PSAT Math Multiple-Choice Question 374: Answer and Explanation

Question: 374

A certain city has 2,625 businesses and has a ratio of 5:2 of businesses that do not require safety inspections to those that do require safety inspections. Of the businesses that were required to have inspections, 12 percent had safety violations. How many businesses that required inspections did NOT have any safety violations?

• A. 90
• B. 315
• C. 660
• D. 2,310

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Percents

Getting to the Answer: Break the actual question into short steps. First, find the number of businesses that were required to have inspections. There are 2,625 businesses. The part-to-part ratio of businesses that require inspections to those that do not is 2:5, so the ratio of those business that require inspections to the total number of businesses is . So, the total number of businesses that need inspections is . This is the number of businesses that had violations; 12% of those is 0.12 × 750 = 90.

Finally, find the number of businesses that did NOT have violations by subtracting 90 from 750 to get 750 - 90 = 660 businesses that did not have any safety issues. Choice (C) is correct.