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This week's question: A survey was sent to 80 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? A.) 2% B.) 5% C.) 14% D.) 28% E.) 63%
Please post your answer, along with the explanation, below. Get cracking!
Edit: This challenge is now closed.
Solution To calculate the percent increase of any value, we use this formula: (New – Old)/Old. In other words, we subtract the original value (Old) from the increased value (New), then divide the result by the original value (Old). Even though the values themselves may be written using percents, we must be sure to divide by the original value.
In this problem, the original response rate is 7/80. The new response rate is 9/63, or 1/7. The difference is 1/7 – 7/80. We convert to common denominators: 80/560 – 49/560 = 31/560. Now, we divide by the original value, 7/80. Doing so is the same as multiplying by 80/7. This gives us (31/560)(80/7) = 31/49. Estimating, we can see that this fraction is slightly more than 30/50, which is 60/100 or 60%. Thus, the correct answer must be (E): 63%.
Note that the response rates may be written as percents. For instance, the original response rate = 7/80 = 0.0875 = 8.75%. Likewise, the new response rate = 9/63 = 1/7 = ~14.3%. However, if you write these rates this way, do not simply take the difference! That difference, approximately 5 or 6%, does NOT represent the percent increase in the response rate. You must divide by the original response rate.
Again, the correct answer is (E).
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A survey was sent to 80 customers, 7 of whom responded. Then the survey was redesigned and sent to another 63 customers, 9 of whom responded. By approximately what percent did the response rate increase from the original survey to the redesigned survey? A.) 2% B.) 5% C.) 14% D.) 28% E.) 63%
7/80 - 9/63 = X (where X is the change in percent) 7 - 720/63 = 80X 441 - 720 = 5040X 279 = 5040X X = 279/5040 X = .055 = 5.5%