PSAT Math Multiple-Choice Question 226: Answer and Explanation

Question: 226

Marion is a city planner. The city she works for recently purchased new property on which it plans to build administrative offices. Marion has been given the task of sizing the lots for new buildings, using the following guidelines:

The square footage of each lot should be greater than or equal to 3,000 square feet, but less than or equal to 15,000 square feet.

Each lot size should be at least 30 percent greater in area than the size before it.

To simplify tax assessment calculations, the square footage of each lot must be a multiple of 1,000 square feet.

Which list of lot sizes meets the city guidelines and includes as many lots as possible?

• A. 3,000; 5,000; 10,000; 15,000
• B. 3,000; 4,500; 6,000; 7,500; 10,000; 15,000
• C. 3,000; 4,000; 6,000; 8,000; 11,000; 15,000
• D. 3,000; 3,900; 5,100; 6,600; 8,600; 11,200; 14,600

Correct Answer: C

Explanation:

C

Difficulty: Medium

Category: Problem Solving and Data Analysis/Rates, Ratios, Proportions, and Percentages

Getting to the Answer: Start with the smallest possible lot size, 3,000 square feet. The next lot must be at least 30% larger, so multiply by 1.3 to get 3,900 square feet. Then, round up to the next thousand (which is not necessarily the nearest thousand) to meet the tax assessment requirement. You must always round up because rounding down would make the subsequent lot size less than 30% larger than the one before it. Continue this process until you reach the maximum square footage allowed, 15,000 square feet:

3,000 × 1.3 = 3,900 → 4,000
4,000 × 1.3 = 5,200 → 6,000
6,000 × 1.3 = 7,800 → 8,000
8,000 × 1.3 = 10,400 → 11,000
11,000 × 1.3 = 14,300 → 15,000

Choice (C) is correct.