PSAT Math Multiple-Choice Question 218: Answer and Explanation

Question: 218

A bakery sells three sizes of muffins—mini, regular, and jumbo. The baker plans daily muffin counts based on the size of his pans and how they fit in the oven, which result in the following ratios: mini to regular equals 5 to 2 and regular to jumbo equals 5 to 4. When the bakery caters events, it usually offers only the regular size, but it recently decided to offer a mix of mini and jumbo instead of regular. If the baker wants to keep the sizes in the same ratio as his daily counts, what ratio of mini to jumbo should he use?

• A. 1:1
• B. 4:2
• C. 5:2
• D. 25:8

Correct Answer: D

Explanation:

D

Difficulty: Hard

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

Getting to the Answer: Read the question, organizing important information as you go. You need to find the ratio of mini muffins to jumbo muffins. You're given two ratios: mini to regular and regular to jumbo. Both of the given ratios contain regular muffin size units, but the regular amounts (2 and 5) are not identical. To directly compare them, find a common multiple (10). Multiply each ratio by the factor that will make the number of regular muffins equal to 10:

Mini to regular: (5:2) × (5:5) = 25:10

Regular to jumbo: (5:4) × (2:2) = 10:8

Now that the number of regular muffins is the same in both ratios (10), you can merge the two ratios to compare mini to jumbo directly: 25:10:8. So, the proper ratio of mini muffins to jumbo muffins is 25:8, which is (D).