Official Explanation
The ratio of the revenue for the 51 - 55 age group to the revenue for all age groups represented is_____________.
In the description of the chart, you are told that the chart represents solely those between the ages of 21 and 70. The percentages represent measures of the entire population surveyed. In other words, even without adding them all together manually you can conclude that the percentages of both revenue and attendance sum to 100%. Any percentage is equivalent to a ratio with the number 100 as the denominator. In this case, 8%, which is the percentage for the 51 - 55 year-olds, is 8% out of a possible total of 100%, or a ratio of 8:100, which can be reduced to 2 : 25.
Answer: D
The group with the highest attendance has revenues that are_____________greater than the revenues of the group with the lowest attendance.
This is a percent change question, so use the percent change formula:
%change \(= \frac{difference}{original} * 100\)
The group with the highest attendance is the 56 - 60 year-olds. The revenues for this group are 5%. The group with the lowest attendance is the 66 – 70 year-olds. The revenues for this group are 2%. The question is: "5 is what percent greater than 2?" It doesn’t matter that these numbers are already percents because they are percents of the same total. Put these numbers into the percent change formula:
%change \(= \frac{difference}{original} * 100\)
%change \(= \frac{3}{2} * 100 = \frac{300}{2} =150\)%
If you got 67%, you put the original number, 3, over the difference, 2. If you got 2%, you just turned the original number into a percent. If you got 3%, you just turned the difference into a percent. If you got 250%, you divided 5 by 2 and converted the quotient into a percent, answering the question, "5 is what percent of 2", when the actual question is "5 is what percent greater than 2".
Answer: D