an expression with a squared term by minimizing the negative component, using the zero minimum of a square; the sweet spot is t equals 5 for maximum depth.

Use rate, distance, and time relationships in a moving-object scenario, applying distance over rate equals time and rate times time equals distance to solve outbound and return times.

Learn to solve a compound interest GMAT problem by isolating x, with two 8% increases, yielding x = w divided by 1.08^2 + 1.08, and identify the correct choice D.

Approximate the sum of 100 reciprocals by treating each term as about 1/300. Use these bounds, noting the total lies between 1/3 and 1/2, which leads to answer choice A.

Plug in comfortable numbers to solve rate-time-work problems with multiple variables. Use the combined-rate formula and the gamma method to derive the rate and identify the correct answer.

Master how to find the median by ordering data, noting odd versus even counts, and averaging the two middle values, as in the example 4, 10, 16.

Master percent rules and benchmarks to estimate and solve a GMAT style problem, using 10.8% of 37 and the blue marbles equal to 1/3 of the total.

Identify the median as the middle item in an ordered set; with 161 employees, the 81st lies in the second group, giving a median between 20 and 29.

Solve a GMAT math question using the median: Ron = Amy + 4, Barbara = R + 1, B = 65 yields R = 64; Ron's height is the median.

Analyze a GMAT problem solving question by rewriting 100x+200y as 100(1+y) using x+y=1, then test 80, 140, and 199 with must-or-maybe reasoning and number plugging.

Learn to maximize a fraction with decimals by increasing the numerator and decreasing the denominator, convert decimals to fractions or multiply by powers of ten, and use benchmarks for division.

Apply a fast, methodical approach to combinations and probability questions by staging steps and multiplying options. Use 'and equals multiplication' and check units digit.

Apply a fast must-question method for GMAT median and average with consecutive integers, using 119, 120, 121 as example; the largest equals 120 plus (Q-1)/2.

explains solving a 30-60-90 triangle problem using the 1 to root 3 to 2 ratio and the steps from hypotenuse to short leg, then to the long leg.

Solve a three-digit code GMAT question using total minus undesired and casework; first digit 8 options, second 0 or 1, third depends on second, yielding 152 and answer B.

apply the weighted average axis to mix 2% and 12% into 5% with total 60, using the inverse ratio to allocate quantities and identify the correct answer E.

Solve a two-equation linear system by isolating S from S = (J-8)/2, substituting into J+S = 278, and deriving J = 188 pounds (answer E).

Explore how standard deviation changes when multiplying by a constant and adding a constant, showing that scaling by 0.8 reduces deviation, while adding 20 leaves it unchanged.

Apply the triple overlap formula for three groups: sum of the groups minus double overlaps, accounting for the triple overlap and neither group. Conclude the result is 67.

Compute the percent change from 320 to 385 by dividing the difference, 65, by 320, then multiplying by 100, noting the result is just over 20 percent.

Interpret remainders in a GMAT problem, converting 12/100 to 3/25, and relate 9/y to 3/25 to determine y as 75.

Learn the zero-product rule to solve PS questions, recognize or versus and relationships, and use a number line with different heights to unify solutions, yielding the correct x values.

Use GMAT geometry techniques with right isosceles triangle ratios 1:1:√2 to compare perimeters of dissimilar shapes, dividing into identical triangles and solving the ratio in ten seconds.

Form two equations from the data on teachers and classes, then subtract to isolate n. Plug in the answer choices to identify the least and greatest possible values of n.

Convert ratio changes into x units, apply cross multiplication, and solve for x to find the current number of teachers in the GMAT official guide example.

Master GMAT exponent rules by solving question 161 from the official guide, rewriting 25 as 5^2 to compare with 5^12; deduce n>6, yielding n=7 (option B).

Discover a fast method for problems involving increasing by a quarter, by multiplying by 5/4 to the fourth power, revealing X = 2560 and option D.

Identify the median by ordering the data and selecting the sixth item in an 11-item set. Use benchmarks such as 200,000 and 300,000 to guesstimate when exact values aren’t provided.

Translate the invented operation into a divisibility rule: b is divisible by a^k but not by a^(k+1). Apply this to 72 to deduce k=3 and yield the correct choice B.

Master the normal distribution curve, focusing on the mean, standard deviation, and key percentiles: 34%, 14%, 84%, and 98%. Use these rules to locate percentiles relative to the mean.

Apply the Bow-tie (Gamma) method to add fractions and use convenient numbers, like 60, to plug in and test GMAT PS questions, then eliminate options to verify the answer.

Solve a two-step probability question about selecting two non-defective pens from twelve, multiply simplified probabilities, and follow a stage-by-stage, chronological approach where 'and' means multiplication.

Use the weighted average axis method to solve two-group mixed-quantity problems, using inverse ratios to relate averages to quantities, as shown with apples and oranges.

Compute percent change by converting percents to fractions, use a common denominator (lcm) to subtract, simplify, then convert to a percent, yielding 44 4/9%.

Analyze light-on and light-off intervals to find gaps over 15 minutes between 8 and 10 a.m. Sum the off minutes to 25, confirming option b.

Apply quadrilateral properties by recognizing a parallelogram that is a rhombus with perpendicular diagonals and angle bisectors, revealing a 30-60-90 triangle and a 1:√3 ratio to select D.

Determine the greatest k such that 3^k divides 30!, by counting 3s from factors in 1–30, including multiples like 9 and 27, yielding k = 14.

Learn to solve complex GMAT powers and divisibility questions by using the difference of squares trick, power rules, and coprime factor reasoning to identify correct factors quickly.

Apply takeaways to solve circle ratio questions quickly: area ratios correspond to squared linear ratios, and similar circles scale radii and circumferences by the same factor.

Explore remainder problems by plugging in convenient numbers, using 4n=5m to show x=23, and determine a remainder of 5 when dividing by 6.

Apply rate-time-work concepts to a reading task, set up 90d = 75(d-6), and solve for d using simple benchmarks to find the total days.

Explore how x equals 3 times a prime squared, test primes 2, 3, 5, and 7 to stay under 100, and conclude there are three possible x values (answer B).

Use the must-question plug-in method: with x letters, codes equal x(x-1)/2, must be at least 12. Compare 4 and 5 letters to conclude 5; note the quadratic approach as backup.

Interpret coordinate geometry in the xy-plane by sketching data and comparing slopes; identify parallel lines with slope 2/3, and verify that y = 2/3 x (choice A) isolates the slope.

Maximize the height by analyzing the quadratic, which peaks at 150 when t = 3; the height at t = 5 is 86 due to parabola symmetry.

Solve a ratios problem by assigning 1 to the smallest ratio, derive D=3, Jeff=1, Paula=6; sum to 10, then apply the bow-tie method to compute 10D/3 and confirm option C.

Apply the combinations formula n(n-1)/2 to count unique pairings among eight teams, showing there are 28 distinct games.

Master solving a GMAT rate and time problem by isolating variables, plugging into the second equation, and applying the quadratic formula or factoring.

Compare separate and combined shipping costs, with x for the first pound and y for each additional pound, and use plug-in values to confirm the combined option is cheaper.

Estimate doubling time using the given compound interest formula; substitute r=8, use a close benchmark 72/8=9 to bound years, and identify the unique correct answer.

Learn rounding and range-question strategies for GMAT problems by using extreme values to bound miles per gallon, comparing 295/11.5 and 285/12.5.

The lecture demonstrates plug-in strategies for must questions on absolute-value inequalities, using zero and -5 to eliminate options and compare answer choices to the given x-range, concluding E is correct.

Learn to apply the weighted average axis to solve GMAT data-analysis questions, using quantities and averages to infer missing values and compute the overall average.

Solve the GMAT question by factorizing 3150 into primes (2, 3, 3, 5, 5, 7) and adding missing factors with y=14 to make every prime exponent even, yielding a square.

Demonstrate solving an invented operation called brackets, the greatest integer less than or equal to x, by rounding down 2.7, 3.4, and -1.6 and summing to 3, yielding option A.

Learn to compute sums of consecutive integers using the average times item count in an arithmetic sequence, then use units-digit tricks and ballparking to identify correct choice quickly.

Identify non-arithmetic sequences and use an orderly plug-in method where x_n depends on the two preceding terms; with x_0=3 and x_1=2, derive x_2=2.5 and x_3=4.

Learn to determine the units digit of powers ending in 3 using a 4-step cycle and convenient numbers, and apply must-versus-maybe reasoning from the GMAT Official Guide 2020.

Use combinations and factorials to count six-person lineups in GMAT questions, recognizing when order matters and multiplying 3! for males by 3! for females to reach 36.

Identify terminating decimals by a denominator composed only of powers of 2 and 5. Apply decimal multiplication by ignoring decimal points and adjusting the decimal position.

Identify all prime factors of 7150 by factorization and divisibility benchmarks, revealing 2, 5, 11, and 13. Learn efficient techniques for prime factorization, including divisibility rules and using similarly-sized factors.

Learn to tackle complex must questions by plugging in convenient numbers, forming price-to-earnings ratios, and computing the percent increase with the bow-tie method.

Apply a fast triple overlap method using whole = group1 + group2 + group3 - 2t - double overlaps + neither; use must questions and convenient numbers to eliminate choices.

Learn to simplify negative powers by flipping numerator and denominator, turning (a/b)^-x into (b/a)^x and b^-x into 1/b^x, with examples like m^-2 = 1/9.

Compute profit as revenue minus cost and express it as a percent of the initial cost, using a $100 plug-in to simplify GMAT official guide 2020 question 210.

Organize the seven items in increasing order to relate averages and medians, then maximize g by minimizing others, yielding a equals 30 and g equals 134 (choice D).

Analyze forming a product of 20 numbers with repetitions to minimize the product, using a large negative times a large positive, yielding minus ten to the twentieth power (option E).

Compute the total arrangements of five items with two identical letters, then subtract adjacent cases by treating the adjacent pair as a single item, yielding 36.

Solve a GMAT percent revenue problem by deriving r in terms of p using fractions, then verify with a plug in approach and classify questions as must or maybe.

Learn the weighted average axis method for a two-quantity GMAT problem, using inverse ratio logic from 90 to 55 and 35 to 5 to find n.

Find the line through (0,2) and (3,0) by plugging coordinates into the line equations, compute the slope, and derive the correct equation 3y+2x=6.

Solve a GMAT reciprocal problem by isolating r: use the gamma method to show 1/r = 1/x + 1/y, yielding r = xy/(x+y); emphasizes cross multiplication

Apply complement rules and multiplication to compute the probability that Zelda does not solve and the two others do, yielding 3/64 for GMAT Official Guide 2020 question 221 PS.

Master the GMAT ps 'maybe' question by testing values, avoiding zero denominators, and using a common denominator to confirm x, with the example yielding -2.

Use must-question tactics: plug in convenient numbers, apply 180(n-2), and leverage isosceles relations to deduce the target angle in a nonagon.

Learn to tackle a challenging GMAT PS problem (question 225, official guide 2020) by using convenient plug-ins to confirm roman numerals and balance estimated versus actual sums through rounding rules.

solve a quadratic by factoring and by the quadratic formula, noting x is not zero; find numbers with product 6 and sum -5, giving roots 2 and 3.

Plug in convenient numbers to distinguish must vs maybe questions, analyze zeros and undefined points, then solve and unify two inequalities to find integer solutions under x<5.

Learn to solve triple-overlap questions using inclusion-exclusion: Whole = sum of groups minus 2 times triple overlap minus double overlap plus neither, with quick number plugging for GMAT problem solving.

Apply the ear method to divide fractions, extract common factors, and use exponent rules (adding powers, handling negative exponents) to simplify GMAT PS questions.

Explore data sufficiency strategies for GMAT ds questions, including pre solving what is needed, interpreting 'per' as a division line, and estimating pages from total words and average words per page.

Analyze data sufficiency in a GMAT problem about tulips and roses: R equals 4T and R plus T equals 20; combining both statements yields sufficient information, with answer C.

Learn how to tackle GMAT data-sufficiency median questions by organizing data, testing each statement, and proving insufficiency with two contradicting conclusions.

Master data sufficiency by using conversion ratios from statement 1 or statement 2 to compare x and y units, recognizing that you should not solve for the exact value.

Solve two linear equations with same two variables to assess data sufficiency in GMAT math, then combine statements to show why the pair is sufficient and the answer is C.

Solve a data-sufficiency geometry problem by recognizing the external angle equals the sum of two interior angles, then test statements with extreme cases to determine sufficiency, yielding A.

Explore a data sufficiency problem with 256 marbles; deduce G=4B from statement 1 and G=192 from statement 2, then combine to obtain B, P, and the blue-purple ratio.

In this data sufficiency question, use X as a connecting factor to combine X:Y = 3:5 and X:Z = 2:1; statements are needed to determine Y:Z, so answer is C.

Explore a ds question by combining two statements to form two linear equations that determine the ratio of for and against; neither statement alone suffices, but together they are sufficient.

Master data sufficiency concepts in GMAT by showing that a ratio of men to women alone is insufficient, and a ratio plus an unrelated quantity does not yield a total.

Apply data-sufficiency reasoning to a rectangle that is actually a square, using statements about side lengths and ratios to deduce z, with or without the pythagorean theorem.

The lecture explains data sufficiency in GMAT math by using percent and 'of' as division and multiplication, showing how statements alone determine sufficiency without solving for y.

Explore a data-sufficiency problem from the GMAT official guide 2020, solving 7A+5B=85 with two statements to determine A and B as positive integers; combining both statements yields sufficiency.

Explore a data sufficiency puzzle on heating bills where F and J satisfy F/J=26/25, showing F>J from statement 1 and its sufficiency, while statement 2 alone is insufficient.

Recognize an arithmetic set in data-sufficiency questions and use first term and common difference with A(n)=A1+(n-1)d to find the 105th item; statements 1 and 2 together suffice (answer C).

Use the 2^4 vs 4^2 equilibrium to deduce that smaller to larger powers dominate; statement 1 alone is insufficient. Combining them shows u^v vs v^u, so the answer is C.

Use data-sufficiency to determine the range between the high and low prices, show that statements 1 and 2 are insufficient alone, and together yield the correct answer E.

Solve a GMAT data-sufficiency question on three prices by analyzing differences between greatest, least, and middle values to determine sufficiency and identify contradictory conclusions.

Apply data sufficiency strategies in GMAT math using two or more equations with the same unknowns. Combine statements to determine if the target value can be found without solving fully.

Multiply both sides by y to simplify, then determine whether xy equals 1. Use statement 1 and 2 to conclude that xy equals 1, yielding the correct choice.

Apply exponent rules to convert w^-2 to 1/w^2, then use data-sufficiency reasoning with two statements to deduce w=2; note even vs odd roots affect sign.

Analyze the difference between the 3rd year and the 1st year interest under compounding, using statements to determine sufficiency in the GMAT Official Guide 2020.

Explore how to determine a circle's circumference from its radius or diameter, show why statement 1 is sufficient and statement 2 is insufficient, and note the radius as 2x pi.

Simplify each data statement to test sufficiency: statement 1 yields t=6, and odd-root reasoning shows statement 2 suffices, so the answer is D.

Explain data-sufficiency strategies for question 263 by using 6% tax on labor and total tax to determine labor, emphasizing orderly work with provided elements only.

Explore a GMAT data sufficiency question about hardcover and paperback fiction and nonfiction, using a four-element number-line method and avoiding Venn diagrams to show why the answer is E.

Use data sufficiency: determine if the expression is positive by testing statements about w and h. Statement 1 is insufficient; statement 2 (w positive) suffices, giving answer B.

Learn to determine the units digit of a product using the units digits of a and b, and apply GMAT data-sufficiency logic by combining statements to reach the correct answer.

Develop data-sufficiency skills for GMAT questions involving donations and profits, applying percentage conventions, interpreting 'of' as multiplication, and combining statements to decide whether an amount exceeds $10,000.

Explore data-sufficiency strategies for a GMAT geometry problem: statement 1 shows not a right triangle, statement 2 bounds side sums, yielding area results both below and above 20.

Learn data sufficiency strategies for GMAT geometry questions using midpoints and ratios, modeling segments with X, and testing statements to determine when data is sufficient or conflicting.

Explain data sufficiency strategies for a GMAT official guide question about Adam and Beth, using statements 1 and 2 to determine sufficiency.

Analyze data sufficiency for a square and circle, using statements on circle area and circumference to determine sufficiency and support the correct option D through inscribed shapes and constant ratios.

Assess data sufficiency for the slope of line k using statements about points on k and m, noting when data yield two contradictory conclusions and sketching to compare parallel lines.

Use a fast double-overlap data-sufficiency approach with a number line. Determine the doctor–lawyer overlap in a 50-person group, then conclude that both statements alone or together are insufficient; answer E.

Master a fast number-line approach to double-overlap data-sufficiency questions, combining two statements to find the sum of cats only and dogs only without using Venn diagrams.

Assess data sufficiency for statements about fraction growth after adding 1 to numerator and denominator. Use sign analysis and plug-in tests to verify conclusions.

Explain data sufficiency for a walking scenario; statement 1 fixes at least 60% of females walk, while statement 2 shows twice as many walk, yielding a feasible 2/3 walk rate.

Explore data sufficiency for inequalities in GMAT problems, translating 'is xy+y greater than xy+x' to 'is y greater than x' and determining statement sufficiency with real-time, stepwise simplification.

Analyze a GMAT data-sufficiency question about whether a/b is less than 9/11. Compare a/b and b/a using decimals like 0.0909…, 0.8181…, and 1.2222…, and learn to spot misleading book explanations.

Analyze a data-sufficiency problem with red or green spheres and cubes to determine the total items. Demonstrate testing statements by constructing two contradicting scenarios to assess sufficiency.

solve ds questions by analyzing when the product xy is even and when x^2+y^2 is divisible by 4, using odd and even cases, reasoning, and convenient number plugging.

Apply parity rules to sum, difference, and product of a and b. Use ab being odd and a-b even to determine sufficiency, plugging in convenient numbers.

Analyze data sufficiency for sqrt(x) plus sqrt(y) using two statements; neither alone suffices, but combined they determine x and y and yield a single value for the sum.

Analyze fuel consumption in gallons per mile to determine the speed when kv^2 equals 1/3, using k from statement 1 and confirming with statement 2.

Explore data sufficiency with GMAT official guide 2020 question 288. Analyze even and odd scenarios, assess each statement's sufficiency, and see how combining them yields a sufficient answer: choice C.

Identify that PQ equals QR makes triangle PQR isosceles, giving x = 58 and enabling y to be determined; both statements are sufficient, leading to option D.

Analyze data sufficiency in a GMAT question about a set S of odd integers, using statements 1 and 2; combine them to show -15 is in S.

Analyze data sufficiency to determine whether x is a 3-digit integer using statements about x as a square; prove insufficiency with contradictions and combine to identify 100, 121, and 144.

Analyze a GMAT data-sufficiency question from the official guide, evaluating two statements about a sequence with odd terms 0 or 2 to determine why the answer is E.

Assess whether the sum of four integers is even using data sufficiency through statements 1 and 2, and understand the role of the average and even-odd properties.

Explore data sufficiency in a GMAT problem with 35x+30y, using two equations or a relative expression to determine the total cost of desks and tables.

Use y to model the youngest's inheritance, with the oldest at y+7,000 and the middle at y+9,000, and show that each statement alone suffices to find X.

Solve via data-sufficiency approach: simplify the expression by canceling z^2 to target x^4/y^2; statement 1 gives x^4 = y^2, yielding quotient 1, while statement 2 provides x and y.

Learn data sufficiency strategies for GMAT, showing how cross multiplication and simplifying information reveal statement 2 is sufficient while statement 1 is not, with visual reasoning and plug-in checks.

Analyze GMAT data-sufficiency on an arithmetic sequence with a difference of 2. Show that statement 1 is insufficient, while statement 2 is sufficient, since any term follows from another.

Develop GMAT data-sufficiency skills in divisibility by examining coprime factors, such as 2 and 5, with p’s cases (10 vs 16) to decide if p is divisible by 5.

Explore how parity and multiples of five determine divisibility by 10 in a ds question, and why combining the two statements remains insufficient.

Master GMAT data sufficiency by applying takeaways to cube roots and odd roots, determining when statements yield x uniquely as +2, and recognizing even versus odd root implications.

Tackles a data sufficiency problem to determine the number of offices from total floor space, using executive office area and average office area, illustrating insufficiency and need to combine statements.

Apply data-sufficiency strategies to a GMAT official guide 2020 problem on three consecutive integers, showing the average x equals 0 from 2x = p+r+s and 3x = p+r+s.

practice tackling data-sufficiency questions by simplifying expressions, foil, and factoring to find m+n from statement 1, recognizing insufficiency of statement 2 and common traps.

Explain how to determine x+y for external angles in a triangle using data sufficiency, with a focus on the external-angle property and the 360-degree sum.

Analyze how the orientation of points R, S, and T on a line with RT=5 and RS=2 determines ST, showing both statements yield ST=7 and are sufficient for DS questions.

Apply the product-equals-zero principle to conclude n is 0 for DS questions; add or subtract any expression, including 0, but never multiply or divide by a possibly zero expression.

Explore data sufficiency in a GMAT official guide map scale problem, using 1/2 inch equals 100 miles to decide if statements give the X–Y distance without calculating it.

Explore GMAT data-sufficiency in remainder problems, examining statements 1 and 2, using algebraic reasoning and plug-in methods to determine the remainder of n divided by 5.

Explore an invented operation question where theta represents a basic algebraic operation; analyze statements to determine sufficiency, finding statement 1 sufficient and statement 2 insufficient, yielding option A.

Determine parity of sign changes in the sequence -1, +1, -1, +1 by analyzing statements on term count and odd length, then use s(k)=(-1)^k to conclude answer C.

Analyze a data sufficiency problem: express apples kept as 76-4y-3t, test statements 1 and 2, find alone insufficient, together sufficient (answer C), and note positive integer constraints.

Analyze two statements about x and y for GMAT data sufficiency; each alone is insufficient, but together they form two solvable equations, yielding the answer C.

Solve a data-sufficiency problem about coffee prices using 5R+3D=21.50, analyze two statements, and apply percent-change reasoning to show the answer is D.

Statement 1 shows a=-3, so a^5<4^b is true; statement 2 is insufficient; the correct answer is A.

Evaluate a DS question on a rhombus with side 1 to compute area via height; statement 1 yields height from a 45-degree angle, statement 2 provides height, so D.

Explore finding the remainder when x is divided by 4 using real-time reasoning, analyze statements 1 and 2 for sufficiency, and use convenient numbers to test outcomes.

Analyze a DS data-sufficiency GMAT question using ratios and linear equations to determine G from Y, W, and G, evaluating statements for sufficiency with cross multiplication.

Simplify the initial information to decide if (x+y+z)/3 is greater than z. Use inequality steps and sufficiency testing to conclude that statement 1 is sufficient and statement 2 is insufficient.

Simplify the problem by recognizing the two overlapping circles have equal area and setting A = C; use convenient numbers to illustrate and deduce B+C = 12.

Analyze a ds data-sufficiency question about small and large green toys, using a 2×2 table to determine the large green fraction, and note statement 2 is sufficient.

Explore data-sufficiency reasoning for quadrilateral PQRS to decide if it is a parallelogram, using statements about adjacent sides, and see how combining statements yields a rhombus or deltoid.

Analyze data sufficiency for GMAT official guide 2020 question 325 by comparing two triangles’ areas via height from y-coordinate and bases. Assess statements 1 and 2 to identify answer B.

Explain data-sufficiency for a sequence where each term equals the sum of all previous terms; use invented-operations, plug in numbers, and assess statements 1 and 2 to determine a5.

Analyze data sufficiency by forming J=2G and G=S+4, then test statements 1 and 2 to determine the value of G.

Identify 24 identical equilateral triangles of side 9 to compute the mosaic area. Apply data-sufficiency analysis to show statement 1 is sufficient and statement 2 is insufficient.

Follow a real-time solution showing triangles EDA and EBC share height, so their area ratio equals AE to EB; statement 2 provides AE and EB, making it sufficient.

Determine the minimum square opening required to pass a sphere, using 3D drawings and data-sufficiency reasoning to show that a 4 by 4 opening (16-inch perimeter) satisfies the condition.

Break down region pqrst into a left triangle and right rectangle, compute areas with base and height and pythagorean relations, and apply data-sufficiency reasoning to determine sufficiency of statements.

Examine how the right triangle's legs x and y relate to the hypotenuse via x^2+y^2, and assess sufficiency of statements to derive xy using the area formula xy/2.

Evaluate data statements for a rectangle and trapezoid to determine pq, showing statement 1 is insufficient and statement 2 yields X=3, making B the correct answer.

This lecture analyzes a ds question from the GMAT guide 2020, solving for t with t^2 = 9 and t^3 = -27; two t values yield a single expression value.

Walk through data sufficiency for a GMAT question by testing statements 1 and 2 on average 75 and SD 5, showing contradictory maxima and unresolved maximum score after combination.

Evaluate data sufficiency to compute the average attendance per cultural performance by combining total attendance across eight performances, using statements about 'at least' and 'exact' averages.

Master data sufficiency strategies for a GMAT apparel problem using benchmarks to test statements 1 and 2, then combine them to conclude more than 1050 jackets.

Determine the greatest common divisor of 12 and n using statement-based sufficiency in DS questions, with guidance on when statements 1 or 2 are sufficient.

Explain data sufficiency reasoning for a GMAT question on a base salary plus 10% commission, showing when statements alone or together are insufficient and avoiding unnecessary calculation.

Analyze a data sufficiency problem about finding X where 2X is a common factor of 18 and 24, with X>1, concluding statement 1 suffices and statement 2 is insufficient.

Solve discount rate problems using data sufficiency, focusing on the ratio of discount to the price before the discount and evaluating statements 1 and 2 to determine sufficiency.

This data-sufficiency GMAT problem asks if a circular rug covers two stains; statement 1 gives rug area to infer diameter, statement 2 gives stain distance, and together they determine sufficiency.

Apply data sufficiency strategies to a ratio problem with blue, green, and red paint, simplify X:Y:Z to two variables, and test statements to determine the number of green gallons.

Solve a DS GMAT question from the official guide 2020 in real time, showing that six unknowns require three more equations, and that the answer is E.

Learn to solve DS questions quickly using key takeaways, including recognizing negative powers, converting decimals to fractions, and applying plug-in checks from the GMAT official guide 2020.

Analyze a data-sufficiency question from the GMAT official guide 2020, where total cost equals a fixed sum plus minutes over 420, using statements about 450 and 400 minutes.

Master data sufficiency in a three-digit comparison by analyzing the tens and hundreds digits, testing statements, and using convenient plug-in numbers to conclude that r is greater than t.

Examine data-sufficiency questions by testing whether xy is divisible by x+y with statements 1 and 2, uncover contradictions, and conclude that the combination yields Yes, option C.

determine whether (-2+b)/sqrt(-2+a) is defined for x = -2 by enforcing denominator nonzero and radical nonnegativity, yielding a > 2; statement 1 is sufficient and statement 2 is insufficient.

Apply data sufficiency to decide if 2p+3.5q exceeds 2000 given p+q=834 and profits per unit of 2 and 3.5. Both statements are insufficient; the answer is E.

Combine statements to assess data-sufficiency in a GMAT ds question, apply the rule that and means multiplication and or means addition, compute p1p2 = 0.2, and identify answer c.

Explore distance, rate, and time reasoning in a data-sufficiency question by converting units and applying time equals distance over rate, to decide if the belt runs under 75 seconds.

Explore a GMAT data sufficiency question in real time, showing that each statement is insufficient and that combining them still fails to yield a single numerical value for (x+z)/2.

Learn data-sufficiency geometry on a rug problem: use the perimeter to get W+L=22, explore cases, and conclude the data are insufficient (choice E) after mentally stretching the drawing.

Apply GMAT data sufficiency strategies to analyze fractions and common factors, recognizing nonzero denominators. Extract a common factor and evaluate statements about X, Y, and Z to determine sufficiency.

explore angle relationships in a parallelogram with two parallel lines cut by a third line, using angle sums to deduce x = 60 and confirm the data-sufficiency answer d.

Master double overlap data sufficiency by treating the whole as 100 and the neither group as 15%; statements 1 and 2 are insufficient, so the answer is E.

Study data sufficiency for x<5 using two methods on a ds question. Learn parabola reasoning, convenient benchmarks, and when a faster solution may fail.

Analyze data sufficiency to determine the total savings 3G from Bela, Gyorgy, and Janos using B=8%Bm and statements about Bm and J.

Analyze data sufficiency for GMAT math by evaluating statements about P and Z, using plug-in numbers and noting Z^4 is nonnegative to explain insufficiency.

Analyze a ds GMAT official guide 2020 problem where -3 or +2 points move 100 to 104, using lcm reasoning to show 7 games but the data stay insufficient.

Demonstrates data sufficiency strategies for GMAT problem 366: break down statements, analyze ratios, and use cross multiplication to determine n, with statement 2 sufficiency leading to n=24.

Apply data-sufficiency techniques to determine if x^3+y^3 is positive using statements 1 and 2. Use plug-in testing with petty numbers and odd powers to assess sufficiency.

Explain a data-sufficiency question from the gmat official guide 2020 about whether tax exceeds 3% of 624 when p+t=624. With p<602, t>22 makes statement 1 sufficient; statement 2 is insufficient.

analyze a ds data-sufficiency question on the perimeter of a regular pentagon, using symmetry, inscribed circle geometry, and diagonal side relationships to determine if the perimeter exceeds 26.

Subtract 6.00 and multiply by 1000 to get 3x > 2y, then test with digits 0–9; statement 1 is sufficient, the second contradicts, the answer is D.

Solve data-sufficiency problems for the volume to surface-area ratio of a rectangular box by testing two statements about its dimensions, including a cube, and combining them for a unique value.

Demonstrate statement 1 is insufficient to determine x equals y, using x=0, y=-1. Conclude statement 2 is sufficient since x-y=0, and avoid the trap of assuming both are needed.

Analyze four consecutive odd integers a, b, c, d with sum 64 to determine d, using statement 1's consecutiveness and statement 2's six-more-than-the-least requirement with distinct values.

Analyze a GMAT data-sufficiency problem using two statements about x and y, compare thresholds like 1000 and 20%, and combine to conclude x>y.

Explore data-sufficiency to determine if 17 is the mode in the full list L. Analyze L1 and L2 arranged in increasing order using statements 1 and 2 and plug-in reasoning.

Analyze how percent increases and hypothetical scenarios determine balances for May 1 and May 30, evaluating statements 1 and 2 to establish data sufficiency.

Demonstrates a fast data-sufficiency method for a GMAT problem on squares of consecutive integers, using the increasing differences between squares (25 and 27) to identify n.

Analyze GMAT 2020 question 381 on data sufficiency, using purchase price 400 and profit Pr = S - 400, showing Pr = S/3 yields S and the answer B.

Explore data sufficiency for a GMAT problem on a library budget and bonus, using benchmarks and rough calculations to determine if the $2,000 bonus is received.

Learn how to find the median in an ordered set, assess sufficiency of statements about X, and explore when the median equals the mean through symmetry versus asymmetry.

Analyze data sufficiency for a GMAT dice problem by evaluating statements 1 and 2, identifying possible results, and combining them to show only 552 is sufficient, confirming a 5 appears.

Evaluate statements 1 and 2 about the distance between r and t to determine data-sufficiency in GMAT, using plug-in numbers and the effect of squaring fractions.

Explore how vertex shape and count determine triangle numbers, using statements about distinct vertices and no 3 points are collinear to apply combinations and 3-vertex selections, yielding 10 triangles.

Analyze data sufficiency for a discounted price comparison by using relative expressions and exact quantities, demonstrating how combining percentage changes and dollar amounts resolves the problem.

Explore how rounding to the nearest tenth and the nearest integer informs whether d is at least 0.5. Apply sufficiency reasoning with plug-in values and rounding subtleties to determine sufficiency.

Solve a GMAT data sufficiency question from the Official Guide 2020 by using unit digit rules to deduce the square and triangle digits, establishing sufficiency of statements.

Explore data sufficiency for a GMAT problem with shirt prices X, Y, Z. See how 30+ and 20+ bounds test whether X+Y+Z exceeds 60, assessing statements 1 and 2.

Demonstrate data sufficiency on a coin problem where B is 1.5 times C, analyze two statements about B and the total B+C, and conclude only C satisfies both.

Analyze a data-sufficiency problem with x processors each handling y calls, total capacity x*y, to decide if it’s at least 500. Statement 1 is sufficient; statement 2 is not.

In a data-sufficiency problem, Kim and Sue buy equal numbers of roses and daisies priced at $1 and $0.50. Statement 2 shows Kim pays more.

Learn to extract data from a GMAT data sufficiency problem by using percentages and totals, including a 1998 to 2000 increase of 40%, to reverse engineer jazz and blues revenue.

Explains how to compute distance and average speed for a two-leg trip using rate and time, and analyzes data-sufficiency reasoning for GMAT questions.

Apply data-sufficiency reasoning to a math problem from the official guide, testing X where sqrt(X) and sqrt(X+24) are integers, and show why statements are insufficient alone and become sufficient together.

solve a gas-tank problem on a horizontal cylinder; depth 2, height 6, diameter 4 show gasoline volume equals half cylinder's volume, using base area times height and two data statements.

Apply ds reasoning using q = -s and plug-in numbers to test r's distance to 0; show statement 1 suffices, while statement 2 is insufficient, illustrating the two contradicting-conclusions technique.

Master data-sufficiency strategies for GMAT questions by evaluating statements independently and jointly, applying integer constraints and common-factor extraction to determine adults and children.

Use base times height over two to find triangle area, given B×H=20, and note statement 2 is insufficient; remember triangles have three possible heights, with external heights for obtuse angles.

Sketch the coordinate data to see R is equidistant from two red points via an isosceles triangle with a height bisecting the base; y = -3 yields insufficient data.

Master weighted average axis problems by using four known values to find the fifth, and recognize how insufficient data persists even when combining statements and inverse quantity ratios affect averages.

Explore solving a two-digit number where the units digit is six more than the tens digit, with n under 40, using convenient numbers and tu decomposition to test sufficiency.

This GMAT data-sufficiency item converts 2^{X+Y} = 2^{2^8} to X+Y=16 using power rules. Statement analysis shows statement 1 is insufficient, statement 2 is sufficient, yielding Y=7.

Solve data sufficiency geometry questions by analyzing statements 1 and 2 for an isosceles right triangle; combine them to deduce equal area ratio.

Learn how to decide if r/s is a terminating decimal by analyzing the denominator factors, specifically powers of 2 and 5, using data sufficiency with statements 1 and 2.

Determine whether r/s is less than s/r using data sufficiency techniques, positivity, cross multiplication, and even roots, by evaluating statements 1 and 2.

Analyze data-sufficiency in GMAT ds with k between 57 and 65, odd from remainder 1, and k+1 divisible by 3, showing both statements yield multiple possibilities and are insufficient.

Explore data sufficiency for x being prime using statements 1 and 2, testing values like 2, 4, and 6, and conclude data are insufficient, so the correct answer is e.

Analyze mortgage payments, real estate taxes, and home insurance totaling 12,000 to find R. Use data-sufficiency reasoning with two statements, convert to equations, and deduce R = 2,000.

Analyze a data sufficiency question on ad<bc using cross-multiplication with positive variables; statement 2 suffices, statement 1 does not, yielding option b.

Analyze data sufficiency for double overlap questions by combining two statements; 20% of X equals 30% of Y, so X is 1.5 times Y, and X > Y.

Explore how the average of consecutive even integers equals the middle value, and use data-sufficiency reasoning from statements about q+s=24 and (q+r)/2=11 to identify sufficiency.

Decode the ceiling operation [x] and apply data-sufficiency strategies by testing statements with convenient numbers, showing how combined information yields a unique value for x.

Evaluate X and Y using data sufficiency: statement 1 alone is insufficient; statement 2 shows Y^X is negative and X is odd; combined, X is greater than Y.

Break an l-shaped polygon into rectangles to relate its area to x and form a quadratic equation. Conclude that statement 1 is sufficient to find x; statement 2 is not.

Solve a data sufficiency GMAT problem using the ratio 9:4:5 for shirts, dresses, and jackets with a total of 18 items, deducing an integer X.

Find the central angle alpha in a pie chart and apply the sector area formula area = (alpha/360) times the circle area, using data sufficiency with statements 1 and 2.

Explain handling x^2 and x^3 inequalities with roots. For even roots, consider both but ignore the positive when x is negative; for odd roots, use a single root and estimate.

Assess how many times smaller dimensions fit into larger ones by comparing carton and can measurements, using a two-statement approach and methodical reasoning for inserting rigid shapes.

Analyze data-sufficiency reasoning for GMAT Official Guide 2020 question 428, deducing r from the sums of v and z and from sums of paired numbers under 1–3 constraints.

Apply the weighted average axis method to a data-sufficiency question from the GMAT official guide 2020, comparing X and Y in a 10 kg mixture.

Analyze a DS question on train speed using a 460-mile, 4-hour trip to derive the average rate. Explain why statement 1 and 2 are insufficient and how DS questions mislead.

Analyze how to find the median from given prices and averages; see why statement 2 suffices to fix the median at 120, while statement 1 does not.

Analyze when x^3 < x^2, showing that statement 1 is insufficient and that statement 2 yields x = -1, illustrating data sufficiency for the GMAT Official Guide 2020.

Solve a tricky GMAT question using an invented min/max operation, translate to verbal logic to compare W with 10, and assess sufficiency of statements about 20 and Z.

Use data sufficiency to determine the median of a 49-item set; with 400 pages on the top shelf and 475 on the bottom shelf, the 25th item is the median.

Analyze whether the median equals the average in a three-number set via data-sufficiency by statements 1 and 2; conclude statement 2 is sufficient, with plug-in examples.

Sketch the data to visualize slope in coordinate geometry, using change in height over distance and the x-intercept and y-intercept to determine the sufficiency of statements.

Compute the intersection of two lines by solving their equations, then plug coordinates into line 3 to determine b. Statements 1 and 2 provide the intersection, proving sufficiency.

Solve a GMAT data sufficiency problem by finding the small triangle's perimeter from external lines, using statements 1 and 2, to determine the larger shape's perimeter.

Analyze a GMAT data-sufficiency problem where T is contained in S, compare the ranges, and show why the data remains insufficient, yielding E.

Explore a right triangle data-sufficiency problem by using a^2+b^2=100 and ab=50 to find a+b. It presents a faster method with (a+b)^2 = a^2+b^2+2ab and notes a right isosceles case.