Strategy 13: Determine Whether a Conclusion Follows from the Information Given

1. 
   

   Quantity A	Quantity B

   (A) Quantity A is greater.
   (B) Quantity B is greater.
   (C) The two quantities are equal.
   (D) The relationship cannot be determined from the information given.

    

   Explanation

   Set up the initial comparison:

   

   Then simplify:

   Step 1: Subtract 2w from both sides and add 4 to both sides to get  

   Step 2: Divide both sides by 5 to get  

   The comparison cannot be simplified any further. Although you are given that  you still don't know how w compares to  or 1.8. For example, if  then  but if  then  In other words, the relationship between w and  cannot be determined. Note that each of these simplification steps is reversible, so in reverse order, each simplification step implies that the relationship cannot be determined in the preceding comparison. Thus, the relationship between Quantities A and B cannot be determined. The correct answer is Choice D, the relationship cannot be determined from the information given.

Annual Percent Change in Dollar Amount of Sales at Five Retail Stores from 2006 to 2008

1. Based on the information given, which of the following statements must be true?

   Indicate all such statements.

   (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.

    

   Explanation

   For Choice A, since the only data given in the figure above 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  and the dollar amount for 2008 is given by  which is  Note that this represents a percent decrease of  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  and the dollar amount for 2008 is given by  which is  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).

   Note: This question and explanation also appear as an example of Strategy 14.