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PSAT Math Multiple-Choice Practice Question 157

Question: 157

A major hospital conducted a study on a new experimental physical therapy method for some of its patients recovering from knee-replacement surgery. At the beginning of the study, 485 patients who had just had knee-replacement surgery were selected for the study; 194 of the patients were given the experimental physical therapy, and the remaining patients were put into conventional physical therapy. A summary of the recovery times for the patients who were in the study is shown in the table below.
Recovery Time for 485 Patients in the Study
Recovery TimeExperimental TherapyConventional Therapy
6 months or less82151
More than 6 months112140

Of the patients in the conventional physical therapy, the ratio of those who had one knee replaced to those who had both knees replaced is approximately 3:7. Which of the following is the best approximation for the number of patients in the conventional physical therapy who had both knees replaced?

Correct Answer: D

Explanation:

D

The question asks for the number of patients who had both knees replaced. The ratio of those who had one knee replaced to those who had both knees replaced is 3:7. Add the parts of the ratio together to determine the number of people in one group, which is 3 + 7 = 10. Now use the chart to determine the actual number of people. The question only refers to those in conventional physical therapy. According to the chart, there is a total of 151 + 140 = 291 patients in the conventional physical therapy. If there are 10 people in a group and 291 people total, divide 291 by 10 to find that there are 29.1 groups. This multiplier can be applied to both parts of the ratio to find the actual numbers. The question asks about those with both knees replaced, which is the 7 in the ratio. Multiply the ratio by the multiplier to find that there were 7 × 29.1 = 203.7 people in conventional therapy that had both knees replaced. The question asks for the best approximation of this number, so round the number to 204. The correct answer is (D).

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