GMAT Prep Course | Problem Solving : 302 Solved Questions

Count the exterior segments to determine the perimeter, merging partial lengths from the top and bottom. The total equals 12, so option B is correct.

Explains how to compare ticket revenue by multiplying price and tickets: minimum revenue with $40 and 200 tickets, maximum revenue with $50 and 300 tickets, and their difference.

Solve an average problem by setting four drivers' speeds to 80 mph, totaling 320; compute the missing miles from 72, 78, and 83 to get 87.

Compute a salesperson's weekly pay by taking 15% of the first 500 and 20% of the additional 800 in weekly sales, totaling 235 dollars.

Apply a 1-to-2 ratio between cover letters and coupons to a 3000-coupon start, subtract mailed coupons, and determine remaining coupons.

Analyze the x and y information to locate a point, identify a 45–45–90 right triangle, and determine the point is at (5, -5).

Apply a simple percent method to find discount: recognize that 150 is three times 50, where 50 is 10 percent of 500, yielding a 30 percent discount.

Identify a pattern in the fraction problem to solve quickly without long subtraction. Recognize that converting to a common denominator shows 1/2 minus 1/6 equals 1/3, yielding answer C.

Calculate total vacation costs by combining weekly moving charges with dog feeding. Use 11 dollars per week for 3 weeks and 4 dollars per day for 21 days, totaling 117.

Solve a GMAT problem on problem solving: in a 48000 distribution with two owners earning three times an employee's pay, ten employees each receive 3000 and each owner 9000.

Apply cross-multiplication to a GMAT currency problem: convert dollars to euros at 1$=0.8€, then convert the remaining 1/4 back at €1=$1.2 to obtain $120.

Count the x and y items (eight) and the v and w items (four), then reduce to a 2:1 ratio of x or y to v or w in order.

Master solving fraction addition and subtraction on the GMAT by choosing a common denominator, converting numerators, and applying quick, times-table based strategies for efficient results.

learn how to solve a linear equation by plugging the point (0, 2) into 2x + k y = 4 and isolating k, showing division to find the constant.

Explain forming bouquets with a white to red tulip ratio of 1:5 using 15 white and 75 red. Conclude five possible bouquets by arranging all flowers in whole-number multiples.

Apply a quick average method by rewriting grocery expenses as 70 plus or minus deviations, factoring out 70, and summing deviations to find the mean of 73.

Apply percent conversion and a 'Beyonce' trick to compute 125% of 5, keeping zeros in the denominator and obtaining 6.25 as the answer.

Learn to determine median duration of power outages from a nine-item list by ordering values and selecting the middle one with the (n+1)/2 rule, using 27 as the example.

Use dimensional analysis to compute miles per gallon from speed and fuel rate, converting 32 mph and 24 gallons per hour to an mpg value of 4/3.

Translate the problem across levels by setting one case to 100 paper clips, then apply the same scale to two cases to obtain the total.

Set up an equation for future ages to solve problem: Rebecca is 34 and her daughter is 8, so 34 + x = 2(8 + x) yields x = 18.

Use a 100-mile total to simplify percentage calculations, showing that traveling 110 miles (start to center plus 10 back) equals 55% of the complete journey.

Define probability as the ratio of favorable outcomes to total cases, count numbers with hundreds digit two from 200–299 within 1–350, and conclude the probability is two-fifths.

explains solving a GMAT problem on tax over 1000 at 7%, using plug‑in with option c and a rule for dividing by multiples of 10 to verify the answer.

Master solving a GMAT problem involving a 25% increase followed by a 1/3 decrease. Set up the equation 100 = (5/6) n and find the original number n = 120.

Test five consecutive integers (1–5) to compare statements about average and median; find the average is 3 and the median is 3, so all three statements are true.

Set up two equations with x tens and y 25 cent coins, totaling 16 coins and 235 cents, then use elimination to solve for y, number of 25 cent coins.

Determine the minimum number of questionnaires to mail so that 60 percent respond, yielding 300 responders. Using 500 as the total, 60 percent equals 300, confirming the solution.

Compute profit by multiplying 20 sets of three eggs by 90 cents and subtracting the $10 cost of five dozen eggs at $2 per dozen, illustrating correct unit alignment.

Compute the probability that a card numbered 1–24 is divisible by 2, 3, or 7 by counting multiples of 6 and multiples of 7, yielding 7 favorable outcomes.

Explore solving for a square’s side when a circle is inscribed, using the circumference 225 pi to deduce x = 25 and the perimeter is 100.

Learn to solve GMAT problem solving questions by plugging in values to test answer choices, compare x+y and z, and use order of operations to identify the largest value.

Solve a GMAT problem by counting elements: eight consecutive numbers form set x, and set y includes their values plus and minus four, yielding 16 numbers, eight more than x.

this lecture teaches solving GMAT problem solving questions without a calculator by using simple rounding and estimation to simplify numbers and identify the correct answer.

Determine how many 2x2 carpet squares fit in an 8 by 10 floor using the big-of-a-small approach, then multiply by the per-square cost to get $240.

Master a GMAT problem-solving trick by rewriting 893×79 as 893×78 plus 893, using the one-unit difference to solve without a calculator.

Define paperback fiction, paperback nonfiction, and hardback nonfiction; set up equations, adjust the lower count by 20 and double to reach parity, then solve for hardback nonfiction.

Set up a four-term average by adding numbers and using the definition that the average is the sum over number of terms. Multiply by four to isolate the unknown.

Explore a GMAT problem using halfway-point relationships among the school and three houses to deduce distances, concluding Abdul’s house is six miles from Kalas’s house.

Apply cross-multiplication to convert hours to minutes and relate fuel usage to driving time. Deduce that the car covers 90 miles at one mile per minute.

Identify five hollow doors and six solid doors, with hollow price 40 and solid price 80, then apply a 25% discount on solids to reach 560.

Solve an absolute value equation by plugging a candidate y and testing against the inequality left side less than 5.5 on GMAT questions.

Solve a triangle angle problem by using the 120-degree angle to deduce two 30-degree base angles, then determine the middle angle APD (and ABD/TBD) in the figure.

Use triangle angle sums and straight-line rules to find x, leveraging 180-degree relationships and angles like 30, 60, and 90.

Explain car x's distance: one mile per minute, five gallons per two hours, and actual 3.75 gallons. Cross-multiply and convert to minutes to get 90 miles.

Solve a GMAT problem combining five hollow pine doors and six solid oak doors, applying a 25% discount on the $80 solid price to compute a total of $560.

This lecture shows solving a GMAT problem with M, R, W summing to 25, where W is the largest; the minimal solution is W=9, M=8, R=8.

calculate total profit by subtracting total costs from total revenue for two bikes, given one sale price and costs, to determine the unknown gross profit of the second bike.

Solve a triangle where the apex angle is 120 degrees, use base angles equality to find each base angle as 30 degrees, then conclude angle ABT equals 30 degrees.

Identify how absolute values determine signs in equations with squares, showing that only the absolute values of k and m must be equal, regardless of sign.

solve a GMAT ratio problem where three workers are paid by hours in a 15:20:30 ratio, reduce numbers, find the hourly rate, and Makoto's pay.

Identify right-triangle side lengths using 3-4-5 and its multiples, determine Ted’s 10 and Mary’s 14, and compute the percent increase as 40%.

Apply plug-in testing on a PS problem with x minus three equals y to identify which answer cannot appear, using elimination and positive numbers to reveal the correct choice.

Set up an equation from spending half on fruits, a third on meats, a tenth on bakery, with six dollars, then use a common denominator to solve for the total.

Tackle a basic algebra problem by dividing by negative one quarter, recognizing it as -0.25, and applying the reciprocal to isolate the variable, yielding -4.

This lecture demonstrates solving a GMAT problem involving a rectangular box with volume 10, showing that doubling each dimension yields a volume of 80.

solve an algebraic fraction problem where an unknown number divided by two thirds equals 9/2; multiply by the reciprocal to eliminate the fraction, simplify to 3, and choose option c.

Analyzing a cube with an inscribed sphere shows that the sphere's radius equals half the cube's side length, yielding eight as the answer.

Apply a GMAT problem solving method to a gasoline price per gallon scenario, compute the increase in price, multiply by gallons bought, and estimate the extra amount paid.

Solve a GMAT problem on calculating phone charges: up to 75 minutes costs $8 after a 20% discount on $10, plus $0.065 per extra minute for 95 minutes, totaling $9.30.

Master GMAT problem solving by combining equations to extract x plus y; learn when to add or subtract equations, and use division by three to reach the answer.

Solve the GMAT problem by expressing city populations in terms: X is four times Y, and Y is two times Z, so X to Z is eight to one.

Compute the difference between the highest and lowest points by subtracting -0.5 from 2.2, noting the negative and that minus minus becomes a plus, yielding 2.7.

Sum the reciprocal squares, noting larger denominators shrink terms, so the first few terms dominate and the total hovers around 1.3–1.4, well under two.

Learn to estimate refunds from defects by applying 0.3% and 0.5% defect rates to 20,000 units, then multiply by $2,500 per unit to obtain a $150,000–$250,000 refund range.

Determine the patio area by subtracting a 20 by 20 square from a 40 by 35 rectangle, yielding 1000 square units.

apply rounding and decimal adjustment to simplify square roots and divisions, turning decimals into near integers like 42 and 400 to identify the closest answer.

Show how a 10 percent raise affects the average salary for five employees. Demonstrate that an old average of 650 becomes 715 after the raise, increasing by 65 dollars.

set up the four-test sum with an average of 78 to 312, then the five-test sum with an average of 80 to 400, and subtract to find e = 88.

Solve a GMAT problem on overtime pay to find the base hourly rate for the first 40 hours when 48 hours are worked, with overtime at 22 per hour.

Explain how a right triangle uses the fact that the non-right angles sum to 90 degrees, derive y = 40, and apply this to a ratio involving angle b.

Explore prime numbers, identify primes such as 2, 3, 5, 7, 11, and 13, and apply reasoning to square and divide by 12, calculating remainders to determine the correct option.

Master solving 2018 edition PS #45 by focusing on denominators, building common denominators, and using the flip-and-multiply rule for fractions.

Learn to add fractions by finding a common denominator, using the copy dot flip technique to convert division to multiplication, and approximate to choose the closest answer.

Explain that the sum of two digit numbers with reversed digits is always a multiple of 11, making 11 a guaranteed factor, illustrated by examples such as 23–32 and 45–54.

Lay out eight numbers starting at minus five with each subsequent term one higher, determine how many are positive, and note that zero is neither positive nor negative.

Explore a letters-to-numbers substitution method for GMAT problem solving: model oranges and boxes, use 100/5=20 boxes, subtract filled boxes to get 16 remaining, and back-substitute to answer.

Master plugging in numbers to test statements in GMAT problem solving. Use consistent values to evaluate choices and eliminate options, revealing the correct answer.

Determine Q's coordinates as the opposite of P's about the midpoint of line P Q, using negative values to solve GMAT PS practice.

Identify which option is not equivalent to 10y^2 = x^2 - 2x by factoring and applying the difference of squares, illustrating how to match or discard potential simplifications.

Compare daily shipping data across five companies to assess standard deviation and data spread; identify company B as having the largest variation in shipments.

Set revenue equal to cost by equating 2q to fixed cost 5040 plus variable cost 0.8q, solving yields 4200 units.

determine when revenue from selling units at $1.20 covers fixed costs of $9,900 plus per-unit cost of $0.65, solving to a break-even quantity of 18,000 units.

Determine the final position after 1,174 intervals by dividing into eight intervals per revolution and using the remainder. The arrow ends at E.

Master GMAT percent increase problems by using clean numbers and the formula increase over original times 100, shown with 80 to 180 for a 125% increase.

When xy = k with k negative, one factor is negative, so the product is negative in quadrants 2 and 4, identifying the solution 2 and 4.

Solve a GMAT problem by modeling the tank capacity as C, with initial fuel C/3 and final fuel 7C/10, then express C in terms of the given variables.

Set up an area equation with a bigger rectangle twice the smaller one and use GMAT answer choices to locate w; testing shows w=50 (B) satisfies the condition.

Explore solving a GMAT problem by evaluating 1/0.75 minus 1, recognizing 0.75 equals 3/4. Use fraction conversion or decimals and flip the denominator, multiplying by the top to get -4.

Compare simple interest and compound interest: with 6% simple interest on $8,000 and 8% compound interest semiannually on $10,000, the combined interest totals $1,296.

Solve a GMAT geometry problem using a semicircle of radius six and a right triangle; apply Pythagoras' theorem and radical simplification to determine the age.

Compute the fraction of the total harvest from the X trees. With total production of 350 and each tree yielding 10, the fraction is 10X/350, i.e., X/35.

Plug in n = 2 and n = 3 to test parity in the 2018 ps #62 problem. The expression 2n is always even, so option c is correct.

Solve fraction addition problems by finding a common denominator via cross-multiplication. Compute 71/72 and identify it lies between 3/4 and 1 for GMAT PS 63.

Compare two cars' fuel use by computing gallons from miles and mpg, using mental math tricks and rounding to estimate the difference between Y and X.

Minimize the expression |23 - 5y| by testing values of y using a table, showing the least value is 2 (at y = 5) per 2018 edition PS #65.

Master a GMAT problem by cross-multiplying to link numerator and denominator, using the fact that the denominator is greater than the numerator, and verify the resulting denominator.

Apply the seesaw principle to maximize two-day production, calculating the least and greatest possible units and revenue when prices are $2 for the first 40 and $2.50 thereafter.

Determine the constant k in the linear equation y equals k x plus three using given y and x values, then compute y for x equals four, obtaining 31.

Estimate square roots to compare expressions without a calculator, using √2 ≈ 1.4 and √3 ≈ 1.7, then judge that 8√5 is largest among 8√5, 7√6, and 6√7.

Apply distance = speed × time and a ds t approach to a two-vehicle problem with different start times; they reach 240 miles apart, ending at 2 pm.

Solve a gmat problem on land use to determine total acreage when 90% is cleared, 40% soybeans, 50% wheat, leaving 10% corn totaling 720 acres.

Track a population starting at three that doubles every month and express the 10th month as 3 × 2^10.

Identify common factors on both sides to simplify equations, factor out one third, and cancel terms by multiplying with reciprocals, as demonstrated in the problem set.

Identify that a y multiple of five and the trailing-zero condition require x to be a multiple of 10.

Analyze expressions with square roots and squares to determine which yield integers, using 82 and noting the square root of 82 is not a perfect square.

Use a multiplier to scale the ratio 2:3:5:6 to 30 hours, test each candidate as the 30-hour worker, sum totals, and find 192 as not possible.

Compute the fill times for two pumps by converting partial capacities to a full tank, apply the flip flop rule to add rates, and determine the 3.6-hour combined time.

Identify the option that makes the parameter k irrelevant by plugging into the linear equation; the correct choice is B, which zeros x and cancels k's influence.

Solve an inequality for x by moving terms, taking the square root with plus or minus, and using case analysis to select the valid continuous interval from the answer choices.

Explore a long GMAT problem solving walkthrough that models reading 50 pages per day across eight books, calculating total days and identifying the correct choice.

Compare the producer's market share in Western Europe from 42% in 1990 to 33% in 1993. Use x as total bikes to show a 0.09x decrease of about 9 percent.

This lecture teaches how to compare fractions to one half by subtracting from 1/2, using common denominators to identify the fraction with the smallest difference.

Prove that k^3 - k is divisible by six for all positive integers k by checking even and odd cases.

Tackle a fraction-based equation by multiplying through by the common denominator to cancel fractions, simplify to a clean equation, and determine the answer.

Use range to determine x as the largest or smallest number, set up equations like x-3=12 or 14-x=12, and apply a double-move strategy to find x.

Solve for a number that is 108 more than two thirds of itself, using a common denominator and the reciprocal to isolate the variable, resulting in 324.

Learn quick percent strategies for GMAT problem solving: treat 15% as 10% plus 5%, use 400 as a friendly test number, and verify with the answer key without a calculator.

Apply proportional reasoning to GMAT problem solving by comparing actual dosage to the standard 16 cm³ for 120 pounds; find the doctor was off by 2 cm³, or 12.5%.

Solve for t in terms of u using f(x) = sqrt(x-10) and the substitution u = f(T). Square both sides after adding 10 to get t = u^2 + 10.

calculate the percent of the 10 pounds that evaporated over 20 days by multiplying the evaporation rate by 20 and converting the result to a percentage.

Use the 5-12-13 triangle to see the diagonal is the circle’s diameter, giving radius 13/2. Compute area as pi r^2 = 169/4 pi, selecting 42.25 pi (B).

Identify the right triangle, apply the 3-4-5 rule to establish a 5 hypotenuse, then solve 1^2 + y^2 = 5^2 to get y = sqrt(24) = 2√6 and pick C.

The GMAT problem analyzes a 30 by 40 ft rectangle, fencing 900 sq ft (three quarters of 1,200), then explores shortening length or width and compares the resulting perimeters.

Apply the 30-60-90 triangle rule to identify the height and compute the area using half the base times height, solving for the correct answer in a GMAT problem.

Solve a GMAT problem by converting a 1 inch by 1 1/3 inch rectangle to 15 by 20 feet, then compute how many 6 by 6 inch tiles fit, yielding 1200.

Learn a GMAT problem solving approach for inequalities with M^2 + P^2 < 100 and M, P < 10. Use bounds and square-root reasoning to maximize MP.

Demonstrates relating x/y to a/b by flipping and cross-multiplying, aligning cd with ab and xy, and showing only the first two options hold while the third fails.

Determine the least k to multiply the long string of decimals by 10 to a certain power to obtain an integer; the solution shows k equals 12.

Learn to solve two quadratics by factoring 24 into 6 and -4, set factors to zero to get a = -6 and b = 4, yielding a+b = -2.

Analyze a GMAT vote distribution problem: 40% independents, 60% party voters; 10% of party voters back Ms. Robinson with 8,000 votes, and total equals 8,000 plus 6% of total.

Identify a right triangle inscribed in a semicircle and use a 3-4-5 type triple to determine the radius, then compute arc length as half the circumference, 5 pi.

Learn how to compute the manufacturer's average revenue per unit for two products priced at $20 and $17, with Q sold twice as many as P, giving $18.

Define glass as a unit and model juice with water volumes; day 1 yields $1.20 from two glasses, day 2 divides that by three for 40 cents per glass.

Compute total jugs by scaling from four per trip to seventeen trips, yielding sixty-eight jugs, then determine captains by dividing by seven and interpreting the final remainder.

Solve the GMAT problem by recognizing four identical rectangles forming a painting; with l = 3w and l×w = 1200, w = 20, so the answer is B.

Solve a GMAT problem on apples and bananas by enforcing integer quantities; show that 4 apples and 7 bananas yield a total of 11.

Identify the slope from the equation of a line by solving for y, yielding y = 9/7 − (3/7)x, so the slope is minus three sevenths.

Apply the machine-days concept to determine the number of machines needed to produce 3x units in four days, using proportional reasoning from x units in six days.

Learn how to solve multi-ratio problems by aligning common terms across groups, using equal multiples to normalize values, and extract the needed first-to-third ratio efficiently.

Analyze a GMAT PS problem by testing subtraction and division between numbers to identify a must-be-true statement. The third option works for both operations, indicating the correct choice.

Set up a proportional relationship between inches and kilometers, cross-multiply to solve for n using 2.3×10^14 inches and 3.9×10^4 inches, then adjust decimals and powers of ten.

Master GMAT problem solving for fractions and percentages by converting percentages to fractions, simplifying across steps, and using cross-divide tricks to isolate the target value.

Compute the circle's radius from center (2,-3) to (5,0) using a 45-45-90 triangle visualization, then compute area with πr^2 to get 18π.

Parse 200 percent more as double the base growth and add the increase to Joe’s 1-inch growth, yielding Sally’s 2-inch growth and a final 3-inch total.

Compute the fraction of techniques that are coupons or store displays by adding 22% and 18% to 40%, while table totals 90%, noting 'or' means plus and 'and' means times.

Solve a GMAT problem solving cost model for pollutant removal using 100000 P/(100−P) to compare removing 90% versus 80%, yielding a cost difference of 500000.

Set t = xy. Solve t^2 - t = 6 to get t = 3 or t = -2, which gives y = 3/x or y = -2/x.

Follow a GMAT problem solving example that converts half a mile to feet, substitutes L = 2 and D in feet, and simplifies without a calculator to arrive at 48.

Learn to simplify GMAT problem solving by rounding numbers, using near squares like 49, and applying square roots as fractional exponents to efficiently reach the answer.

the lecture demonstrates a flip-flop method to solve a three-printer work-rate problem, using combined and partial times to find the single-printer time of 20 hours.

Solve a GMAT problem by comparing volumes of three spheres, using their diameters to radii, factoring out common terms, and applying cube roots to find the big sphere's diameter.

Master the arithmetic concept of adding negative and positive integers across zero. Recognize opposite pairs cancel, leaving -25 and -24, which sum to -49.

Identify that the average of the three values is (s + t − r)/3, since r is negative on the left of zero.

Translate a word problem about Mark and Anna selling boxes into a linear inequality, solve for n under a less-than constraint, and identify 11 as the solution.

Identify a two-set Venn diagram with music and art, account for the intersection, and compute 5000 minus X minus Y plus Z to find remaining students.

Apply a 20 percent increase model to a total of 2400 stocks, solving with higher as 1.2 times lower to yield 1100 lower and 1320 higher price stocks.

Solve a two-set Venn diagram problem by identifying the stockholders and employees intersection, using 62% and 47% to find 9% both, then 53% stockholders only.

Determine the lowest class size that can form teams of eight and twelve, a GMAT problem, ensuring no remainders and using the answer key order to pick 24.

Compare spent versus budgeted amounts for payroll taxes and insurance using quick percent tricks, including 6 percent, 1 percent, and 10 percent methods. Identify which accounts show a budget variance.

Determine the rotation angle when moving point B to A around center P by plotting 90-degree increments, locating E between 180 and 270 degrees to find 240 degrees.

Solve a GMAT problem about a two-thirds majority: with 40 members, determine the greatest number who can vote against while still passing, which is 13.

Learn how to calculate percentage change by dividing the change by the original value, multiply by 100, and compare transitions to find the largest change, illustrated with table values.

Master divisibility of factorial expressions by splitting the denominator across top factors and applying the divisibility test, using 20 factorial divided by 15, 17, and 19 as a guide.

Learn to solve a pair of negative numbers with product 160 in this GMAT problem-solving lecture by forming and factoring a quadratic, yielding y = -8 as the valid solution.

Identify a downward-opening quadratic in a GMAT problem about filling a tank, revealing the maximum at t = 5 hours. The peak occurs seven hours after the start.

Analyze a gmats problem by tracing a runner’s southward distance and timing at eight minutes per mile to determine miles south he can run and still return using fractions.

Apply compound interest at 8 percent to a deposit x, then add x after year one; express total as W = (1.08)^2 x + 1.08 x and solve for x.

Explore how reciprocals flip large and small numbers, and estimate the sum of reciprocals using examples like 1/300 and 1/200, guided by the answer key.

Learn to solve two-machine work problems by modeling combined rate with a fraction, canceling 800 nails, and using a common denominator to isolate the time B.

Apply a 5:2:1 household budget ratio by introducing a variable N, solve 8N = 1800 to find N = 225, and determine food expenses as 2N = 450.

Learn to find the median by arranging four numbers in ascending order and averaging the two middle values, as shown by the 10 and 16 example that yields 13.

Solve a three-bag marbles problem where a third of all marbles are blue. Use percentages and fraction tricks to compute X and conclude the unknown bag contains 9 marbles.

This GMAT problem demonstrates removing decimals by multiplying numerator and denominator by the same power of ten, balancing top and bottom, and simplifying to solve decimal division without a calculator.

Solve a GMAT problem on divisibility by three for n>6 by testing n=7 and n=8 and checking expressions n, n+1, and n-4 to find the divisible option.

Learn how to compute the median using the (n+1)/2 formula and locate the median position in a data set of 161 employees, identifying the median age in the 20-29 range.

Translate height relationships into equations, deduce Ron and Barbara's heights, then arrange the results to identify the median.

This GMAT problem solving lecture substitutes y = 1 - x into 100x + 200y to reduce to one variable and test options, finding 199 yields positive x and y.

Maximize the division in this GMAT problem by making the numerator high and the denominator low, using decimal shifting to compute 190 divided by 21, yielding about 9.

Apply the slot method to count four-book selections from ten approved books by assigning four slots and multiplying 10, 9, 8, and 7 for the total.

Find the least n such that the product 1×2×...×n is divisible by 990 by ensuring the factors 9, 10, and 11 are covered; thus the smallest n is 11.

Compute the probability that M or R occurs when they cannot both occur. Add P(M)=0.2 and P(R)=0.4 to obtain 0.6 and note OR means addition, while AND means multiplication.

Compute total cost and revenue for 20,000 tools to determine profitability. Deduce profit per tool as 4.5 dollars, with total profit of 90,000.

This lecture analyzes an odd q with the median of q consecutive integers equal to 120, showing the largest number equals 120 plus (q-1)/2 and confirming with q=3 and q=5.

Apply the 30-60-90 triangle rule to a ladder problem, using a 70-foot ladder to find x = 35 and determine the height of the ladder above the ground.

Compute the area of a shape formed by a rectangle and a semicircle by adding the rectangle area (32) to the semicircle area (pi r^2/2), yielding 2 pi plus 32.

Solve a GMAT problem by testing t values against the fewer-than-eight-zeros rule, showing 3, 5, and 9 fail and none of the options satisfy the condition.

Determine the valid 3-digit codes from digits 0-9 given: first digit not 0 or 1, second digit 0 or 1, and second and third not both zero; yields 152 codes.

this lecture solves a GMAT mixture problem with 2 percent and 12 percent solutions totaling 60 liters at 5 percent, finding 42 liters of the 2 percent solution.

Jake and his sister's weights are modeled with J minus eight equals twice S and J plus S equals 78. They solve by substitution using initial-letter naming.

The lecture demonstrates that multiplying data by 0.8 changes the standard deviation, while adding a constant does not; the SD goes from 20 to 16 in the example.

Analyze a three-set Venn diagram of travelers to England, France, and Italy, identifying overlaps. Count disjoint regions to determine how many traveled to at least one country, yielding 67.

Apply the percent increase formula by dividing the sales increase by the original lower value, then approximate without a calculator using rounding to estimate a roughly 20 percent result.

Explore how remainders relate to divisors, convert to decimals, and master long division and cross-multiplication strategies for GMAT problem solving, including calculator-free steps.

Explore solving a zero-product scenario with two expressions; identify x from x(2x+1)=0 and (x+1/2)(2x-3)=0, then choose the common zero x = -3/2.

Determine the x over y ratio in a square-rectangle figure tiled with identical 45-45-90 triangles, using diagonal intersection and equal legs to compute perimeters.

Analyze an experimental math program across 32 schools where 37 teachers taught one, two, or three classes. The maximum number teaching three classes is 13, and the minimum is 0.

Calculate the mean and median for a five-term data set. The mean is 3 and the median is 2, so the difference is 1.

Solve a GMAT problem on a rectangular box using a 3:2:2 ratio and a volume x, apply a scale to find the height via a cube root.

Learn to treat a student–teacher ratio as a variable, adjust for enrollment and staff changes, and use cross-multiplication to determine the original number of teachers.

Solve an exponential inequality by converting bases: 25^n > 5^12 becomes 5^{2n} > 5^{12}, so 2n > 12 and n > 6; the smallest integer is 7.

Compute the probability of a woman who is a lawyer by multiplying P(W)=0.60 and P(L)=0.45 to get P(W and L)=0.27, using decimal placement and the and/or distinction.

Solve a four-year growth problem where an orchard increases by 25% each year. Use backward calculation with five time points and 4/5 to find the initial count (2560) trees.

Apply the median formula using N+1 over 2 to a bar chart of shipments, identifying the 6th tallest bar as the median and reading it around 310,000.

Learn to determine when a power of two divides 72 and when its next power does not, using prime factorization and step-by-step divisibility checks for k.

Explore the empirical rule and bell curve concepts, including mean, standard deviation, and the 68-95-99.7% ranges, with a problem-solving approach to symmetric distributions.

Model the problem of sharing sandwiches as fractions, use a common denominator to combine terms, adjust for four students who refuse the last sandwich, and obtain (4m-12)/(m-4).

Solve a GMAT quadratic problem by reversing a root to form an equation, and derive x^2 - 2x - 1 = 0 by expanding (x - 1)^2.

Start with 100 workers, note 16% unemployed in 1992 and 9% in 1996 after a 20% increase to 120; unemployment becomes 10.8, a 32.5% change.

Calculate the probability of drawing two non-defective pens without replacement from 12 pens (9 good, 3 defective). Multiply 9/12 by 8/11 to obtain 6/11.

Apply problem-solving techniques to timing-based door-light questions: track entry times, apply the 15-minute reset rule, and compute off intervals to determine total off time.

Calculate the percent decrease in the royalties-to-sales ratio from 3/20 to 9/108, using fraction flipping and a common denominator to estimate about 45 percent.

Model 10 fruits with algebraic equations: apples at 40¢ and oranges at 60¢; compute counts for a 56¢ average, then find oranges needed for a 52¢ average.

Solve a rhombus problem by applying 30-60-90 triangle rules to relate diagonals, revealing the ratio of the shorter to longer diagonal as 1 to √3.

Determine the largest k such that 3^k divides the product 1 through 30 by counting threes in multiples of three and summing their contributions.

Count the factors of three in the product 1 through 30 to determine the maximum k for which 3^k divides this product; there are 14 threes, so choose option c.

Break down 3^8 minus 2^8 via prime factors and the difference of squares, identifying 97, 13, and 5 as factors while spotting 35 as not a factor.

From two concentric circles, shaded area equals large minus small and equals three times small area, giving R = 2 r; thus large circumference is twice the small circumference.

Analyze a club seating problem using remainders: total leaves remainder 3 when divided by four and by five, yielding candidates like 23 or 43; with six per table, five remain.

Learn to solve GMAT problem solving questions by modeling averages with sums, daily pages, and days; use totals like 690 pages over 16 days to set up and solve equations.

Solve a problem with a square root by squaring both sides to eliminate the root, then isolate r in terms of s, using cross-multiplication to complete the steps.

Determine x between 3 and 100 where x/3 equals the square of a prime by setting x = 3p^2 and testing primes; find three valid values, 12, 27, and 75.

Learn how to label 12 participants with the fewest letters by using single and double digit letter combinations in organized slots; ab, ac, ad, bc, bd, cd appear, answer b.

Identify parallel and perpendicular lines by slope, then compute the slope with rise over run to select the correct option in a GMAT problem.

Model height with a downward opening quadratic, identifying the max at t=3 and height 150 feet. Compute the five-second height as 86 feet.

Solve each inequality by moving terms, yielding x > 4 and x ≤ 8; combine them to show x lies between four and eight, pointing to the correct option.

Solve a problem where David is three times Jeff and Paula is twice Jeff, then express G and P in terms of D and compute D + G + P (answer C).

Count the matches among eight teams by pairing each team with every other. Use the combination formula nCr (8 choose 2) with factorial to get 28.

Form two equations from the 336-dollar proposal and revised hours, solve for the hourly rate and hours, and confirm the actual hours equal 24.

Use a simple example like 3/5 to see that if p/q < 1 with positive numbers, flipping yields q/p > 1, helping you pick the option greater than one.

Compare shipping costs for three and five pounds with first-pound cost x cents and additional pounds at y cents, show that combining eight pounds is cheaper and calculate the savings.

Apply the rule of 70 to estimate doubling time for an 8% rate and solve a compound interest problem over 18 years, showing how $5,000 grows to $20,000.

Learn to interpret rounding and ranges around miles and gallons in GMAT problem solving, converting nearest-ten miles and nearest-gallon data into a clear min-max analysis of miles per gallon.

Analyze the number line from minus five to three with shading, translating into an inequality. Solve |x+1|<4 by two cases to determine the correct solution.

Apply the average formula to a 10-day revenue scenario: use six days at 360 and 400 per day to solve for the four unknown days, yielding 460 per day.

Factor the left-hand expression into pairs; the missing factors are 2 and 7, so y must be 14 to make the product a perfect square.

Explore how to apply the floor function to positive and negative numbers, identifying the greatest integer less than or equal to a given value.

Apply the head tail principle to quickly sum a sequence of consecutive numbers, as shown with Nancy’s weekly dollar savings, yielding 1378 after 52 weeks.

Plug in the known values and use the recurrence to compute x3 from x2 and x1, derive x2 from the same form, and conclude that x3 equals 4 (option c).

Compute the average speed of a 100-mile journey split between 40 mph and 60 mph using percent splits, the DST triangle, and distance over time.

Master units digit reasoning in GMAT problem solving by tracking the units digit of powers and identifying cycles, enabling quick solutions without full multiplications.

Explore counting alternating male-female lineups for a team of three males and three females using the slop method, multiplying choices across six positions.

Find the border width around an 8 by 10 rectangle by subtracting the inner area from the outer, solving a quadratic to obtain a valid width of 3 inches.

Express a fraction as a terminating decimal by factoring and pulling common terms, using powers of ten to shift decimals, and counting nonzero digits.

Use the head-tail principle to sum evens from 100 to 300; each pair yields 400, with 101 evens forming 50.5 pairs, for a total of 20200.

The lecture guides you through factoring 450, identifying distinct prime factors, and counting primes 2, 5, 11, and 13, with emphasis on counting duplicates once.

Describe a GMAT sequence where every other term equals the product of preceding terms after the second; a two-apart comparison reveals a fourth power, yielding option d.

Plug in simple, round numbers to model price per share and earnings per share. Compute the ratio's percent change and validate the answer by plugging numbers into the choices.

Model A, B, and C for one, two, and three effects in 300 subjects; derive C = 15 and A = 180 from 35% two effects and 435 occurrences.

Identify that m^-1 equals 1/3, square both sides to find m^-2 = 1/9, yielding the solution. Focus on the exponent pattern and what is being asked.

Convert the 20 percent markup to cost by dividing 250 by 1.2, compute total cost for 60 cameras, adjust for 54 sold, and conclude a profit of about 13 percent.

Use seven-item average with 68 as the mean, the median 84, and longest as 14 more than four times the shortest. The seesaw principle gives a maximum length of 134.

Use the general term formula to locate the 5th and 6th terms of a sequence. Compute their values as 21 and 38 and find the difference, 17.

This lecture shows how to minimize the least value among twenty numbers from -10 to 10 by using the largest digit with a negative sign, i.e., -10 repeated twenty times.

Learn to count letter arrangements with the rule that the i's are not adjacent; count six placements for i and six for d g t to get 36 total.

Use substitution strategy for percentage questions by plugging in numbers, such as 100 newspapers with 60% A and 40% B at $1 and $1.25, then compute revenue share.

Identify a difference of two squares to simplify a complex gmat problem, convert decimals to powers of ten, and derive the range four to six as the solution.

Solve a GMAT problem using average concepts, sum, and cross-multiplication to find that there were seven days with average 50, given a new 90-unit day raises the average to 55.

Identify the line’s x- and y-intercepts (0,2) and (3,0). Then verify candidate equations by plugging these points; the correct result is 2x+3y=6.

By comparing a two-digit number xy with its reverse yx, the difference is 27, which simplifies to 9(x−y)=27, giving x−y=3. The method extends to three-digit numbers xyz, built as 100x+10y+z.

Compute parallel resistance by summing reciprocals. Derive R from X and Y as R = XY/(X+Y), focusing on reciprocals.

Apply independent probability to a GMAT problem: find the chance that Xavier and Yuvan solve the problem while Zelda does not, using probabilities 1/4, 1/2, and 3/8, giving 3/64.

Explore GMAT problem solving by plugging in answer choices to make the left side equal the right side, testing x = -2 and starting with option c.

Master solving GMAT style problems with fractions and exponents by rewriting terms with a common base, combining powers, and simplifying to pick the correct option.

Solve nine-sided polygon interior angle problems by applying the polygon angle-sum formula (n-2)×180, using isosceles triangle properties to find a specific interior angle.

Learn to solve a 30-decimal GMAT problem by splitting even and odd tenth digits, applying rounding up or down, and evaluating E minus S across cases.

Clear the fraction by multiplying by x, form the quadratic x^2−5x+6=0, factor to (x−3)(x−2), and find x=3 or x=2 for GMAT problem solving.

Determine the share of x in the final seed mix by focusing on ryegrass content and solving the 40% vs 25% ryegrass equation with 30% mixture ryegrass.

Solve a three-category venn diagram gmat problem with 150 houses, using given totals and none/all counts to find the number with exactly two amenities, which equals 55.

In this GMAT problem solving video for question 230, learn to factor out 2 to the negative 17 and balance exponents to find the multiplier 3, leading to answer c.

Read the GMAT graph to determine the y-value when x equals 3 by tracing from the x-axis to the graph and confirming y = 1.

Demonstrates solving a GMAT percent problem by clarifying percent meaning, the subtraction order, and how 'off' indicates multiplication, with emphasis on writing the last term before the first.

Move the decimal six places to form 64/10^6, take the cube root to get 0.04, then the square root to obtain 0.2, using the beyonce rule to simplify.

Convert quantities across levels by translating boxes to cases to paperclips. Multiply by two for two cases to compute the total.

Calculate the probability that the hundreds digit is two for numbers 1 to 350 by counting 200–299 as favorable and dividing by 350; the result is 100/350, or 2/7.

Learn a GMAT problem-solving approach for tax on the amount over 1000: plug in numbers, start with C, and apply the Beyonce rule for dividing by ten.

Define x as the number of 10-cent coins and y as the number of 25-cent coins, with x+y=16 and 10x+25y=235, then apply elimination to find y=5.

Solve a rectangle perimeter problem by setting width as w and length as 2w; use 6w = 360 to find w = 60, then the length equals 120.

Solve an absolute value equation by testing a candidate y and evaluating the left side; pick the middle answer, C = 11/2, and verify the result is less than 11/2.

Analyze a GMAT problem with fractions: half on fruits, a third on meats, and a tenth on bakery. Use a common denominator and a reciprocal to find the total.

Compute the overall average by converting mixed fractions to improper fractions, sum the eight-packages total and the four-packages total, then divide 160 pounds by 12 to get 13 1/3.

Master decimal multiplication by ignoring decimals, multiplying the integers, and then reapplying the correct number of decimal places. Apply this technique to solve GMAT problem solving questions efficiently.

Visualize a base rectangular box with volume 10, then double its length, width, and height to obtain a second volume of 80, eight times the original.

In this problem, a bakery starts with 40 dozen donuts, half sold by noon, and 80 percent of the remainder sold by closing, leaving 4 dozen unsold.

Translate the word problem into math by treating percent as over 100 and of as times 30; apply the reciprocal method to cancel factors and solve for 500 percent.

Solve the ratio 2 to 1/3 by flipping the denominator and multiplying, yielding 6 to 1; practice this fraction-in-denominator technique to simplify similar GMAT problems.

Apply averages and sums to solve a GMAT problem: four tests at 78 total 312; five tests at 80 total 400; the missing score is 88.

Define prime numbers and show examples like 2,3,5,7,11,13, noting 1 is not prime; illustrate that squaring primes greater than 3 and dividing by 12 leaves a remainder of 1.

Focus on the denominators to create a common denominator, convert 1 to 3/3 and 2/2, and use flip-and-multiply to simplify complex fractions before subtracting to get 1/12.

Apply factoring techniques from the problem set, including dividing by constants and using the difference of squares to identify equivalent expressions and select the non-equivalent option.

Solve a GMAT problem by converting 0.75 to 3/4, subtracting 1, and flipping the fraction to multiply against the top, yielding a negative four as the answer.

Apply a plug in approach by testing two and three for each option to determine which yields even results in all cases, explaining why option c is correct.

Demonstrate adding fractions by obtaining a common denominator and using a quick cross-multiplication trick; the sum 71/72 lies between 3/4 and 1.

Using a GMAT problem, compare gallons used by two cars over 12,000 miles with 25 and 11.9 mpg, applying division, rounding, and quick mental math tricks for efficient solving.

this lecture demonstrates solving a GMAT problem by building a table to minimize the absolute value of 23 − 5y, testing values to show the least value is 2.

Break each radical into perfect squares, extract the square roots, and combine to obtain 9 sqrt5.

Determine the constant k in the equation y = kx + 3 from given y and x, then compute y for x = 4, giving 31.

Learn to access an adaptive GMAT practice test on successprep.com, then log in to view analytics, pacing, and data on math and verbal performance, with benchmarks against top schools.

Analyze a ratio of 2:3:5:6 to anchor 30 hours, scale with multipliers, and compute individual and total hours, identifying 192 as the only impossible total.

Determine the percent evaporated from 10 pounds by multiplying the daily rate 0.1 by 20 days and converting the evaporated amount to a percent of the original.

On day one, mix orange juice and water equally to make two glasses at 60 cents each. Day two yields three glasses sharing $1.20, i.e., 20 cents per glass.

Convert to cents using 70c apples and 50c bananas, enforce integer counts, and deduce that the sum of apples and bananas is 11.

Solve for y to express the line in y = mx + b form, then identify the slope m as -3/7 from the coefficient of x.

Learn how to solve complex ratios by aligning shared terms across the second-to-fourth, first-to-second, and third-to-fourth ratios, scaling to common values, and deriving the first-to-third ratio, which reduces to 4:5.

Set up a cross-multiplied ratio between kilometers and inches, with inches at the bottom, to solve the sun-to-planet distance; use rounding and powers of ten to match the answer key.

Master the average formula by linking the total sum of 10 tests to the known average of five students, then compute the remaining group's average.

Compute the circle’s radius using a right triangle from center (2,-3) to (5,0) with legs 3 and 3, giving r = 3√2, then find area πr^2 = 18π.

Solve a GMAT problem by treating L as lanes, D as highway length in feet, and s as speed in mph, converting miles to feet and simplifying without a calculator.

Compute how many of 2400 stocks closed higher versus lower by applying a 20% higher-price relation. Solve for the counts and verify with the total.

Recognize the equation y = (3x - 5)/2, divide by y, multiply by two, and add five to isolate x.

Identify the lowest possible number of students that can be evenly split into teams of eight and twelve by testing answer choices from the smallest upward, as illustrated by a GMAT problem.

Practice problem solving on GMAT style geometry by determining the degree measure when rotating segment B to A, using quadrant reasoning to identify angles between 180 and 270, specifically 240.

Solve a two-thirds majority problem by turning two-thirds of 40 into 27 in favor and 13 against, identifying 13 as the greatest possible number voting against.

Apply a 5:2:1 budget ratio to a three-category household total of 1800, attach a variable to the ratio, and compute the food expense of 450.

Explain semiannual compounding at 8% on $10,000, yielding 4% per half-year, $400 first six months, $416 second half, total interest $816.

Learn to divide decimals on the GMAT by removing decimals through adjusting the denominator and top numbers. Balance top and bottom to solve without a calculator.

Test numbers n>6 for divisibility by three by evaluating n, n+1, and n-4 for n=7 and n=8, starting with option a; only the first works.

Apply order of operations to simplify nested fractions in a problem, use reciprocals for division, compute a common denominator, and see the expression reduce to zero.

Solve a water composition problem by using hydrogen to oxygen ratios, set up a proportion with 144 g of water, and cross‑multiply to find the grams of oxygen.

Interpret the question as radiation intensity; each step from n to n+1 multiplies by ten. From three to eight yields ten to the fifth power, so the answer is C.

Learn to solve for k by isolating the variable and eliminating left-side terms, using multiplication and subtraction to simplify, leading to the final answer d.

Explore how squaring and cubing decimals with negatives affects their order on the number line. Learn to rank a^2 and a^3 by sign and magnitude.

The lecture solves a GMAT problem: Mary earns 60% more than Tim, who earns 40% less than one, so Mary’s income is 0.96 of one’s income, answer C.

This lecture explains solving a grid distance problem by analyzing a 5x5 case to count unique city distances and extending to 30x30 to yield 435.

Apply cross-multiplication to a GMAT problem with a length-to-width ratio of 3.3:2 to find the length when width is 8, yielding about 13.

Develop GMAT problem solving skills by interpreting a fraction setup, applying zero over one rules, and solving for the variable C when the top equals zero.

Solve a GMAT problem: calculate the average price per person for 15 diners with a 15% gratuity, using fractions and reciprocals to get $12 per person.

Apply the flip flip rule to two-machine work rate problems, convert hours into rates, add them, and flip back to find the total time.

Use powers of ten to simplify 1.2×10^12 expenditure by 240 million population to show a per capita expenditure of about $5,000 per year.

Analyze a GMAT problem by counting options at each crossroad in a maze, and multiply those choices to determine the total number of paths.

Decode the dot circle notation and simplify square roots by factoring into perfect squares, as shown with 5×45 and 60, to solve GMAT problem solving questions.

Decode a GMAT problem by applying foil, recognizing the repeating decimal bar, and shifting the decimal with positive and negative powers of ten to obtain the final value.

Choose day-crew numbers to relate night-crew output, compute night boxes as three-fourths of day output, and show day crews account for 5/8 of all boxes.

Explain a GMAT problem about rain probability over three days, requiring rain on Monday and no rain on the other two days, yielding 0.128 (option B).

Apply the triangle area formula in a coordinate setup to solve for height, using area 12 and base 4 to find height 6, and identify the corresponding y-coordinate.

master the distance-speed-time triangle to solve relative-speed problems, find catch-up time, and compute total distance between cars using relative speed and time formulas.

Substitute every x with 1/x in the expression, then use a common denominator and flip the bottom fraction to simplify the squared form.

Use parallel lines and corresponding angles in a right triangle with a 50-degree angle; apply the 180-degree angle sum to find x and y, concluding with 270 degrees.

The lecture shows using a 45-45-90 right triangle and the Pythagorean theorem to solve for the circle radius r from the center to origin, giving r = k/√2.

Use a division-by-point-value approach to solve the beads problem; divide the total by red (7), yellow (5), green (3), and blue (2) to reveal counts, showing two red beads.

Solve a two-set Venn diagram problem for biology and chemistry students using totals of 200, biology 150, chemistry 130, and at least 30 outside to determine the intersection.

Access a computer adaptive GMAT practice test with timed sessions, detailed analytics, pace, and data on problem solving and data sufficiency.