GMAT® Math | Official Guide 2019

Examine the statistical analysis of the GMAT Official Guide 2019 math questions, covering 404 items across problem solving and data sufficiency, with focus on types, techniques, and live data visuals.

Master GMAT math with the popularity matrix tool, learning to sort, search, and filter 404 questions by takeaways, question types, and difficulty to target weak areas.

Master problem solving and data sufficiency in GMAT math, focusing on algebra's dominance, tougher topics like statistics and powers and roots, and essential techniques to boost accuracy.

Analyze problem solving and data sufficiency, highlighting top techniques—handling ugly numbers, simplification, must questions, and plugging in convenient numbers—plus note triple overlap at about the 85th percentile.

Explain the data sufficiency question format, with a blurred stem and a question mark, using statement 1 and 2 to determine sufficiency and immutable answer choices like B or E.

Learn how to determine data sufficiency using a flowchart that leads to two contradicting conclusions, via convenient and petty numbers, to decide if statements are sufficient or insufficient.

Learn data sufficiency in geometry problems by stretching the diagram to test whether Alpha changes under each statement, then combine Delta and Beta to fix Alpha.

Use data sufficiency to find x. Statement 1 gives a linear equation with no single value, while statement 2 yields a quadratic x^2+6x+9=0, which gives x=-3.

Learn data sufficiency strategies for GMAT geometry, using statement 1 and statement 2 analysis, DS flowcharts, and determining sufficiency by arriving at two different conclusions.

Learn the timesaver method for a GMAT math question by using the sum of distances from the average equals zero, deducing the missing value as 87 for the given data.

Demonstrate real-time solution of a GMAT percent problem using a 10% chunk method to compute 15% and 20% of amounts, and highlight two key takeaways for quick, accurate calculations.

Apply the percent-change template by dividing the difference by the original value and multiplying by 100 to convert fractions or decimals to percent, with practice using 150 over 500.

Cancel opposing fractional terms and simplify expressions using the least common multiple, then seek easier methods before heavy calculations to solve tricky GMAT fraction questions.

Learn efficient ratio techniques for GMAT math, including recognizing vertical versus horizontal ratios, reducing ratios, respecting the order of terms, and identifying common traps to the correct choice.

Explain solving a GMAT ratio problem by dividing by a common factor and using gcd to create integer counts for white and red tulips per bouquet.

Explore solving a GMAT question by using the sum of distances from an assumed average, then raise the average from 70 to 73 to remove the surplus.

Learn to compute 125% of 5 using percent-to-fraction conversion, benchmarks, and ugly numbers, breaking into easy parts. Recognize 125% as 1.25 to obtain 6.25.

Organize median questions by sorting data in increasing order and identifying the 5th item in a 9-item set. For the example, the answer is C.

Apply the per concept to convert units by dividing miles per hour by gallons per hour. Use the ear-method to cancel units and obtain miles per gallon.

Realize that the to-and-from drive makes the total exceed 50% in GMAT percent questions. Use a 100 total distance to confirm 55% as the correct answer.

Learn to treat increases and decreases by fractions as multiplicative factors; for example, 1/4 becomes 5/4 and 1/3 becomes 2/3, then multiply and simplify to solve for X quickly.

This GMAT statistics takeaway shows that for five consecutive integers, the median equals the average, and for an even-size set the median equals the mean when the difference is constant.

Solve a GMAT® math coin problem by modeling 16 coins totaling 235 cents with a single equation to find the number of 25-cent coins.

Interpret percent problems by treating 'of' as multiplication and 'is' as equality; simplify before multiplying, convert 60% to 3/5, compute X from 300, yielding X=500 and answer D.

Learn to solve an integers probability problem by using divisibility by 6 to count qualifying numbers, recognizing coprime factors, and calculating probability as desired over total options.

Explain the inscribed circle in a square, showing the circumference to perimeter ratio equals pi/4; apply a diameter-based formula to quickly solve, 25 pi yields 100.

Plug in convenient numbers, such as x=2, y=3, z=4, to identify which of the following is greatest or least. Eliminate options as you go until the correct choice remains.

Use close-by benchmarks and guesstimates to handle approximate results in GMAT math questions; recognize when values like 60.2 approximate 60 and 1.03x4.86 is near 5, guiding answer choices.

Use close by benchmarks to simplify ugly numbers, breaking 893 × 79 into 893 × 78 plus 893, yielding a P plus 893 and the correct answer D.

Rely on the scale of the drawing, estimate angles near 90 degrees, and use the external angle theorem to solve for X in the triangle.

the lecture demonstrates calculating the total cost of pine and oak doors after a 25% discount, using fractions to simplify percent calculations, as in GMAT official guide 2019.

The problem distributes 25 apple crates among Winesap, Macintosh, and Rome, with Winesap greater than the others. Using the least value plug in method, W=9 and M=R=8.

Master isosceles triangle properties and angle relationships in this GMAT geometry walkthrough. Learn how equal sides force equal angles, how heights bisect sides and angles, and the polygon angle-sum rule.

Master solving absolute value equations by using K^2 = M^2 to get K = ±M and using must questions with convenient numbers to eliminate options, considering positive and negative values.

Check answer choices quickly in 'which of the following' questions, memorize and recognize common powers of 4, and use elimination to identify y values that yield a positive integer x.

Learn to divide fractions using the ear method and reciprocal multiplication, simplify before multiplying, and apply this approach to GMAT fraction questions such as X divided by 2/3 equals 9/2.

Explain how a sphere inscribed in a cube yields edge equals twice the radius, and how using a unit radius simplifies Must questions and accurate drawings for GMAT geometry.

Showcases solving a GMAT price-per-gallon problem by using a 17-cent rise from 1.65 per gallon to estimate total and relate gallons via unit conversion, yielding more than a 10% increase.

Learn to read a graph by identifying axis labels and a single extreme datum, then express it in a sentence. Use the process to find the greatest difference, here 2.7.

Compute total value by applying the percent of units; use 0.5% of 20,000 for the upper limit (100 items, 2,500 each, total 250,000) and 0.3% for the lower limit.

Learn to find the area of an unfamiliar polygon by breaking it into rectangles, using opposite sides equal, to combine 300 and 700 for the final total.

Compute x by forming a linear equation from total pay: 40x + 8*22 = 816, then simplify to x = 16, demonstrating algebraic reasoning and quick mental math.

Explore how to add, subtract, and divide fractions, including coprime denominators using the gamma method and visualizing division with the ear method, with practical example 7/8 plus 1/9.

Identify the fastest GMAT solving approach by balancing calculations and counts, as in a sequence with eight items and two positives; avoid chasing tricks.

Apply the plug-in numbers technique to a GMAT math question from the official guide 2019, using S, r, and n to find boxes as S/r - n and eliminate options.

learn to solve roman numeral must questions by plugging in values to eliminate options and simplify inequalities; ii is always correct, so the answer is b.

Learn to solve a GMAT percent problem fast by simplifying before multiplying, using answer choices, and applying benchmarks to compute x from 2x = 0.8x + 5040.

Explore modular arithmetic strategies for GMAT math: determine 1174's remainder by using divisibility by 8, analyze revolutions after 8-interval cycles, and identify the correct option E.

Identify must versus maybe questions, plug in convenient values, and test quadrants to eliminate options in xy = k problems. Recognize asymptotes at x = 0 and y = 0.

Plug in convenient numbers to solve fraction-based questions, then use a common denominator and least common multiple to subtract fractions, isolate X, and verify with the answer choices.

Factor a quadratic arising from area comparisons to solve the GMAT algebra problem, identify w's positive root as 50, and note that this is an algebra question, not geometry.

Master quick percent reasoning and compound interest concepts by comparing simple and compound interest, using ballparking, semi-annual compounding, per-cycle rates, and the (a+b)^2 trick to estimate and verify answers.

Solve a real-time GMAT geometry question by applying the pythagorean theorem to a right triangle, simplifying square roots, and using close-by benchmarks for estimation, with two key takeaways.

Solve X/(X+16) = 4/5 using cross multiplication to get X=64 and the denominator X+16=80, so the correct choice is D.

Apply the at least 30 units per day constraint with $2 and $2.5 per unit to determine the maximum daily units, yielding 56.

Learn how to determine the greatest value quickly by squaring all positive terms and applying root and power rules, using benchmarks, and eliminating options.

A population starts at 3 and doubles every month, becoming 3(2^n) after n months, as shown in question 84 of the GMAT Official Guide 2019.

Explore a fast GMAT math trick: extract a common factor and recognize symmetry to simplify complex fractions, avoid heavy calculations, and confirm r equals 3 for the correct choice.

Tackle a must-question by plugging in convenient numbers for y using y = 5n to simplify 3x+4y=200, and use the co-prime relationship of 3 and 20 to eliminate answer choices.

Compute the combined rate: A is 1/6, B is 1/9 tank per hour, totaling 5/18. With 1 tank of work, time equals 18/5 hours (3.6 hours).

Explains solving inequalities with even roots by using must versus maybe questions, plugging in convenient numbers, and locating x between minus and plus the square root of 2.

break down each book into days at 50 pages per day, totaling eight books in 28 days, and use estimation or skipping for data-heavy GMAT questions.

Solve percent questions by plugging in 100, use must questions, and compute a decrease of 9 from 42% to 33% in Western Europe bicycles produced and sold.

Master remainder and divisibility on the GMAT by plugging in convenient numbers, recognizing must questions, and using factorization to show products of consecutive integers are divisible by 6 or 24.

Solve a GMAT math question by simplifying fractions and using the Gamma method to handle nonzero p, then test values with must questions and plug in numbers to eliminate choices.

Understand the range, the difference between the greatest and smallest numbers, from a set containing 3 and 14. To obtain a 12 range, x is 2 or 15; answer D.

Solve a GMAT arithmetic problem by translating verbal cues into an equation, set up x = (2/3)x + 108, and deduce x = 324 using benchmarks.

Treat 460 as 115% of x to compute x = 400, yielding the correct answer, option B.

Apply plug-in and petty-number testing for a must-question with positive integers m and p, sum less than 100; show that m=p=7 gives 98 and mp=49, eliminating E and confirming D.

Factor the quadratic x^2 + 2x - 24 = 0 by finding two numbers with product -24 and sum 2, yielding roots -6 and 4.

Apply a percent tree to solve a GMAT® percent problem, decoding 40 percent independent voters and 60 percent registered, with 10 percent of the registered voting for her.

Learn to apply the weighted average axis for two groups with different quantities and averages, use elimination criteria, and apply the inverse ratio to pinpoint the weighted average.

Solve a remainder-style GMAT question by packing 68 jugs (4 per trip) into cartons of 7, using benchmarks to find full cartons and the remaining jugs.

Break the polygon into rectangles, set total area to 4800, use l = 3w to reduce to 3w^2 = 1200, solve w = 20, yielding option b.

Explore the clones work-question strategy for GMAT math, revealing how to use rate formulas to solve identical-rate machine problems quickly, including simplifying and reducing to single clone rate.

Explore algebraic and percent reasoning for GMAT official guide 2019 question 112, including simplifying to 2n=3m and applying the must-question approach by plugging in values to find 12n/m.

Explore percent changes by treating them as a multiplier of (100 plus the percent change) over 100, and distinguish increases and decreases using the whole as the base.

Interpret percent problems by identifying the whole, using the word 'of', and applying convenient benchmarks to add percentages and derive ratios such as 4/9.

An invented operation question uses the formula cost = 100,000 × P/(100−P) to compare pollutant removal costs for P = 90 and P = 80, yielding a 500,000 difference.

Combine rates of presses r, s, and t to a rate of 1 job in 4 hours. Subtract (s+t) from (r+s+t) to isolate r, yielding 1/20 job per hour.

Plug in comfortable numbers to solve absolute value questions, mapping coordinates to s, t, and r, and compare substitution with testing answer choices; correct is e.

Interpret 'at least' as greater than or equal to, solve multiple inequalities for n, and unify solutions on a number line using 'and' conditions, yielding n=11.

Solve double overlap questions with a number line, using whole 5,000, x for music, y for art, z for overlap, and neither as 5,000 − x − y + z.

Use a number line to solve double overlap questions, placing the whole at 100 and groups at 62 and 47 to reveal a 9 overlap and 53 stockholders not employees.

Learn to compute percent change by dividing the difference by the original number and multiplying by 100, recognizing the whole after 'of', and eliminating non-matching answer choices.

Master percent-change problems by computing difference over the original, using the previous value as the whole, and applying quick benchmarks and simplifications for up to five calculations.

Explore factorial properties and divisibility by extracting common factors to show why 20 factorial plus 17 is divisible by 17, and how factorials align with multiples.

Solve negative numbers with product 160 by substituting B=2A-4, forming a quadratic that factors to A=-8 and B=-20.

Apply rate, distance, and time concepts to a 3.25 mile path run at 1 mile per 8 minutes to determine the distance before turning back within 50 minutes.

Learn to estimate percent problems with benchmarks and convert between percents, fractions, and decimals. Solve a GMAT practice question by setting up equations and removing denominators to find x.

Determine the median by locating the 81st item in an ordered set of 161 employees, revealing the median lies between 20 and 29 within the second group.

Apply the given equations Ron=Amy+4 and Barbara=R+1 to find R=64 when B=65, then identify Ron's height as the median.

Analyze a GMAT roman numeral problem by factoring 100x+200y as 100(1+y) with x+y=1, test feasible values, and apply must-or-maybe reasoning to confirm the answer.

Master decimal and fraction strategies to maximize a fraction by increasing the numerator and decreasing the denominator. Learn converting decimals to fractions, using benchmarks, and efficient division methods.

Master a go-to method for GMAT combinatorics: mark stages, multiply possibilities, distinguish lists from collections, and use unit/tens-digit elimination to quickly verify answers.

The lecture shows how to find the least n where n! is divisible by 990 by factoring 990 into coprime parts and showing 11 must appear, so n equals 11.

Use probability basics: not M is 0.8 and not R is 0.6, so M=0.2 and R=0.4; since M and R cannot occur together, M or R equals 0.6 (3/5).

Compute the profit per tool in a GMAT style problem: total cost is 70,000, revenue is 160,000 for 20,000 tools, yielding 4.5 dollars per tool (choice C).

Learn to solve median and average problems with consecutive integers using a must question approach, plug in numbers, and logic for the largest item, illustrated with Q=3.

Master the 30-60-90 triangle and its side ratios of 1:√3:2 and the angle relationships. Divide the hypotenuse by 2, multiply the short leg by √3, then add 7.

explains how to tackle a three-digit code question by calculating total combinations, subtracting undesired ones, and applying 'and' for multiplication and 'or' for addition.

Master the weighted average axis for mixing solutions, solving 2% and 12% to a 5% mix with inverse ratios, total volume 60, yielding x=6 and 7x=42.

Compute the percent change from 320 to 385 by dividing the 65 difference by 320, yielding slightly more than 20 percent.

Learn to solve zero-product problems by setting each factor to zero and using a number line to unify 'or' solutions and 'and' solutions, with x values like −1/2 and 3/2.

Learn to recognize the right isosceles triangle (45–45–90) with sides 1, 1, root 2, and use unit ratios to compare perimeters of dissimilar shapes by partitioning into identical triangles.

This lecture shows how to solve a 3-variable equation system by subtracting equations to isolate n. It also demonstrates using least and greatest plug-ins from answer choices to eliminate options.

Apply ratio reasoning and plug-in numbers to solve a GMAT volume problem, using base area times height, cubic roots, and elimination to identify option B.

Write x next to the ratio units, then treat 30x+50 and x+5 as regular quantities. Cross-multiply to solve (30x+50)/(x+5)=25, find x=15, revealing the current number of teachers.

Rewrite 25^n as 5^{2n} and apply the power rule to compare with 5^{12}. Since 2n > 12, n > 6, so for integers n = 7, which is choice B.

Learn to compute percent of a percent using a fraction tree, by assuming a total of 100, finding 60 women and 27 women lawyers, then determining probability as 27/100.

Apply the quick rule for a quarter increase by multiplying by 5/4 four times. Compute 5^4 and 4^4 as 625 and 256, then divide to find x equals 2560.

interpret the operation as: b is divisible by a to the k but not by a to the (k+1); for 72 with 2 to the k, k equals 3.

Solve a GMAT fraction problem using the bow-tie method for four sandwiches shared among m people. Learn to plug in convenient numbers, like 60, and apply must-question elimination.

Tackle a GMAT quadratic root problem by moving terms and squaring to remove radicals, then use factoring or the quadratic formula to obtain roots like 1 ± √2.

Apply the weighted average axis method to two-group mixture problems, using inverse range-to-quantity ratios to determine that totals drop from 10 to 5 when fruit is put back.

Solve the GMAT question in real time, then apply the difference of squares and divisibility by coprime factors to decide which factors divide the product 65 times 97.

Master three takeaways for GMAT circle questions: relate area ratios to radii, use similarity to deduce linear and circumference ratios.

Master remainder problems by modeling x as 4n+3 and 5m+3, distributing into groups of 4 or 5, and using plug in convenient numbers with a must-question approach and coprime factors.

X must satisfy x/3 is a prime squared, so x = 3 p^2. Primes 2, 3, and 5 give 12, 27, 75 under 100, so three values (answer B).

Demonstrates solving a GMAT combinatorics question on two-letter codes from X letters, using X(X-1)/2 and a quadratic inequality to determine the least X yielding at least 12 codes.

Compute slope from change in height over distance (+2 over +3 equals 2/3), then use parallel lines’ identical slopes to identify the answer, yielding y = 2/3 x (choice A).

Maximize the height expression by optimizing a quadratic, yielding a maximum height of 150, with the trajectory forming a symmetric parabola about t = 3.

Solve two inequalities in x, then unite their solutions on a number line showing x > 4 and x ≤ 8; distinguish and from or by solution heights.

Solve a GMAT ratio question by assigning the smallest ratio as 1, deriving Jeff, David, and Paula relationships (D=3J, P=2D), and confirming the total using plug-in and algebraic methods.

Compare separate and combined shipping for eight pounds, using x for the first pound and y for the rest; use must-question takeaways to show the combined option is cheaper.

Estimate doubling time in compound interest using the 70 over r rule, substituting r=8 and using 72 as a benchmark to approximate nine years for doubling.

Apply the weighted average axis to a two-group GMAT problem with 6 and 4 days, a 360 group average, and an overall 400, deducing the unknown 460.

Factorize 3150 into prime factors, and show that making all prime factor counts even requires y to supply 2 and 7; the smallest y is 14, giving a perfect square.

Apply the invented operation brackets, defined as greatest integer less than or equal to x, three times to 2.7, 3.4, -1.6, and sum to 3 in GMAT official guide 2019.

Explore non-arithmetic sequences by plugging in numbers in order, using the recurrence x_n = 2 x_{n-1} - 1/2 x_{n-2} with x_0=3 and x_1=2 to find x_3=4.

Master solving distance-rate-time questions by plugging in convenient values, eliminating options, and deriving average speed as total distance over total time using algebraic, ear, and least common multiple methods.

Treat the lineup as a combinations problem, indicate a line for each stage, and multiply the chronological options using factorials, recognizing that order matters in the arrangement.

Solve the GMAT border-width problem by decomposing the border into rectangles, forming a quadratic x^2+9x-36=0, and using factoring or strategic plugging to find the width.

Understand terminating decimals when the denominator is a product of 2s and 5s. Learn to convert, multiply decimals, and count zeros before nonzero digits.

Learn how to factor 7150 into prime factors 2, 5, 11, and 13 using real-time and alternative approaches. Master divisibility checks, including the 11 rule, for efficient prime factorization.

Identify a pattern in the sequence where each term equals the previous term squared; using n=3 shows a_n=t, a_{n+1}=t^2, and a_{n+2}=t^4.

Plug in convenient values to simplify ratios and percent increase, then apply the bow-tie method to derive the percent change using P and E and the (k−m)/(100+m)×100 formula.

Apply the triple overlap formula: whole equals group1 plus group2 plus group3 minus twice the triple overlap minus the double overlaps plus the neither; use must questions for quick answers.

Master negative exponent rules on GMAT math by flipping numerator and denominator to convert b^(-x) to 1/b^x and (a/b)^(-x) to (b/a)^x, enabling quick simplification.

Plug in 100 to simplify percent calculations, then use revenue minus cost to compute profit as a percent of initial cost, with markup and factor cancellation guiding the solution.

Organize the seven numbers in increasing order; use that d = 84 and g = 4a + 14; with average 68, maximize g by minimizing others.

Compute a5 and a6 from the sequence a_n = n + 2^(n-1), then determine their difference, which is 17.

Learn GMAT combinatorics counting by computing total arrangements as 5! / 2!, evaluating adjacent cases as a single block (4! with 1 internal arrangement), and subtracting to get non-adjacent counts.

Develop the solution for GMAT questions by converting elements to scientific notation, applying (a^2−b^2)=(a+b)(a−b), and using plug in numbers to grasp concepts; cancel terms to reveal the answer.

Plug in the coordinates (0,2) and (3,0) to verify a line through both points, compute the slope, and derive the equation 2x+3y=6.

Learn to solve 1/r = 1/x + 1/y via the gamma method to derive r = xy/(x+y), using reciprocal relations, cross multiplication, and isolating r.

Learn to tackle the GMAT Official Guide maybe questions by testing values, ensuring nonzero denominators, and using a common denominator to verify x equals -2, highlighting a practical solution strategy.

Master exponent rules for negative powers, powers of powers, and combining like bases, with a GMAT official guide example.

Use must-question strategy: plug in convenient numbers and apply the polygon angle-sum formula to a regular nonagon, distinguishing equiangular from equilateral shapes.

Explore a challenging GMAT official guide 'Maybe' question, confirming roman numerals by plugging in convenient numbers to compare actual sum against the estimated sum after rounding evens and odds.

Use the ear method to divide the fraction by 2^-17, extract a common factor, cancel it, and simplify to 3 by evaluating 8+4+2+1 over 5.

In a GMAT data-sufficiency problem for apples and grapes, 10A+2G=12 determines A; statement 1 gives G=2 (sufficient), while statement 2 (2A<G) is insufficient, so A is correct.

Learn how to solve median data-sufficiency questions by evaluating statements 1 and 2, using plug-ins and the two contradicting conclusions approach to determine sufficiency.

Master data sufficiency using conversion ratios, as statements 1 and 2 yield sufficient information without computing the actual value, saving time.

Assess data sufficiency for a 20-quart mixture by analyzing two statements about total volume and yellow paint, using a ratio with x to determine sufficiency.

Apply data sufficiency reasoning to a GMAT ratio table with X, Y, and Z. Combine statements 1 and 2 to determine the greatest unknown, yielding answer choice C.

Determine the average cans per student using the total cans and total students, assess statements 1 and 2 for sufficiency, then combine to conclude the answer is C.

Analyze probability with marbles by using the complement rule. Given 24 total marbles and 8 red, plus white probability 1/2, blue equals 4 and its probability is 1/6.

Apply fast percentage reasoning to data sufficiency in GMAT problems: interpret 5% of Y as 60, and 80% of 1500 to judge sufficiency.

Analyze statements to assess data sufficiency, start with statement 2 to test sufficiency, then use statement 1, and finally combine to determine a and b from 7a+5b=85 with positive integers.

Identify whether a set is arithmetic by looking for a constant difference. Combine statements 1 and 2 to determine the 105th item, using A(n)=A1+(n-1)d to compute values quickly.

Explore when smaller to larger power exceeds larger to smaller using the 2^4 = 4^2 equilibrium; show statements 1 and 2 are insufficient, but together they yield C.

Analyze how high and low prices determine the range using statements 1 and 2. Combine, plug in numbers, and conclude that the range is not fixed at 16, yielding E.

Analyze a GMAT question on whether the product r times w equals zero, given statements; show that neither statement alone nor together resolves the product, so the answer is E.

Explore a GMAT data-sufficiency problem on compound interest, analyzing how 4% annual growth affects the 1st and 3rd year and using the formula X(1.04)^n to judge sufficiency of statements.

Simplify the expressions to isolate t; with t cubed equal to 216, an odd root yields a single value, so statement 2 suffices and the answer is D.

Map hardcover fiction, paperback fiction, hardcover nonfiction, and paperback nonfiction on a number line to reveal four elements. This distribution helps justify option E without using Venn diagrams.

Analyze how the units digit of a product depends on the units digits of a and b. Show that each statement alone is insufficient, but combined reveal the units digit.

Compute that total 32 and front-plus-behind 18 imply 12 between Adam and Beth; show that both statements are insufficient alone, but together they solve for x as C.

Analyze the area of a square inscribed in a circle using circle area or circumference data to assess data sufficiency, guided by 4 to pi to 2 area ratios.

Stretch the drawing to extremes to test sufficiency in geometry DS questions, using statements 1 and 2 and the Pythagorean theorem to decide if the truck can go through.

Master the double overlap data-sufficiency method on a 50-person group using a number line, not a Venn diagram, to determine overlap of doctors and lawyers.

Master the double-overlap data-sufficiency method using a simple number line, solving cat-or-dog problems and avoiding Venn diagrams for faster GMAT questions.

we analyze a GMAT inequality with positive x,y, translating 'is xy+y greater than xy+x?' to 'is y greater than x?' via cross-multiplication; statement 1 insufficient, statement 2 sufficient.

Explain a data-sufficiency GMAT fraction comparison about whether a fraction is less than 9/11, using positive a, b, inequality signs, and statements 1 and 2 with reciprocals.

Analyze GMAT objects that are spheres or cubes in red or green colors. Evaluate statement sufficiency and combine statements to determine total items without contradictions.

Master GMAT data-sufficiency strategies to determine the speed that makes a truck’s fuel consumption match a target, using a kv^2 model and statements about k and 30 mph.

Learn to simplify initial information and decide what's needed before reading statements, using a rent and utilities refund scenario to show why statements alone may be insufficient.

Using t^2 = 9 or t^3 = -27, calculate (2t)^2 - (t/3)^2; both yield 35, establishing a single numerical value and the correct choice D.

Solve a GMAT data-sufficiency problem by calculating the total student attendance from the average per performance across 8 musical performances.

Analyze sufficiency of two statements about wool and cotton jackets using benchmarks to estimate jacket counts. Combine the statements to conclude more than 1050 jackets, yielding a definitive yes.

Assess GMAT data sufficiency with base salary B and 10% commission on prices P for 15 cars, showing that neither statement alone nor both together provide enough information, yielding E.

Learn to compute the discount rate from before and after prices using the ratio, with data-sufficiency analysis of statements 1 and 2 and practical plug-in examples.

Determine when 10^(-n) exceeds 10^n to decide if n is negative. Apply statements 1 and 2 with 0 or 1 plug-ins to conclude the answer is E.

Solve a three-digit digits comparison using data sufficiency and plug-in numbers. Combine statements to conclude that r's hundreds digit is greater than t's.

Analyze the data sufficiency question: is xy divisible by x+y? Use plug-ins and two contradicting conclusions, then combine statements to show yes when x=y=2, yielding option C.

Analyze a GMAT problem with p+q=834 and profits per unit 2 and 3.5 to decide if 2p+3.5q exceeds 2000, via substitution and by multiplying by 10/10.

Analyze a GMAT probability data sufficiency question by evaluating two statements about job offers, using 'and' for multiplication and 'or' for addition to determine P1 times P2.

Apply the distance over rate relationship to link time and distance, convert units, and assess if statements about total time prove distance under 90 m on a conveyor belt.

Analyze the GMAT data-sufficiency question on the average (x+z)/2, showing statements 1 and 2 are each insufficient and combined still fail to yield a single numerical value.

Analyze double overlap data-sufficiency questions by combining statement 1 and statement 2 to map relief, side effects, and the neither group, noting that four data points are usually needed.

Analyze a GMAT style question by comparing statements about x as well as x^2, using inequality reasoning, parabola concepts, and convenient benchmarks to decide when x is less than 5.

Assess whether two statements determine if P×Z^4 is negative, using sign reasoning and the fact that even powers yield nonnegative results, then apply GMAT data-sufficiency strategies.

Break down complex GMAT data-sufficiency prompts by chunking statements, analyzing ratios and totals. The lecture shows deriving n as 24 from the two statements, with both statements sufficient.

Learn a real-time data sufficiency approach to determine whether x^3+y^3 is positive using statement 1 and statement 2, with plug-in testing and odd-power rules.

Assess the sufficiency of the sum of two integers using statements 1 and 2; only -1 and 1 yield a sum of 0, so the correct choice is C.

Four consecutive odd integers relate as d, d-2, d-4, d-6 with sum 64; and the greatest and least must differ by 6, with all values distinct.

Evaluate two statements about coat and sweater discounts to determine which discount is greater; using plug in numbers and sufficiency reasoning, the combined data are insufficient.

Assess feasibility from the statements: consecutive-square pairs with differences 25 or 27 fix 144–169 and 169–196, enabling a fast, calculation-free determination of n.

Evaluate a budgeting word problem to decide if the library earns a $2,000 bonus for more than 5,000 checked-out books, using average cost per book and statements 1 and 2.

Learn data-sufficiency reasoning in GMAT math by analyzing two statements, identifying the 552 scenario, and applying practical takeaways for solving without shortcuts.

analyze statement sufficiency for t<0 using r and distances, and apply the plug-in number method to show how combining statements yields a definite conclusion.

Explore solving a GMAT discount question by using percent calculations and relative expressions, evaluate data sufficiency of each statement, and combine statements to determine discounted prices.

Explore how rounding rules determine whether d is at least 0.5, using statements about rounding to the nearest tenth and to the nearest integer, with emphasis on sufficiency.

Analyze ratios among MQ, QN, and MN to determine a numeric outcome. Demonstrate that statement 1 is sufficient while statement 2 adds no new information, yielding answer A.

Extracts information from percent statements to solve a GMAT data sufficiency problem about jazz and blues revenue; use the 40% rise to reverse engineer the 1998 value.

Examine data sufficiency by testing statements about X and X+24, identify contradictions, and combine conditions to determine when both square roots yield integers.

Explore how to determine which variable is closest to zero in a GMAT data sufficiency problem by testing opposite numbers and distances, using statements 1 and 2 with concrete examples.

This lecture teaches data sufficiency strategies for GMAT questions: evaluate statements 1 and 2, then combine them to form two equations with two unknowns, using integers and common factors.

Compute triangle area as base times height over 2, using B·H=20 for sufficiency in GMAT question 346; grasp that heights can be internal or external with respect to obtuse triangles.

Master weighted average axis problems by identifying four data points to infer the missing fifth, and assess sufficiency when combining statements and inverse ratios.

Convert bases to powers of two and apply the power-to-a-power rule to obtain X+Y=16. Then use Y=16−X and explore statement sufficiency with X^2 and X−Y=2.

Learn how to compute commissions with a base amount and 5% of the excess above 1000, and determine data sufficiency using sales and commission statements.

Using data sufficiency for a geometry problem, combine statements to show two areas are equal in an isosceles right triangle; plug in units and mentally stretch the diagram.

Determine if r/s yields a terminating decimal by inspecting the denominator for powers of 2 and 5, and use statement 1 and 2 reasoning to assess sufficiency.

Determine k, odd integer between 57 and 65, from two statements; statement 2 says k+1 is divisible by 3, yet the statements yield insufficient data, so the answer is E.

Analyze a data-sufficiency problem on x plus y from GMAT official guide 2019, using a double inequality and integer constraints; both statements yield 7, so the correct answer is D.

Learn data-sufficiency using a GMAT mortgage problem with payments, taxes, and insurance. Convert wording to math, derive R from 20% real estate and a 12,000 total, and assess sufficiency.

Explore double overlap data sufficiency by combining statements to compare X and Y, using 60 as a plug-in, and applying 'of' as multiplication and percent rules, and avoid venn diagrams.

Learn how the average of consecutive even integers equals the middle value, and how statements 1 and 2 identify the middle number using q+s=24 and (q+r)/2=11.

Break the l-shaped polygon into two rectangles to express area as 15x and x(15−x), solve x^2−30x+189=0 for x=9; statement 1 is sufficient, statement 2 is not.

Solve a GMAT ratio problem with shirts, dresses, and jackets by assigning x to scale 9, 4, and 5, ensuring integers, and determine statement sufficiency to find the total.

Compute sector area by finding alpha as a fraction of 360 and applying area = (alpha/360) times pie chart area. Use data sufficiency reasoning with statements 1 and 2.

Analyze how to use even-root and odd-root rules to determine X's sign and the sufficiency of statements about X, emphasizing single-root outcomes for odd roots and benchmark estimation.

Examine a GMAT data-sufficiency problem to determine r from two statements. With v+z = 6 and numbers limited to 1, 2, 3, r must be 3, supporting option D.

Apply the weighted average axis to a two-quantity price mix; the ratio is inverse to quantities. Statement 2 is sufficient to prove X > Y; Statement 1 is not.

analyze how distance over time yields average rate and why average figures may mislead in data-sufficiency questions, without assuming constant speed, illustrated by a 460-mile trip in 4 hours.

Determine when statements about the median are sufficient using the given average and the sum of distances from the average equals zero.

Analyze a GMAT question where x^3 < x^2, noting x is negative or a fractional. Use plug-in methods to assess sufficiency, showing statement 2 yields x = -1.

Use statement 1 and statement 2 to determine the larger and smaller radii, then find the white area by subtracting the shaded areas from the large circle.

Explore when the median equals the average in a three-number set by analyzing two statements, using range and sum properties, and confirm sufficiency with plug-in reasoning.

Use the pythagorean theorem and (a+b)^2 = a^2+b^2+2ab to find a+b from a^2+b^2=100 and ab=50. Recognize the right isosceles case a=b=10/(root2) for sufficiency.

Plug in convenient numbers, like 60, to simplify division problems and compute fractional values for shipments; inspect statements to determine which shipments belong to each truck.

Study data-sufficiency strategies for digit-addition problems by verifying tens sums (b+e=h) and units sums (c+f=i) with carryover considerations, including a+d=g, using vertical layouts and convenient number plugs for digits 0–9.

Explore divisibility with variables n and m, analyzing when 3n is divisible by m and when 13n is divisible by m, and determine sufficiency through prime factors.

Apply absolute-value reasoning and number plug-ins to assess statement sufficiency in a GMAT-style question; determine that statement 1 is sufficient (q<s<t) while statement 2 is insufficient.

Use two statements to determine if 15 numbers are equal: total sum 60 and sum of any three numbers is 12, indicating all values 4. Emphasize averages and standard deviation.

Solve a GMAT data-sufficiency problem by using statements 1 and 2 to show all numbers equal 75; the average stays 75, so the data are sufficient (answer D).

Evaluate why statements 1 and 2 are individually insufficient to determine commissions, and show that even combined, 5% of the sales total and monthly averages leave the problem unsolvable.

Solve a GMAT right triangle problem by combining area and Pythagorean relations to form three equations, with either statement 1 or 2 proving sufficiency.

Explore data sufficiency strategies for a GMAT question using scientific notation, orders of magnitude, and even root extraction to determine a unique value of k.

The lecture explains direct proportionality among production, efficiency, and investment, using constant ratios to assess data sufficiency, showing that statement 1 is insufficient while statement 2 is sufficient.

solve a two-equation problem with x and t to determine the expression's value; assess statement sufficiency, showing statement 1 suffices and the result is 4.