Peterson's Master the Gre 2010 - Part book includes 9 full-length practice tests , thorough reviews of every section on the exam, and expert tips and strategies from a test prep pro. GRE (Graduage Record Examination General Test) is a commercially-run standardized test and an admission requirement for many graduate schools in USA and other English-speaking countries. GRE can earn you between 200-800 points. | Chapter 10 Math Review Number Theory and Algebra 243 24. a b 30 2b 60 - 2a Column A Column B a b A The quantity in Column A is greater. B The quantity in Column B is greater. C The quantities are equal. D The relationship cannot be determined from the information given. The correct answer is D . An unwary test taker might waste time trying to find the values of a and b because the centered data appears at first glance to provide a system of two linear equations with two unknowns. But you can easily manipulate the second equation so that it is identical to the first 2b 60 - 2a 2b 2 30 - a b 30 - a a b 30 As you can see you re really dealing with only one equation. Since you cannot solve one equation in two unknowns you cannot make the comparison. Whenever you encounter a Quantitative Comparison question that calls for solving one or more linear equations stop in your tracks before taking pencil to paper. Size up the equation to see whether it s one of the two unsolvable kinds you learned about here. If so unless you re given more information the correct answer will be choice D . FACTORABLE QUADRATIC EXPRESSIONS WITH ONE VARIABLE A quadratic expression includes a squared variable such as x2. An equation is quadratic if you can express it in this general form ax2 bx c 0 Where x is the variable a b and c are constants numbers a A 0 b can equal 0 c can equal 0 Here are four examples notice that the b-term and c-term are not essential in other words either b or c or both can equal zero 0 If the centered information in a Quantitative Comparison consists of one or more linear equations never assume you can solve for the variable s . 244 PART IV Quantitative Reasoning Quadratic Equation 2w2 16 x2 3x 3y 4 - y2 7z 2z2 - 15 Same Equation but in the Form ax2 bx c 0 2w2 16 0 no 6-term x2 3x 0 no c-term y2 3y 4 0 2z2 7z 15 0 Every quadratic equation has exactly two solutions called roots. But the two roots might be the same. On the GRE you can often find the two