2. 外语
  3. Based on the information given, which of the following statements must be true? Indicate all such statements.

Based on the information given, which of the following statements must be true? Indicate all such statements.

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问题 Based on the information given, which of the following statements must be true? Indicate all such statements.
选项 A、For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores.
B、The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006.
C、The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006.
答案C
解析 For Choice A, since the only data given in Figure 8 are percent changes from year to year, there is no way to compare the actual dollar amount of sales at the stores for 2008 or for any other year. Even though Store R had the greatest percent increase from 2006 to 2008, its actual dollar amount of sales for 2008 may have been much smaller than that for any of the other four stores, and therefore Choice A is not necessarily true.
For Choice B, even though the sum of the two percent decreases would suggest a 22 percent decrease, the bases of the percents are different. If B is the dollar amount of sales at Store S for 2006, then the dollar amount for 2007 is 93 percent of B, or 0.93B, and the dollar amount for 2008 is given by(0.85)(0.93)B, which is 0.7905B. Note that this represents a percent decrease of 100 - 79.05 = 20.95 percent, which is not equal to 22 percent, and so Choice B is not true.
For Choice C, if C is the dollar amount of sales at Store R for 2006, then the dollar amount for 2007 is given by 1.05C and the dollar amount for 2008 is given by(1.12)(1.05)C, which is 1.176C. Note that this represents a 17.6 percent increase, which is greater than 17 percent, so Choice C must be true.
Therefore the correct answer consists of only Choice C(The dollar amount of sales at Store R for 2008 was more than 17 percent greater than that for 2006).
This explanation uses the following strategies.
Strategy 1: Translate from Words to an Arithmetic or Algebraic Representation
Strategy 4: Translate from a Figure to an Arithmetic or Algebraic Representation
Strategy 5: Simplify an Arithmetic or Algebraic Representation
Strategy 13: Determine Whether a Conclusion Follows from the Information Given
Strategy 14: Determine What Additional Information Is Sufficient to Solve a Problem
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