PSAT Math Multiple-Choice Question 567: Answer and Explanation

Question: 567

David is developing a fitness plan and wants to get his weight to a level that will be considered healthy in terms of the body mass index (BMI) calculation. The currently recommended BMI is between 18.6 and 24.9. To calculate BMI using inches and pounds, David takes his weight in pounds and divides it by the square of his height in inches. Then he multiplies the entire result by 703. David is 6 feet, 3 inches tall and currently weighs 260 pounds. To the nearest whole pound, what is the least number of whole pounds he needs to lose in order for his BMI to be within the healthy range

• A. 61
• B. 68
• C. 75
• D. 83

Correct Answer: A

Explanation:

(A) First solve for the weight that David must be in order to have a BMI of 24.9 given his height since this would put the BMI within the appropriate range. Use the wording in the question to set up an equation, "To calculate BMI using inches and pounds, David takes his weight in pounds and divides it by the square of his height in inches. Then he multiplies the entire result by 703." This gives the following BMI equation:

Since David is 6 feet, 3 inches tall, his height is (12 × 6) + 3 = 75 inches. Plug in 24.9 for the BMI and 75 for the height into the equation, and solve for the weight:

Then subtract the desired weight from David's current weight to determine how many whole pounds he should lose:

260 - 199 = 61