TAILIEUCHUNG - – THE GRE QUANTITATIVE SECTION – Example of solving an equation: 3x + 5 = 20 –5 = –5 3x =

– THE GRE QUANTITATIVE SECTION – Example of solving an equation: 3x + 5 = 20 –5 = –5 3x = 15 3x 3 = 3 x=5 15 Cross Multiplying You can solve an equation that sets one fraction equal to another by cross multiplication. Cross multiplication involves setting the products of opposite pairs of numerators and denominators equal. Example: x 6 = x + 10 12 becomes 12x = (x) + 6(10) 12x = 6x + 60 12x – 6x = 6x – 6x + 60 6x = 60 6x 60 6 = 6 x = 10 Checking Solutions To check a solution, substitute the number equal to the variable in the original. | THE GRE QUANTITATIVE SECTION Example of solving an equation 3x 5 20 -5 -5 3x 15 3x _ 15 3 3 x 5 Cross Multiplying You can solve an equation that sets one fraction equal to another by cross multiplication. Cross multiplication involves setting the products of opposite pairs of numerators and denominators equal. Example x x I210 becomes 12x x 6 10 12x 6x 60 12x - 6x 6x - 6x 60 6x 60 6x 60 6 6 x 10 Checking Solutions To check a solution substitute the number equal to the variable in the original equation. Example To check the equation from the previous example substitute the number 10 for the variable x. x x 10 10 _ 10 10 6 12 w 20 w 6 12 6 Because this statement is true you know the answer x 10 must be correct. 166 THE GRE QUANTITATIVE SECTION Special Tips for Checking Solutions 1. If time permits be sure to check all solutions. 2. If you get stuck on a problem with an equation check each answer beginning with choice c. If choice c is not correct pick an answer choice that is either larger or smaller. This process will be further explained in the strategies for answering five-choice questions. 3. Be careful to answer the question that is being asked. Sometimes this involves solving for a variable and then performing another operation. Example If the question asks the value of x - 2 and you find x 2 the answer is not 2 but 2 - 2. Thus the answer is 0. Equations with More than One Variable Many equations have more than one variable. To find the solution solve for one variable in terms of the other s . To do this follow the rule regarding variables and numbers on opposite sides of the equal sign. Isolate only one variable. Example Solve for x. 2x 4y 12 To isolate the x variable move the 4y to the other side. -4y -4y 2x 12 - 4y Then divide both sides by the coefficient of 2. 2x 12 - 4y 2 2 Simplify your answer. x 6 - 2y This expression for x is written in terms of y Polynomials A polynomial is the sum or difference of two or more unlike terms. Like terms have exactly the

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