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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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

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.

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.

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.

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).

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).

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.

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.

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.

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.

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.

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.

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.

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).

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.

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.

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.

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.

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 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.

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.

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.

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.

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).

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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 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.

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

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.

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.

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.

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.

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.

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.

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.

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.

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.