SAT Math Multiple Choice Question 389: Answer and Explanation

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Question: 389

14. A self-storage company has three sizes of storage units. The ratio of small to medium units is 3:5. The ratio of medium to large units is 3:2. The company analyzes its business model and current consumer demand and determines that it can benefit from utilizing larger economies of scale. In other words, it decides to grow its business based on current economic conditions and plans to build a second, larger self-storage building. The company's research indicates that the new market would benefit from having only two sizes of storage units, small and large, in the same ratio as its current facility. What ratio of small to large units should it use?

  • A. 1:1
  • B. 3:2
  • C. 5:3
  • D. 9:10

Correct Answer: D

Explanation:

D

Difficulty: Hard

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

Strategic Advice: Read the question, organizing important information as you go. You need to find the ratio of small units to large units. You're given two ratios: small to medium and medium to large.

Getting to the Answer: Both of the given ratios contain medium size units, but the medium amounts (5 and 3) are not identical. To directly compare them, find a common multiple (15). Multiply each ratio by the factor that will make the number of medium units equal to 15.

small to medium: (3:5) × (3:3) = 9:15

medium to large: (3:2) × (5:5) = 15:10

Now that the number of medium units needed is the same in both ratios, you can merge the two ratios to compare small to large directly: 9:15:10. Therefore, the proper ratio of small units to large units is 9:10.

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