GMAT® Math | Official Guide 2018

See how the matrix links each lecture and worksheet to solving Official Guide questions, with examples like problems 11, 140, and 142 from Combinations and Probability, for virtual-class participants.

Use a table to locate questions with similar elements, such as absolute value, and start solving related items by searching for 025. Leave a comment if data is inaccurate.

The bubble chart shows that harder GMAT questions cluster in statistics, powers and roots, overlaps, combinations and probability, and integers, so focus on these five types with targeted techniques.

Explore the top 20 GMAT math question-types and techniques, including two-conclusion checks, ugly numbers, and focused 2D geometry and algebra strategies.

Reveal how the question types chart presents the relative popularity of all 11 question types, using data from the bubble chart but without percentiles.

Explore problem solving and data sufficiency questions, identify the top problem solving types including algebra and triple overlap, and learn which hard subtypes yield the highest percentiles.

Explore the top 10 data sufficiency question-types and takeaways, emphasizing when statements yield two conclusions, key techniques, and the role of statistics, geometry, and algebra subtypes in data sufficiency.

The top subtypes charts identify the most common question subtypes and takeaways across GMAT math topics, from equations and inequalities to geometry and statistics.

Review this statistical analysis and apply it to your GMAT math preparation, and contact the instructor at info@NeatPrep.com with any questions.

Learn data sufficiency techniques for GMAT math, focusing on sufficiency rather than solving. Explore topics like percentages, integers, averages, algebra, and geometry with a quick-solve flow for 95% of questions.

Learn the data sufficiency question format: start with initial information and a question, evaluate one or two statements for sufficiency, and recognize immutable answer choices on exam day.

Determine sufficiency by arriving at two contradicting conclusions from the data, using a flowchart and plug-in numbers to distinguish terminating versus not terminating decimals.

Explore the true meaning of GMAT answer choices and master statement sufficiency, identifying whether statement 1 alone, statement 2 alone, or both together are sufficient.

Apply the data sufficiency flowchart to determine if statements 1, 2, or their combination are sufficient, and identify terminating decimals by denominators with only powers of 2 or 5.

Solve a GMAT data-sufficiency problem in 30 seconds using algebra and factoring 5(a+2p), and assess statements 1 and 2 for sufficiency.

Learn a fast data-sufficiency approach to geometry by stretching the drawing to test if the target angle is fixed, using statements 1, 2, and their combination.

Discover how data sufficiency frames GMAT speed problems: average speed equals distance over time, but halfway speeds and partial totals may not reveal the full distance or time.

Analyze data sufficiency on a quadratic, showing how one statement can determine x and how two statements may still yield a single value, with quick factoring strategies.

Master data sufficiency by learning to derive two contrasting conclusions from statements, recognizing sufficient versus insufficient data, using statements separately, and simplifying problems for geometry questions.

Apply the percent increase/decrease template: compute the difference over the original, multiply by 100, to find any percent change and to convert fractions or decimals to percent.

Analyze a ratio question by finding the greatest common divisor to create integer batches, understand divisibility by 5, and apply prime factors to determine the correct bouquet combination.

Learn to solve percent problems by converting percents to fractions, using benchmarks, and breaking numbers into easy parts, including 125 percent as 125/100.

model ages over time by setting x years from now, Rebecca at 34+X and daughter at 8+X. use the is cue for equality, set 34+X = 16+2X, solve for X=18.

Divide miles per hour by gallons per hour to obtain miles per gallon, cancel units, and use benchmarks to compute 32/24 as four-thirds miles per gallon.

Learn to solve GMAT percent questions by recognizing that the combined journey exceeds 50% and by plugging in a total distance to identify 55%.

Calculate the probability that the hundreds digit is 2 by counting favorable numbers from 200 to 299 and total options using the gaps method, yielding 100/250, simplified to 2/5.

Apply the concept that the whole appears after the of, set 7% of the excess over 1000 as 87.5, and compute x = 1250.

Set up a single equation with 16 coins totaling 235 cents to find x, the number of 25-cent coins; solving yields x = 5 and the answer is B.

Explore when the average equals the median in average and median questions by ordering data, noting constant differences, and using consecutive-number examples.

Solve percent problems by translating percent and 'of' as multiplication, simplify before multiplying, and compute X from 60% of X equals 300.

Learn to solve which of the following questions by plugging in convenient numbers, focusing on answer choices, and eliminating options to find the must-be greatest.

solve a geometry perimeter problem using quadrilaterals like deltoid, parallelogram, and rectangle, with 2(side_A+side_B) and a 360 perimeter to find X and 2X.

Identify the ratio between paperback fiction and paperback non-fiction using X for the smaller quantity. Solve 2(X+20) + (X+20) + X = 140 to obtain X = 20.

Solve a GMAT style average problem by setting the sum of items over their count equal to the given average, then derive the missing value n = 21.

Apply GMAT math strategies by using a midpoint and a variable X to convert absolute quantities, skim for distances, and determine Abdul and Carlos's road distance, yielding the correct option.

Learn to solve rate problems by applying rate times time equals work, using direct proportionality between time and work, and flexibly handling units to simplify calculations.

Solve a door-cost problem with pine and oak doors, using discounts and percent-to-fraction conversions to determine a total of 560 and illustrate why converting percents to fractions helps.

Learn to solve absolute value inequalities by plugging in comfy numbers, considering positive and negative cases, and using a 'maybe' question approach to confirm possible answer choices.

Analyze isosceles triangles by redraw; equal sides yield equal opposite angles, height bisects sides and angles, and avoid relying on not-to-scale drawings, using the angle-sum rule 180(n-2).

GMAT ratio problems treat proportion as ratios, assign ratio units X to 3, 4, and 6, and solve 13X = 780 to find X = 60.

Identify right-triangle side lengths using known pythagorean triples, especially 6:8:10; when a value rises from 10 to 14, compute the 4 difference over 10 to get 40 percent.

Apply fraction addition by finding the least common multiple of denominators, here 30, convert 1/2, 1/3, and 1/10 to equivalent terms, then solve 28X+180=30X to get X=90.

Explore how similar shapes yield volume ratios by cubing linear scale factors; double each side results in an 8x volume increase, illustrated with boxes and cones.

Understand how a sphere is inscribed in a cube, so the edge is twice the radius, and visualize it with 3d projection and cross-sections while solving must questions.

Master quick system solving by elimination: add or subtract equations when variables align, use factoring, and multiply to eliminate variables in multiplicative relations, illustrated by x+y=4 and x^2=36, yielding x=-6.

Link X:Y and Y:Z with a single three-column table, using Y as the connecting factor. Multiply to move from 4:1 and 2:1 to X:Z = 8:1, preserving integers.

Read the graph by noting axis labels and select an extreme datum. Put it into a sentence, then find the greatest difference (2.7) between 2.2 and -0.5.

Learn to compute total value from units and item value using percent-to-decimal conversion and simplification; 0.5% of 20,000 equals 100, giving 250,000 total.

Break unfamiliar polygons into familiar shapes, especially rectangles, to calculate area. Use given dimensions to compute partial areas (300 and 700) and combine for the result, choice C.

Recognize when every number in a set changes by the same percentage, the average changes by that percentage, as shown by increasing all terms by 10% to raise the average.

Use the weighted average axis when quantities and averages differ, as shown with a four-item group at 78 and unknown item, giving overall 80; the inverse ratio guides the calculation.

Solve a GMAT math question by modeling 40 regular hours and 8 overtime at rate X, using 40X + 8 times 22 = 816 to find X = 16.

Master division of mixed fractions using the ear method and reciprocal, then apply the bow tie method to subtract, yielding the correct answer choice D.

This lesson shows AB and BA, two-digit reverse numbers, yield AB+BA divisible by 11 and AB-BA divisible by 9; plug numbers to eliminate choices in must questions, answer D.

Identify efficient counting strategies for sequence questions, choosing straightforward calculations over tricks, using up to five calculations or twelve simple counts to solve questions quickly.

Use plug-in numbers to eliminate answer choices in GMAT math, showing the number of boxes is S divided by r and the expression is S divided by r minus n.

Learn a step-by-step GMAT strategy for Must questions using Roman numerals: plug in numbers, eliminate choices, and simplify inequalities to identify the correct option.

Plug in numbers for must questions, sketch data in coordinate geometry, and apply the midpoint formula to deduce Q = (-r, -s) from P = (r, s) as the midpoint.

Compare five companies to identify which has the greater standard deviation by analyzing the range, items farther from the average, and the implied variance.

Use divisibility by 8 and last three digits to simplify 1174, noting 1000 is divisible by 8; track revolutions to land on e as the correct choice.

Learn to use approximate reasoning and close benchmarks to estimate percent change, calculating difference over the original number and multiplying by 100.

Apply the must question approach, plug in convenient numbers (k=-1) to test quadrants 2 and 4, and eliminate options; note asymptotes at x=0 and y=0 for xy=-1.

Learn to solve GMAT® fraction problems by plugging convenient numbers, using the least common multiple rather than the gamma method, solving for X, and verifying via substitution in the options.

Factor the quadratic by finding two numbers with product -15000 and sum -250, giving roots -300 and 50 and w = 50. The takeaway marks it as algebra.

Learn how to solve GMAT must-questions by plugging in convenient numbers, using X=2 and 10 bushels each, to simplify x/35 from a 350-bushel total.

Learn the fastest way to identify evenness by using the definition of even numbers, testing integers like zero, and plugging in numbers to eliminate answer choices.

Understand how the word 'per' represents division, cancel units, and convert miles per gallon to gallons by dividing numbers; use benchmarks to approximate values and estimate answers.

We substitute x=2, y=17 into y = kx + 3 to find k = 7. Then we compute y for x=4 as y = 7x + 3, which equals 31.

Learn strategies for solving greatest-value questions in GMAT math, including squaring terms, using benchmarks, and eliminating options with root and power rules.

Apply a percent tree to convert nested percents to a simple equation. Note that 720 is 10% of 90%, so 9X/100 = 720; thus X = 8000 (answer D).

Explain exponential population growth by doubling each month, starting at 3 and giving 3(2^n) after n months; as shown, after one month it's 3(2^1) and after two months it's 3(2^2).

Spot symmetry and extract a common factor to simplify a complex fraction, then multiply numerators and denominators to solve for r quickly. Apply benchmarks over brute-force LCM calculations.

Solve a must-question GMAT problem by plugging in convenient values, using co-prime 3 and 20, and eliminating options to find x from 3x+4y=200 with y multiple of 5.

Learn to quickly determine when expressions with square roots are integers by simplifying using root properties, as demonstrated in question 74 of the GMAT official guide 2018.

Apply ratio analysis to determine total hours by setting the parts as 2x, 3x, 5x, and 6x, summing to 16x, and use answer choices to test feasibility.

Compute individual rates by dividing work by time (A: 1/6 tank per hour; B: 1/9 tank per hour), sum for the combined rate (5/18), then time equals work over rate (3.6 hours).

By plugging in coordinates, this lecture shows that the point (0,2) lies on every line kx+3y=6, since 3y=6 regardless of k.

Solve x squared less than 2 by placing x between the negative and positive root of 2, then use must or maybe questions and convenient numbers to eliminate choices.

Solve data-heavy GMAT questions quickly by counting days and pages per book. Use benchmarks and the rule that you cannot finish one book and start another on the same day.

Plug in 100 to simplify percent problems and use must questions to eliminate options; recognize that 'of' means multiplication and the decrease from 42% to 33% is 9.

Master remainder and divisibility problems by plugging in convenient numbers, mastering must questions, and using four consecutive integers to show divisibility by 24 (three by 6).

Use the gamma method to subtract fractions with unlike denominators and compute their differences. Benchmark using 1/2 to compare differences and confirm that choice D is correct.

Set up an equation: x = two thirds of x plus 108, so 1/3 x = 108 and x = 324. Learn to map words to math and use benchmarks.

Learn how to handle ratio problems by multiplying both sides to simplify. Compute the percent increase from 16 to 18 as 2 over 16, which equals 12.5%.

Translate percent statements into multiplication by turning percentages into decimals; use 'of' as multiplication, so 460 is 115% of x and x equals 400.

Plug in convenient numbers and use elimination to solve must questions, testing positive integers m and p with sum under 100 to compare m^2+p^2 and mp in GMAT math.

Learn to manipulate ratios to compare x and y with a and b, by inverting and equating expressions, and evaluate answer choices for equivalence.

Factor the quadratic to find two numbers with product -24 and sum 2, giving roots -6 and 4 in the GMAT Official Guide 2018.

Use a percent tree to solve percent-of-a-percent questions, organize data with 40% independent voters and 60% registered, then compute 6% of n by simplifying before multiplying.

Identify a right triangle from the circle: inscribed angles opposite a diameter are right, recognize 6-8-10, compute radius 5, then arc length is 5 pi as half the circumference.

Use the weighted average axis for two groups with quantities 2x and x and averages 17 and 20; place the smaller average top left, since it lies toward larger quantity.

Utilize a 1:1 ratio to model orangeade volumes, compute revenue at 60 cents per glass, and distribute the total among three glasses to identify the correct answer D.

Solve a remainder-style GMAT problem by grouping 68 jugs into cartons of 7, recognizing when a final carton needs 2 more jugs, and using benchmarks to compute the remainder.

Break polygon into rectangles, use area relations; total area 4800 gives each rectangle area 1200. With l = 3w, w = 20, so answer B.

Apply a fast GMAT pricing trick by converting to cents, using 7A+5B=63, extracting a common factor, and confirming A=4, B=7 for a total of 11.

Isolate y from 3x+7y=… to obtain y=(-3/7)x, revealing the slope as -3/7; this lesson clarifies deriving slope from a line with integer coefficients.

Create a single ratio table to unify all ratios, bring values to the same level, then convert to integers and reduce the first-to-third ratio to 4:5.

Learn algebraic strategies for GMAT math: use percent rules, fraction conversions, and simplify before multiplying, then apply must questions by plugging in convenient values for n and m.

Explore two approaches by sketching data and building right triangles on the coordinate plane; use the pythagorean theorem to derive the distance, radius, and circle area pi r^2.

Solve a disguised quadratic by setting A = xy and solving A^2 - A - 6 = 0; then use GMAT roman numeral plug-ins to eliminate options.

Convert half a mile to feet, simplify the expression, and use nearby benchmarks to estimate 528 divided by 11, leading to the correct choice D.

Compute the single press rate by subtracting the two-press rate from the three-press rate, yielding r = 1/20 job per hour, i.e., 20 hours per job.

Sum volumes of spheres with radii 1, 2, and 3 using 4/3 pi r^3 to get 36, so large radius is cubic root of 36 and diameter is twice that.

Cancel out negative and positive numbers to reduce the problem to a simple sum of consecutive integers, then apply the average times the number of items formula.

Apply absolute value techniques by plugging in comfortable numbers, such as -3, 1, 2, to get s=1, t=2, r=3, and use substitution or test choices to find average and E.

Learn to solve percent questions by treating the whole as 100, reduce 100:120 to 5:6, and identify the higher stocks in GMAT percent problems.

Use a 100-unit number line to solve double overlap questions, find a 9-unit overlap for 62 stockholders and 47 employees, yielding 53 stockholders not employees and the correct answer D.

Compute percent change by dividing the difference by the original number and multiplying by 100, identify the whole after 'of', then apply elimination with payroll and insurance examples.

Learn how regular polygons break into isosceles triangles to determine central angles, memorize equilateral triangle angles (60 degrees), and apply 360/n for quick GMAT geometry solutions.

Interpret 'at least' as a minimum threshold and determine whether two-thirds of 40 can be in favor, with against at most one-third.

Show how 20 factorial plus 17 is divisible by 17 by factoring out 17 and using factorial divisibility. Highlight a shortcut: adding a multiple preserves divisibility by that number.

Maximize the expression by minimizing the squared negative term; set t to 5 to zero the squared factor, giving depth 500 and making the correct choice B.

Demonstrates solving a moving-object rate problem by using distance, rate, and time. Apply the basic formulas to find how far he goes before turning back in 50 minutes.

Isolate x in a two-cycle compounded interest problem by applying the standard formula, recognizing 8% increases as 1.08 per cycle, and solving w = x(1.08^2 + 1.08).

Use a must-question approach by plugging in comfortable numbers to eliminate choices. Then apply rate-time-work, compute the combined rate as 800/x, and solve for time with b = 800(y−x)/xy.

Apply a quick ratio approach: eight parts of a 1800 total equal a quarter, 450. Recognize eight units and divide by four to obtain 450, confirming the correct answer.

Resolve percent problems by using whole times percent and estimate with benchmarks. Apply algebra to set blue as one third of the total and multiply by three to clear denominator.

Convert decimals to simple fractions using 10^n denominators, then multiply by reciprocals and simplify before multiplying to cancel terms; estimate with order-of-magnitude checks.

Discover a fast approach to divisibility by 3 using three consecutive numbers, and master plug-in elimination for must-be-divisible questions in GMAT math.

Apply factoring and simplification to 100x+200y given x+y=1, then test feasible values using a must-or-maybe approach for roman numerals. Plug in numbers to confirm which options could be true.

Maximize the fraction by maximizing the numerator and minimizing the denominator; X=9 and Y=1. Convert decimals to fractions or use a stacked method multiplying by powers of ten with benchmarks.

Know the 30-60-90 triangle and its ratios 1:√3:2, with angles 30, 60, 90. Convert a 70 hypotenuse to 35 short leg, 35√3 long leg, then add 7 for final answer.

Solve a tricky GMAT powers and roots question by using a fast plug-in method, benchmarks, and known powers to determine the number of zeros before the first nonzero digit.

Demonstrates using the weighted average axis to solve mixture questions with two solutions, applying inverse ratios to split the range and find volumes and concentrations.

Use the standard deviation concept: it measures distance from the mean. Multiplying all scores by the same factor scales the deviation; adding a constant leaves it unchanged.

Use the triple-overlap formula: whole equals the sum of groups minus twice the triple overlap minus double overlaps plus the neither group; England, France, and Italy yield 67.

Compute percent change by dividing the difference (65) by the original (320) and multiplying by 100. Use comfy numbers like 64 and 10% steps to estimate about a 20% increase.

This lecture clarifies how to interpret remainders in GMAT style questions, connecting x/y and decimals to fractions, and shows y = 75 with remainder concepts, answer choice B.

Solve zero-product equations by listing all zero factors, handling simultaneous zeros, and unifying solutions on a number line using or and and at different heights.

Solve a GMAT geometry problem by recognizing a right isosceles triangle with 45-45-90 angles, then compare perimeters of dissimilar shapes using unit substitution and a 2√2 to 3 ratio.

Solve a GMAT problem by forming two totals: l+m+n=37 and l+2m+3n=64. Derive n's range and use a plug-in method to select least and greatest values from the answer choices.

Learn to solve a GMAT math question by comparing the median and mean, using a single variable n and plug-in numbers, including positive numbers, to identify the correct answer.

Plug in a comfortable ratio to simplify the box dimensions, treat volume as base area times height, and use cubic roots to test choices, eliminating incorrect ones until B remains.

Assign a ratio unit x to represent changes, treat the quantities as regular numbers, and cross-multiply to solve for x, finding the current number of teachers.

Solve an exponent inequality by applying power rules; convert 25^n to (5^2)^n = 5^{2n}, compare with 5^{12}, and conclude n>6 (n=7 for integers), option B.

Increase by a quarter equals multiplying by 5/4; apply the fourth power to solve x=2560, using 5^4=625 and 4^4=256.

Order the years from 2000 to 1990 to form eleven items, then identify the median as the sixth item with five on each side; use rough benchmarks to guesstimate.

Master the normal distribution curve by heart, recognizing its symmetry around the mean and that 34% lies within one standard deviation and 14% within two, placing 84th and 98th percentiles.

Apply the bow-tie method to add fractions in a GMAT distribution problem, distributing three sandwiches among m and the fourth among m-4, then verify choices by plugging in convenient numbers.

Apply the percent change formula, difference over original times 100, illustrated by a 16% decrease; use benchmarks to estimate ugly numbers and select B.

Solve a probability problem by selecting two non-defective pens from twelve, multiplying sequential probabilities after simplification. Apply a two-stage chronological approach with a line per stage.

Convert percents to fractions, use the LCM to subtract (3/20 - 1/12), then divide by the original and simplify; the result is 4/9, or 44 4/9 percent (choice C).

Learn to solve GMAT style questions by applying the difference of squares to simplify large powers, convert powers to familiar benchmarks, and test divisibility using coprime factors.

Explore how an area ratio of 1 to 4 between circles implies a radius and circumference ratio of 1 to 2, because similar circles scale linearly and area scales squared.

Master remainder questions by plugging in convenient numbers, equating 4n and 5m, revealing x=23 (between 10 and 40) and a final remainder of 5 when dividing by 6.

Isolate the root to express r in terms of s, then raise both sides to the appropriate power, yielding r = s^3 for the example; confirm the solution.

Because x/3 is a prime squared, x equals 3 p^2 for a prime p. With p = 2,3,5, x = 12, 27, 75, giving three values (answer B).

Sketch the data on the xy-plane and use slope as change in height over distance; parallel lines share the same slope. Here the slope is 2/3, derived from 3y-2x=0.

Maximize the height expression to obtain a maximum of 150. Observe that the height two seconds after the max equals 86, due to the parabola's symmetry about t = 3.

Apply the n(n-1)/2 formula to count pairs in a group; for 8 teams, 28 games show how combinations count without regard to order.

Solve a GMAT rate-time-work problem by equating R·T = 336 and (R−2)(T+4) = 336, then substitute to reduce to a single quadratic in time, yielding the positive solution.

Learn how switching the numerator and denominator flips inequalities, apply the must-question plug-in method to eliminate choices, and show p/q < 1 implies q/p > 1.

Compare separate and combined shipping costs using x and y, and apply plug-in values to question and answer choices to identify the cheaper option, showing the correct answer is A.

Use the approximate doubling-time estimate 72 over r years. With r = 8%, the amount doubles in about 9 years, then reaches 20,000 by year 18; answer A.

apply rounding rules to miles and gallons, interpret the per as division, and use extreme values to bound and maximize or minimize the miles per gallon.

Use the plug-in method for must questions in GMAT math, testing 0, 3, and -5 to eliminate options, then compare with the x-range and absolute value inequalities.

Apply the weighted average axis to two groups—6 days at 360 and 4 days with an unknown average—given an overall 400 and a 3:2 quantity ratio, yielding 460.

Discover how to find the smallest y so that 3150y is a perfect square by using prime factorization and even exponents, yielding y = 14.

Solve consecutive-number problems with arithmetic sequences, using sum equals average times items, number of items equals gaps plus one, and units-digit ballparking to spot the correct choice.

Identify non-arithmetic sequences by dependence on previous terms and plug values in an orderly fashion; use x_n = 2x_{n-1} - 1/2 x_{n-2} to compute x_2 and x_3.

Break the units digit pattern of 3 from powers into a 4-cycle plus remainder, then plug in convenient numbers using a must-question mindset to solve the GMAT problem.

Demonstrate counting lineups of six people by applying 3 factorial to males and to females, then multiply options for total arrangements; show how 'and' implies multiplication and order matters.

Explore how to identify terminating decimals by expressing fractions with denominators of 2 and 5, convert decimals through multiplication, and use decimal-point placement to count nonzero digits or zeros.

Compute the sum of even numbers from 100 to 300 using the average times the number of terms, illustrating the arithmetic set method and the evens counting trick.

Show that from a_3 onward, a_(n+1) equals a_n squared and a_(n+2) equals a_n to the fourth, so the pattern yields the correct choice D.

Plug in convenient numbers to form the price over earnings ratio, then compute the percent increase as [(100+k)/(100+m) - 1] × 100, yielding option D.

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

Compute profit as a percent of the initial cost by simplifying with a 100 benchmark, separating revenue and cost, and using a convenient plug-in to cancel factors.

Organize seven numbers in increasing order and use the average of 68 to analyze medians and maxima, showing how minimizing others with smallest a and largest 4a+14 yields the result.

Plug in values for a sequence using the relation a_n = n + 2^(n-1) and compute a_5 and a_6 to find their difference, which equals 17.

Learn to count arrangements with identical items and separation constraints by using totals minus adjacent cases, applying factorials and the adjacent-item trick for GMAT style questions.

We plug in a 100 newspaper example to solve a must-question with multiple variables. We derive r in terms of p, yielding r = 400p/(500 - p).

Solve the GMAT official guide 2018 question 216, page 178 live, mastering denominator simplifications with decimal places, converting expressions with scientific notation, and using (a+b)(a-b) to simplify quadratic forms.

Solve weighted average axis problems quickly by using the inverse ratio principle, linking quantities to range splits. Here n to 1 corresponds to 35 to 5, so n equals 7.

Derive the line through (0,2) and (3,0) by plug-and-check and slope calculation; obtain y = -2/3 x + 2 or 3y + 2x = 6.

Solve a two-digit AB-BA puzzle by showing AB−BA = 9(A−B) and AB+BA = 11(A+B); deduce A−B = 3 from the difference 27, noting divisibility insights.

Demonstrates how to compute a multi-person probability using a complement and multiplication, combining 1/4, 1/2, and 3/8. Concludes the final probability is 3/64 and option E is correct.

Learn to tackle a GMAT 'maybe' question by plugging in numbers, testing denominators, and using a common denominator to solve for x, yielding x equals plus or minus two.

The lecture demonstrates simplifying expressions with negative exponents by keeping negative powers and applying the power-to-a-power rule and adding exponents for same bases.

Solve a quadratic by factoring: product 6, sum -5, roots 2 and 3; ensure x ≠ 0 when multiplying, or use the quadratic formula.

Explore the weighted average axis to solve two-mixture problems. Use ryegrass concentrations and a 30% overall average to derive a 2:1 ratio and 33 1/3%.

Plug in convenient numbers to test the inequality, identify zeros and undefined points, and unify two single-variable inequalities to reveal integers -3, -2, 3, and 4.

Learn to solve triple overlap questions fast by memorizing the Whole = sum of groups minus 2 times triple minus double plus neither, demonstrated with 150 as the total.

Master the ear method to divide fractions with negative powers, extract a common factor like 2^(-17), and add exponents when multiplying identical bases.

Solve data-sufficiency geometry questions by analyzing external angles and mentally stretching the drawing to extremes to determine insufficiency, as shown in the GMAT Official Guide 2018 lecture.

Explore data sufficiency for GMAT questions using two equations with two unknowns, divisibility rules, and a graphical solution to determine sufficiency.

Learn to determine data sufficiency in GMAT questions by evaluating each statement and then combining them to decide if the yellow paint meets the 20-quart mixture requirement, using ratio reasoning.

Sketch on the x-y plane to decide if triangle q p r is right; analyze equal coordinates and perpendicularity to determine sufficiency that q p is perpendicular to p r.

Compute blue marble probability from the total and red and white counts; with 24 marbles, red 8, white half, blue equals 4, giving blue probability 1/6.

Analyze how statement one shows a rectangle with a 90-degree angle, yielding a square with opposite sides equal; combine the statements to deduce w=2 and select answer C.

Determine the combined rate by subtracting the outlet from the inlet rate. Use statement 2 (10 gal/min in, 4 gal/min out) to obtain 6 gal/min; statement 1 is insufficient.

Learn to remove roots by isolating the root expression and raising to the root’s power, applying exponent rules that treat a root as the bottom exponent.

Learn to compute total auditorium seats using an arithmetic sequence: first term 18, common difference 2, with 27 rows, via average times items or sum formula.

Analyze power comparisons for two numbers using the equilibrium concept, and apply data-sufficiency reasoning by plugging in numbers to arrive at two contradicting conclusions, confirming the correct choice is C.

Master double overlap questions by layering group one on the whole, then group two on top, compute overlaps and neither, and test data sufficiency across statements.

Compute average speed as total distance over total time using 50 miles split into 30 miles at 60 mph and 20 miles at 50 mph, totaling 0.9 hours.

Practice data-sufficiency reasoning by simplifying expressions, recognizing when odd powers yield a single value, and using statements to determine T in GMAT style questions.

Analyze a GMAT Official Guide problem by modeling total charges as parts plus labor plus 6 percent sales tax, then solve for labor.

Evaluate whether the expression is greater than zero using GMAT-style statement-based sufficiency. Learn how age and W values lead to contradictory conclusions or sufficiency, with even powers guaranteeing nonnegativity.

determine the boys-to-girls ratio using the facts that girls are three times as many as boys and that boys are a quarter of the total for a GMAT ratio question.

Master data sufficiency for GMAT math by recognizing arithmetic sequences, using the first term and common difference to derive other items, and evaluating whether statements alone or together suffice.

Assess the units digit of a product by testing statement sufficiency on unit digits, then combine results; the units digit depends only on the last digits of the factors.

Analyze data sufficiency for a GMAT geometry problem by testing statements about a non-right triangle and area, using Pythagorean reasoning and strategic plug-in methods.

Solve ratio problems by assigning x to the smallest segment, use midpoint facts to express all segments, deduce x>4 from ac>8, and determine cd>6 to compare with 5.

The lecture demonstrates a GMAT data-sufficiency approach: define x as people behind Beth; statement 1 implies a total of 32, statement 2 is insufficient, but together yield a unique x.

Determine the area of a square inscribed in a circle by using circle area or circumference data, and apply data-sufficiency reasoning with fixed area ratios.

Analyze whether line k's slope is positive using two statements and sketching the data; conclude the data are insufficient, even with parallel lines having identical slopes.

Apply a fast, diagram-free number-line method to double-overlap data-sufficiency questions. Combine both and neither data (as shown with cats and dogs in a 50-household example) to reach C.

This GMAT official guide 2018 lecture analyzes a walking to non-walking ratio, finds the smallest unit, and shows that 66 2/3 percent walk, illustrating a yes/no sufficiency question.

Analyze how profit does not rise linearly with units sold, considering 350k–380k units and changing setup costs to show why the GMAT problem leads to answer B.

Explore data sufficiency with parity and quadratic identities, testing odd and even cases to uncover two contradictory conclusions. Conclude that the correct choice is D.

Explore how to use rate times time to calculate weekly pay and how a $1.50/hour increase changes hours worked, illustrating inverse proportionality and unit analysis with fractions.

Explore a GMAT style sufficiency problem on billing time: compute total charges with 92 for up to 4 hours and 23 per extra hour, and assess two statements.

Learn how to analyze a GMAT inequality by cross-multiplying with a positive factor, assess the sufficiency of statements 1 and 2, and simplify to y > x.

Explore how to compare fractions and decimals in a GMAT inequality, using positive multipliers and reciprocal thinking, with data-sufficiency insight showing statement two alone suffices.

Determine the total number of objects when shapes are spheres or cubes and colors are red or green, using data-sufficiency reasoning with two statements and contradictory scenarios.

Solve a GMAT-style parity problem, showing when xy is even and when x^2+y^2 is divisible by 4, based on x and y being even or odd.

Assess the parity of a+b using odd-even rules, determine the sufficiency of statements about ab and a-b, and apply the odd factor principle with convenient example pairs.

Analyze a GMAT data sufficiency problem on fuel consumption, equating K·V^2 to one third, derive speed from V^2 = 1/(3K), and compare statements 1 and 2 to verify sufficiency.

Explore evaluating expressions with t, noting that even roots give ± values while odd roots give a single value, guiding statements 1 and 2 toward the numeric GMAT expression result.

Examine GMAT® math problems from the official guide 2018 using cotton in pounds and jacket production, estimate division with benchmarks, and determine sufficiency when combining statements to exceed 1,000 jackets.

Identify a GMAT data-sufficiency problem by isolating base salary B and total price P. B alone is insufficient; 8-car data is insufficient; combined, the answer is E; avoid unnecessary math.

Explore common factors of 18 and 24 to determine integer x greater than 1. Analyze data sufficiency: statement 1 is sufficient, statement 2 is not, yielding answer a.

Analyze a GMAT percent discount problem where the after price is 100 and the before price is 25% higher; identify the 20% discount and emphasize the whole for data sufficiency.

Master data sufficiency in a geometry problem about covering two stains with a circular rug, using rug area, stain distance, and combined statements to determine feasibility.

Apply power rules to compare negative powers and 10-based expressions, simplify thoroughly, and use convenient plug-in numbers to test the sufficiency of statements one and two for a GMAT question.

Assess a GMAT data-sufficiency problem with a total cost comprising a fixed sum and a per-minute charge for minutes over 420; evaluate statements to determine sufficiency, highlighting statement 2.

Solve a three-digit number comparison in real time, analyzing r and t with statements about tens and hundreds digits, using plug-in strategies and data-sufficiency reasoning to reach the answer C.

Explore how to determine whether xy is divisible by x+y using data sufficiency, evaluating statements 1 and 2, and showing that combined statements yield yes.

Develop skills to apply average reasoning, compute totals, and analyze sales tax implications for items above 80 in GMAT math data-sufficiency problems.

This lecture defines standard deviation as how much items deviate from the average, using eggs in nests to illustrate, and shows equal counts yield zero deviation; statement 2 is sufficient.

Visualize distance questions by placing distance above a line and rate below to reveal the formula, then convert units and apply distance = rate × time.

Solve a deceptively difficult data sufficiency GMAT question about the average of x and z, using two statements and a quick unifying approach.

Test data sufficiency in a GMAT rug problem by exploring border width and dimensions with w + l = 22, showing areas of 32 and 80, proving data are insufficient.

Solve a GMAT probability data-sufficiency question about red, white, blue, and green cards. Identify sufficiency of each statement and show that combined data remain insufficient.

Analyze whether x is less than 5 using data sufficiency, solving with quadratic inequalities and parabola behavior. Conclude that statement 2 is sufficient, aided by convenient benchmarks and root insights.

Express the bases as powers of the same base, deduce x+y=15, and show that 1 and 2 together are sufficient to determine x and y in this GMAT problem.

Utilize data sufficiency techniques to determine when a product is negative by analyzing signs of p and z, including the impact of even powers and algebraic constraints, with example-driven reasoning.

Determine the minimum number of games using statement sufficiency and the least common multiple of 2 and 3, illustrated by going down three and up two to reach 104.

Break down a complex verbal expression into manageable chunks, compute end-of-year totals, and test two statements for sufficiency to identify the correct GMAT answer.

Examine data sufficiency for whether a 2400 square inch glass sheet can cover a 36 by 60 table top, using two statements and mentally stretching the drawing.

Evaluate data sufficiency for inequalities involving x and y, using A, B, C, and D relations, and validate sufficiency by plugging in numbers and contradiction principles.

Learn a number-line approach to double-overlap data-sufficiency questions, determine overlap between two groups, and decide sufficiency by combining statements, illustrated with a 12 vs 8 vs 17 example.

Apply plugging in convenient numbers to test sufficiency when X and Y are positive and satisfy X<10<Y, using symmetry around 10 to isolate and verify.

Evaluate data sufficiency for discounts by comparing coat and sweater prices, applying percentage relationships and numerical examples to determine if statements yield a unique conclusion.

Analyze a GMAT data-sufficiency cost problem with a two-variable model, where a single equation from the first statement is insufficient, while combining both statements yields a solvable system.

Identify that the difference between squares of consecutive integers equals 25 or 27 and deduce the pairs 144 and 169 (and 169 and 196) accordingly.

Demonstrates data-sufficient reasoning for percent change problems by showing how a 4 percent gross income increase and a 15 percent deduction can leave net income indeterminate.

Determine whether the library earns a $2,000 bonus by analyzing annual purchases and checkouts: 600 new books at $28 and about 5,400 total checkouts.

Explore solving data sufficiency with gift certificates: use x and y, $10 and $50 proofs, integer constraints, and contradiction strategy to determine sufficiency.

Explore a fast, remainder-based approach to GMAT data-sufficiency: use the algebraic remainder definition, move the remainder, plug in numbers, and decide sufficiency by whether statements yield consistent conclusions.

Solve data-sufficiency problems by testing statements separately and in combination, using convenient distance values and considering positive and negative directions to determine if t crosses zero.

Explore how to count triangles using combinations: determine the necessary shape and number of points, apply a three-vertex selection from five, and divide by three factorial to count distinct triangles.

Analyze price discounts using percentages and dollar amounts to determine data sufficiency in a GMAT style price comparison.

Explore a GMAT data sufficiency puzzle by using the units digit property in products. Determine the square and triangle digits from statements 1 and 2.

Set the total distance as x, so MQ is 2x/3 and Q is x/3, giving a 1:2 ratio. Statement 1 suffices; statement 2 adds nothing; answer is A.

Analyze a GMAT data-sufficiency question from the official guide about three shirt prices over 60. Statement 1 is insufficient; statement 2 is sufficient, given the least expensive price exceeds 20.

This lecture uses two variables B and C to compare ratio and total, showing that combining statements with integer constraints yields C = 10 and B = 15.

Evaluate a data sufficiency question on total capacity equal to X times Y. Statement 1 alone suffices, while statement 2 alone does not; the correct answer is A.

Analyze a data sufficiency question about Kim and Sue buying an equal number of flowers, priced at $1 for roses and $0.50 for daisies, to determine who pays more.

Master distance, rate, and time problems by applying distance equals rate times time, calculating total distance and total time, and determining average speed from two travel legs.

Explore data sufficiency in a GMAT math problem by testing x values that produce integer square roots and reveal contradictions. Combine both statements to determine the correct answer.

Examine a horizontal cylindrical tank where the gasoline depth equals the radius, showing volume via base area times height is half the cylinder, using GMAT data-sufficiency reasoning.

Master data-sufficiency strategies for a two-variable problem by using integer constraints and extracting a common factor to determine adults and children, showing that two statements together are sufficient.

Learn how to compute triangle area via base times height, and remember every triangle has three heights, including external heights for obtuse angles.

Explore weighted average problems with two groups, determine the missing fifth value, and assess data sufficiency using ratio and inverse ratio concepts to decide if data are enough.

Solve exponents with the power-of-a-power rule. Apply data-sufficiency reasoning to determine x and y from the equations, yielding y = 7.

Solve a GMAT data-sufficiency problem with a base amount and a 5 percent commission, showing that statement 2 suffices and the correct answer is D.

Relate donuts and bagels through a two-variable equation to determine 5D+3B, extract a common factor, and assess data-sufficiency by noting one statement suffices while another does not.

Explore how to assess data sufficiency for a GMAT geometry question by testing extreme configurations, analyzing area ratios in an isosceles right triangle, and using strategic plugging in values.

Check if a reduced fraction yields a terminating decimal by having a denominator with only powers of 2 and 5; e.g., 1/2 and 52/100 terminate, while 1/3 does not.

Explore solving a GMAT inequality with positive r and s by preserving the inequality through multiplication and cross-multiplication, and using even-root reasoning to compare r and s.

Reveal that k is odd and k+1 is divisible by 3, using digit-sum reasoning, and show the combined data are insufficient.

Deduce that x and y are integers with x+y between 6 and 8, so x+y = 7; show that statement two alone fixes x and y, confirming x+y = 7.

Analyze mortgage payments, real estate taxes, and home insurance totaling 12000 using algebra to form a single equation and assess sufficiency.

Evaluate how to determine inequality sufficiency in GMAT by cross-multiplying positive quantities, showing ad < bc and that dividing by a positive fraction preserves the result, making statement 2 sufficient.

Learn to solve GMAT data-sufficiency overlap questions by analyzing two groups, using percent relationships (20% of x = 30% of y), and plugging numbers (x=60, y=40).

Learn to solve the GMAT data sufficiency questions by interpreting the ceiling operation ⌈x⌉, plugging in convenient numbers, and deciding when individual or combined statements are sufficient.

This lecture analyzes a data sufficiency question about x and y using two statements: x+y>0 and y^x<0. It shows that y<0 and x is odd, and together they imply x>y.

Decompose an L-shaped figure into rectangles to form a quadratic from the area, solve for x, and assess data sufficiency: area alone suffices, perimeter alone does not.

Apply a ratio-based approach to a clothing-count problem by assigning x to the ratio, using total constraints, and assessing statement sufficiency for shirts, jackets, and dresses.

Compute the central angle of a pie-chart sector from the circle area and sector area using the ratio angle/360 = sector area / circle area. Avoid relying on drawings.

Learn to solve inequalities with even and odd roots using single-root logic and benchmarks to estimate values, such as determining when x is less than minus two or minus three.

Explore inserting a cylinder into a carton by comparing can and carton dimensions, calculating how many cans fit per dimension, and multiplying, while recognizing when combined statements are insufficient.

Apply the weighted average axis to two-group mixtures; the ratio is inverse to quantities. Use x kilograms at $3 and y kilograms at $5 to determine sufficiency (B).

The lecture shows that with a constant difference, the median equals the average, here 120. Shifting one value by -5 and another by +5 preserves the average and the median.

Analyze an invented min/max operation and conditional definitions to determine min(10, w) in GMAT style, using data-sufficiency reasoning about w relative to 10 and 20.

Explore median concepts in an ordered data set and GMAT data sufficiency strategies, using statements 1 and 2, plug-in methods, and combining data to decide sufficiency.

Apply a fast, visual approach to GMAT Official Guide 2018 questions on time, distance, and rate, testing the two statements' sufficiency via quick plug-ins.

Sketch data to find a line's slope from height over distance; with statement 1, x-intercept is twice the y-intercept and slope is -1/2, hence sufficiency; statement 2 is insufficient.

Solve a GMAT® data sufficiency geometry problem by subtracting the inner triangle's perimeter from the outer perimeter of two equal triangles, then assess sufficiency by mentally stretching the drawing.

Assess data sufficiency by examining statements about sets S and T, their item counts and ranges, and determine if combined data yields two contradictory conclusions.

Apply the Pythagorean theorem to a right triangle, revealing an isosceles right triangle with equal legs. Either statement alone suffices to determine the target value in this GMAT data-sufficiency problem.

Analyze digit-based data sufficiency problems for three- and two-digit numbers by exploring carries, tens and units sums, and using vertical layout and convenient numbers to test sufficiency.

Explore a number-line overlap approach to GMAT data-sufficiency questions about voters' favorable and not-favorable groups, and determine when statements 1 or 2 are sufficient.

This lecture demonstrates solving a GMAT data-sufficiency problem on divisibility by testing statements, primes, and using plug-in numbers to determine when n is divisible by m.

Apply absolute-value reasoning to determine whether q < s < t using statements 1 and 2. Use a plug-in method with positive and negative values to test sufficiency.

In this data-sufficiency GMAT question, profit equals revenue minus expenses, and revenue per unit is $5, showing how unit count depends on price and total revenue.

explain gmat official guide 2018 question 395, where 15 numbers sum to 60 and any three numbers total 12, using standard deviation for sufficiency and show statement two is sufficient.

Assess data sufficiency for six numbers with average 75 under none less than 75 or none greater than 75, concluding the data are sufficient; note the zero standard deviation argument.

In a right triangle, the area is (a times b)/2 and a^2 + b^2 = c^2. Either statement 1 or 2 suffices to solve the three-equation system.

Assess a GMAT data-sufficiency style problem using scientific notation and orders of magnitude to determine a single positive value for k, applying even-root extraction and benchmark estimates.

Learn that external angles in polygons sum to 360 and apply to data-sufficiency questions by subtracting sums and evaluating statements A, B, C, and E to find x plus y.

Analyze data-sufficiency strategies for a GMAT math problem, evaluating whether statement 1 or 2 yields a unique value, using plug-ins and recognizing non-contradictory versus contradictory conclusions.

Explore data-sufficiency strategies for GMAT math by solving two equations in x and t, using cross multiplication and substitution, and assessing whether statement one or two suffices.