GMAT Prep Course | Problem Solving : 302 Solved Questions

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.

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.

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.

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.

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.

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.

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 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.

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

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.

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.

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.

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 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 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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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

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.

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.

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.

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.

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.

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.

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.

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

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.

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.