rdlc barcode c# THE QUANTITATIVE SECTION in Software

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THE QUANTITATIVE SECTION
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Algebraic Equations and Analytical Geometry
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THE IMPORTANCE OF ALGEBRA
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Understanding algebra is essential in analyzing almost any significant quantitative business problem; therefore it is one of the central mathematical skills tested on the GMAT Indeed, several university studies of the GMAT scores of MBA students have indicated that a low quantitative score is an excellent predictor of which students will struggle in their first-year classes High GMAT scores do not guarantee success, but low quantitative GMAT scores make admissions directors nervous Thus, admissions committees are generally more interested in an applicant s quantitative score than in his or her verbal score If you attend one of the more quantitatively rigorous programs, you will probably need to understand calculus as well For now, at least, you will not need that for the GMAT, but you will need algebra Consider the following problem
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Application: The Breakeven Point
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Hector runs a one-product widget shop Each month, his fixed costs, whether he produces anything or not, amount to x dollars The marginal cost of producing and selling one widget is a constant y dollars, regardless of the number he produces He generally can sell widgets for z dollars each What is the minimum number of widgets he must produce, assuming he sells every widget he produces, to break even (neither make a profit nor incur a loss) in a given month A x (y z )
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x B (z y ) C x x D z x E y In its general form, the breakeven point is an important question for any business, and so it appears in a number of different forms on the GMAT The essence of dealing with a question like this is to take the facts and conditions given in the question and turn them into a mathematical equation that can give you the information you need Algebra the manipulation of variables in equations and inequalities is the tool that will enable you to do this
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You are going to see a lot of word problems on the GMAT, and you will need to take the information in the question and turn it into a form you can work with In the preceding question, you are going to need to form an equation before you can use any of your algebraic tools Your first step is to consider the different items that need to have a place in your equation The problem gives you the following: Fixed costs: Marginal cost: Revenue: x y per widget z per widget
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You also need to consider the value that you re solving for Since you re looking for the number of widgets, add that to your list: Number of widgets: n The problem asks for the point at which the total cost equals the revenue, so you need to set up an equation that puts all the costs on one side of the equal sign and all the revenues on the other Your equation might look like this: x + ny = nz This equation adds the fixed costs to the total marginal costs (number of widgets times the marginal cost per widget), and sets that equal to the total revenue (number of widgets times the selling price per widget) Now, since the problem asks you for n, the number of widgets Hector sells, you need to solve for n
Solving Algebraic Equations
Solving simple algebraic equations is a straightforward and easily repeated process
Method: Solving an Algebraic Equation The basic approach to solving an algebraic equation
in one variable is to isolate that variable You do this by rearranging terms until all the variable terms are on one side of the equation, and all the constants are on the other side Then, combine the variable terms together and the constants together until there is only one variable and one constant left In the equation we just formed, we need to isolate n, which is the number we re looking for: To get the n on one side of the equation, subtract ny from both sides x + ny ny = nz ny
x = nz ny Now it s time to get n alone To simplify matters, factor out the n on the right side x = n(z y) Now to get n alone, all you have to do is divide by (z y)
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