Break Away - GMAT Problem Solving - 65 Solved And Explained

Use fractions and ratios to solve a three-friend salary problem by setting one income as x and others as 1.5x and 3x, then compute Sam’s savings share as 3/55.

Break down the expression into prime factors and simplify to test divisibility. Check divisibility by 77, 135, and 14 to identify the correct option.

Two cars start from the same point on a circular track, one at 6 mph and the other at 8 mph in opposite directions, to find their meeting time.

Explore how to count combinations of four fruits from two baskets, each with five varieties. Apply the combination formulas and factorials to determine all distribution cases from each basket.

Explore how substituting values into a speed equation reveals when a car exceeds 50 mph, with 0 and 3 seconds meeting the threshold while 1 second does not.

A three-set Venn diagram helps solve a classic problem about English, science, and history registrations in a class of 100, revealing how many registered for only one subject: 73.

Learn to solve a three-set GMAT problem with a Venn diagram by expressing counts in terms of the all-games variable and computing the at-least-one fraction.

The lecture models a 1-meter pipe with marks at fractions like 1/5 and 1/15, then computes distances between marks to determine which options fit as piece lengths.

Solve for the relationship between A, B, and C using exponentials with the same base, and confirm option B as the correct answer.

Explore a geometry problem: derive the area of a square using a rectangle and the Pythagorean theorem, with x and y, to identify the correct option, option B.

Explain how to compute the probability all three fail by taking complements of X, Y, Z success and multiplying. Conclude that option B is correct.

From the 200 square inch total, frame area is 50 and the picture area is 150, with the picture’s length twice its width; the square’s area matches 150 square inches.

Explore angle relationships in a figure by analyzing corresponding angles, triangle angle sum of 180 degrees, and straight-line angle properties to identify the not true statement.

Represent each item in terms of a base unit x, with blue bags 2x and yellow bags x, then use totals 500 and 300 to find yellow shoes as 100.

Analyze how a shop uses two offer options to determine a fair price, solving equations like 25% of x equals 500 plus a percentage of x.

Solve a speed-distance work problem where A and B work together, determine B’s fraction of the job, using speed, ratios, and work-time relationships.

Learn how to count seating arrangements for four people in four seats under two driving restrictions: any one may drive, or only X or Y may drive, using factorial methods.

Explore a GMAT problem where the town's population doubles in even years and halves in odd years, using a backbone approach to deduce end-of-year populations from 150 million.

Solve a GMAT problem by tracking the units digit of an expression with a and B, where B is the cube of an even prime. Conclude 6.

The lecture explains how to form all three-digit and two-digit numbers from the digits a, b, and c, using permutations to count distinct arrangements (3P3 = 6, 3P2 = 6).

apply the definition of averages to a GMAT production problem to analyze 14-day and 15-day totals. solve for the daily productions x and y to determine the 15th day's output.

Analyze how the class average evolves as students leave and join, using the start-of-month average, end-of-month average, and counts to derive the start-to-end ratio.

A horse and a car race for speed, using 80 mph and an eight-hour head start to illustrate that the same distance yields inverse speed ratios.

calculate the meeting point for two trains from opposite ends of a 1400-mile line at 60 mph and 80 mph, and determine the 200-mile difference in distances traveled.

Solve a GMAT mixture problem where one-third of a tank is a mixture of chemicals and water; water evaporates, and equal proportions yield a 60-gallon capacity.

Apply proportion and ratio reasoning to a GMAT problem with apples, oranges, and bananas, solving for fixed and changing quantities.

rewrite 216 as a power with a common base, equate the exponents, and solve the inequality to find the smallest integer x; the solution yields x = 4.

Analyze a GMAT problem by comparing engineers to managers and determining how many more managers to hire while keeping engineers fixed. The result shows 25 percent as the required increase.

Learn to compute profit from buying price and selling price for 15 identical boxes, using cost per box and selling price per box to arrive at 40 percent profit.

Compute the combined production rate by summing the individual speeds of machines x and y, then multiply by 60 hours to determine total units.

Solve a GMAT problem on applying sequential discounts to a product's price, showing why successive discounts aren't additive and how to compute the final price, which yields 28 from 100.

Evaluate a GMAT problem by turning a divisor in the denominator into a multiplier in the numerator, applying the concept of inverting fractions to simplify the expression.

Solve a GMAT-style geometry problem: a triangle inside a square, use a 3:4 ratio for the legs, apply Pythagoras, and compute the area as 54 square inches.

Form equations from ages x and y, using six years ago and nine years from now, including Billy's age is four times Sile's age, then equate to find their ages.

The lecture demonstrates evaluating an algebraic expression by substituting a negative value for x, explains how multiplying an odd number of negatives yields negative, and shows the result as -14/3.

Show how equal averages of X, Y, Z and A, B, C imply X+Y+Z = A+B+C, proving the first statement true; the second and third need information not provided.

Explore interchanging digits in a two-digit number, derive the difference between the original and reversed numbers when the digits differ by 1, and confirm the difference is 9.

Breaks down a complex divisibility problem by factoring the given number and testing each option, concluding that seven is not a divisor.

solve a gmat problem solving exercise by comparing working and non-working lights on football field crossings, using fractions, ratios, and an equation to find the unknown lights and 50 percent.

Solve a GMAT problem by comparing two leasing agencies, formulating equations from fixed charges and usage costs, and finding the hours where costs are equal.

Count right-angled triangles with integer coordinates in -7 < x < 5 and 3 < y < 13 on the xy-plane, with a vertex on the x-axis.

Identify positive integer values of x that make 14x/60 an integer, use prime factorization to cancel the denominator, conclude x is a multiple of 30, and count eight options.

Solve a quadratic equation involving fractions to find y, showing y^2 = 4 and y = ±2, with the correct option B being negative.

Offset a 20 percent drop in the workforce with a 25 percent wage rise to keep weekly income constant, illustrating percentage change in GMAT problem solving.

Break down a three million product of fruit points to determine the ratio of oranges to figs, using prime-factor reasoning and GMAT problem-solving techniques.