PSAT Math Multiple-Choice Question 553: Answer and Explanation

Question: 553

A cardiologist uses the guidelines for maximum recommended heart rate (measured in beats per minute) shown in the table below, which vary based on a patient's age. One of the cardiologist's patients, age 55, wants to start an exercise program. The cardiologist recommends that the patient maintain a heart rate greater than 50% and less than 85% of the maximum recommended heart rate while exercising. Which of the following expressions gives the range in which the patient's heart rate, H, should be during exercise?

Age	Maximum Recommended Heart Rate
50	165
55	160
60	155
65	150

• A. 50 < H < 85
• B. 80 < H < 136
• C. 85 < H < 160
• D. 150 < H < 160

Correct Answer: B

Explanation:

(B) Use the table to find the maximum recommended heart rate for a 55-year-old
person—160 beats per minute. Then take 50% and 85% of 160 to determine the lower and upper bounds of the recommended heart rate:

50% of 160 = 0.50 × 160 = 80

85% of 160 = 0.85 × 160 = 136

So the range is between 80 and 136 beats per minute, which is expressed as the inequality 80 < H < 136.