SAT Math Multiple Choice Question 840: Answer and Explanation

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Question: 840

15. An all-natural health clinic stocks teas and herbs in a 5:11 ratio at one of its warehouses.In an effort to cut overhead costs, the owners close this warehouse and transfer itsstock to a larger warehouse, increasing that warehouse's inventory of items by 20%.Which of the following could be the number of items at the larger warehouse afterthe transfer?

  • A. 198
  • B. 386
  • C. 480
  • D. 573

Correct Answer: C



Difficulty: Hard

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

Strategic Advice: When given a ratio, you can always add an x to each term. For example, if the ratio of boys to girls is 2:3, then you know that there are 2x boys, 3x girls, and 5x boys and girls in total.

Getting to the Answer: The ratio of teas to herbs is 5:11, which means that the total number of teas and herbs is. Because this represents a 20% increase in the larger warehouse's stock, it follows that 16x is 20%, or, of the large warehouse's initial stock:. The final stock in the warehouse is therefore. This means that the answer must be a multiple of 96, or in other words, evenly divisible by 96. Use your calculator to quickly test each answer choice: Of the numbers given, 480 is the only one that is evenly divisible by 96, making (C) the correct answer.

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