PSAT Math Multiple-Choice Question 533: Answer and Explanation

Question: 533

A random sample of 200 widgets was tested from the 5,913 widgets produced by a factory one day. If 41 of the widgets were defective, approximately how many widgets produced in the factory that day would be expected to be defective?

• A. 1,200
• B. 2,200
• C. 3,000
• D. 4,700

Correct Answer: A

Explanation:

A

The question asks about the number of defective widgets based on information about a random sample of the total produced. Since the widgets were randomly selected, the incidence of those defective in the sample should match that of the total produced. Start by ballparking. Less than half the widgets were defective, so the answer must be less than half of 5,913. Eliminate (D), which is too large. To extrapolate the sample results, set up a proportion. In this case, the proportion is based on the number of defective widgets out of the total of each group: . Cross-multiply to get 200x = 242,433. Divide both sides by 200 to get x = 1,212.165, or approximately 1,200. The correct answer is (A).