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n( z y ) x = (z y ) (z y )
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When you cancel out, you re left with x answer choices is (z y ) , or B
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Solving equations involving just one variable is really quite simple: put your variable on one side and do the arithmetic The trick, of course, is setting up the equation properly in the first place; the best way to practice this is to scan through the word problems in the practice test and then put their facts and conditions into algebraic form by writing an equation for each one Another single-variable problem that is similar to the breakeven problem is that old classic, the time and distance problem This sort of problem could look like this: Greg can bike from his home to Monkey Hill in 4 hours if he rides at a speed of 30 miles an hour How much time in hours will it take him to return home if he bikes back on the same route at a pace of 20 miles per hour What are your constants and variables Distance between home and Monkey Hill: let s call this D Pace on ride to Monkey Hill: 30 miles per hour Time of ride to Monkey Hill: 4 hours Pace of return trip: 20 miles per hour Time of return trip: the unknown The essence of any time and distance problem is the formula distance = rate time This formula has three equivalent forms It is important to be familiar with all three forms so that you can use the one that is most efficient for what you need to find D = R T D R =T D T = R To solve this problem, you actually need to set up two single-variable equations First, you need to determine the distance from home to Monkey Hill: D=R T D = (30 miles/hour) (4 hours) D = 120 miles Then, you set up an equation for the return trip, but this time solving for time: D =T R 120 = 6 hours 20 Therefore, it will take Greg 6 hours to bike back home
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Other similar problem types include: Fuel efficiency: distance = quantity of fuel distance per unit of fuel Production of multiple units: number of total products = (production rate of unit A time) + (production rate of unit B time) The units here could be printers, lawnmowers, pretzel makers, or anything else All of these word problems can be solved by following the same simple steps: 1 Understand what is being asked 2 Identify the constants and variables 3 State them as an equation 4 Isolate the desired variable and solve the equation
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The GMAT does not write out the algebra of word problems for you that s what makes them word problems The simplest and probably most common type of algebraic equation that you are going to see printed in GMAT questions is the linear equation Linear equations take the form y = mx + b Each of the constants and variables in a linear equation has a specific name and function: x is the independent variable, y is the dependent variable, and m and b are constants The variables x and y are termed independent and dependent, respectively, because the value of y is said to depend on that of x, whereas the value of x is taken to be generally independent of that of any other variable Equations of this form are called linear because they graph as straight lines More specifically, following this form, m is the slope of the line, and b is the y-intercept, the point where the line meets the y axis Graphically, the slope is the rate by which the y value (the dependent one) increases as the x value (the independent one) increases Accordingly, it is the steepness with which the line moves up or down (in the positive y direction or in the negative y direction) as it moves to the right (in the positive x direction) It can also be calculated as the rise over the run that is, the number of units that the line rises divided by the number of units that it runs, going from any one point on the line to another point on the line For example, if you wanted to graph the equation y = 2x + 6, it would look like the following:
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