Some problems cannot be solved directly from the information given, and you need to determine what other information will help you answer the question. In that case, it is useful to list all the information given in the problem, along with the information that would be contained in a complete solution, and then evaluate what is missing. Sometimes the missing information can be derived from the information given, and sometimes it cannot.
• This strategy is used in the following sample question.
This is a Multiple-Choice — Select One or More Answer Choices question.
Annual Percent Change in Dollar Amount of Sales at Five Retail Stores from 2006 to 2008
Store Percent Change
from 2006 to 2007
from 2007 to 2008
P 10 –10 Q –20 9 R 5 12 S –7 –15 T 17 –8
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.
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 13.