Questions 1 to 3 are based on the following data.
Annual Percent Change in Dollar Amount of Sales at Five Retail Stores from 2006 to 2008
from 2006 to 2007
from 2007 to 2008
- If the dollar amount of sales at Store P was $800,000 for 2006, what was the dollar amount of sales at that store for 2008?
According to Figure 8, if the dollar amount of sales at Store P was $800,000 for 2006, then it was 10 percent greater for 2007, which is 110 percent of that amount, or $880,000. For 2008 the amount was 90 percent of $880,000, which is $792,000. The correct answer is Choice B, $792,000.
Note that an increase of 10 percent for one year and a decrease of 10 percent for the following year does not result in the same dollar amount as the original dollar amount because the base that is used in computing the percents is $800,000 for the first change but $880,000 for the second change.
At Store T, the dollar amount of sales for 2007 was what percent of the dollar amount of sales for 2008?
Give your answer to the nearest 0.1 percent.
If A is the dollar amount of sales at Store T for 2007, then 8 percent of A, or is the amount of decrease from 2007 to 2008. Thus is the dollar amount for 2008. Therefore, the desired percent can be obtained by dividing A by which equals Expressed as a percent and rounded to the nearest 0.1 percent, this number is 108.7%. Thus the correct answer is 108.7% (or equivalent).
Based on the information given, which of the following statements must be true?
Indicate all such statements.
- For 2008 the dollar amount of sales at Store R was greater than that at each of the other four stores.
- The dollar amount of sales at Store S for 2008 was 22 percent less than that for 2006.
- 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 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 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).
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