GRE Sample Test 2 Quantitative Reasoning 2

The problem asks for the number of households that viewed both Program x and Program y, so this is a group problem. Use the group formula, which is Total = Group 1 + Group 2 − Both + Neither. Evaluate the information in the graph and the question stem to determine the values for the variables in the formula. The total is provided by the question stem, which states there were 80 million television households, so Total is equal to 80. Because this problem asks for approximates, choose numbers that are easy to work with. In 1984, approximately 15% of television households viewed Program x, so there were 0.15 × 80 = 12 million households who viewed Program x. Therefore, Group 1 is 12. In 1984, approximately 14.5% of television households viewed program y. This is close to 15%, so use 15% again to determine that approximately 0.15 × 80 = 12 million households who viewed Program y.
Therefore, Group 2 is 12. The problem states that 65 million television households viewed neither Program x nor Program y, so Neither is 65. Now insert all of these numbers into the group formula and solve for the value of Both. So, 80 = 12 + 12 − Both + 65 and 80 = 89 − Both, which means that −9 = − Both and Both = 9. Because the value for Program y was rounded up from 14.5% to 15%, this number is greater than the actual number. The only number less than 9 is 8.6. The correct answer is (A).