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 7 Problem Solving 163 Know When and When Not to Work Backward If a multiple-choice question asks for a number value and if you draw a blank as far as how to set up and solve the problem don t panic. You might be able to work backward by testing the answer choices in turn. 8. A ball is dropped from 192 inches above level ground and after the third bounce it rises to a height of 24 inches. If the height to which the ball rises after each bounce is always the same fraction of the height reached on its previous bounce what is this fraction A 8 B 4 C - 3 D - 2 E 2 3 In multiple-choice Problem Solving questions numerical answer choices are listed in order of value from least to greatest. To work backward from the answer choices start with choice C . If choice C is too great then you can assume choices D and E are incorrect and try choices A or B instead. The correct answer is D . The fastest route to a solution is to plug in an answer. Try choice C and see what happens. If the ball bounces up as high as it started then after the first bounce it will rise up as high as 192 inches or 64 inches. After a second bounce it will rise as high or about 21 inches. But the problem states that the ball rises to 24 inches after the third bounce. Obviously if the ball rises less than that after two bounces it will be too low after three. So choice C cannot be the correct answer. We can see that the ball must be bouncing higher than one third of the way so the correct answer must be a larger fraction meaning either choice D or choice E . You ve already narrowed your odds to 50 . Try plugging in choice D and you ll see that it works of 192 is 96 of 96 is 48 and of 48 is 24. 22 Although it would be possible to develop a formula to answer question 8 it s not worthwhile considering how quickly and easily you can work backward from the answer choices. In multiple-choice questions working backward from numerical answer choices works well when the numbers are easy and when few .
