PSAT Math Multiple-Choice Question 535: Answer and Explanation

Question: 535

A teacher asks his students to estimate the weight of the snow on their porches after a light snowfall given the weight of snow per cubic meter. One student’s porch is a rectangle measuring 305 centimeters by 425 centimeters and is covered by an even layer of snow 5 millimeters thick. What are the dimensions of the layer of snow (width by length by thickness) in meters? (Note: 1 centimeter = 10 millimeters and 1 meter = 100 centimeters)

• A. 3,050 meters by 4,250 meters by 50 meters
• B. 3,050 meters by 4,250 meters by 5,000 meters
• C. 3.05 meters by 4.25 meters by meters
• D. 3.05 meters by 4.25 meters by meters

Correct Answer: D

Explanation:

D

The question asks for measurements and gives conflicting units. Start by ballparking. The given measurements are in centimeters and millimeters, which are smaller than meters. Therefore, the number of meters for each measurement will be smaller than the number of centimeters and millimeters. Eliminate (A) and (B), which have very large measurements. Compare the remaining answers. The only difference is the third measurement. Start by converting the 5 millimeters to centimeters. The question states that 1 centimeter = 10 millimeters. Set up a proportion to determine how many centimeters are in 5 millimeters, being sure to match up units: . Cross-multiply to get 10x = 5. Divide both sides by 10 to get x = 0.5 centimeters. Next, convert 0.5 centimeters to meters. The question states that 1 meter = 100 centimeters. Set up a proportion to determine how many meters are in 0.5 centimeters, being sure to match up units: . Cross-multiply to get 100x = 0.5. Divide both sides by 100 to get x = 0.005 meters. As a fraction, this is . The correct answer is (D).