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Math Expert V
Joined: 02 Sep 2009
Posts: 58453

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Difficulty:   45% (medium)

Question Stats: 61% (01:28) correct 39% (01:57) wrong based on 36 sessions

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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%

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Math Expert V
Joined: 02 Sep 2009
Posts: 58453

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Official Solution:

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%

To calculate the percent increase of any value, we use this formula: $$\frac{\text{New} - \text{Old}}{\text{Old}}$$. In other words, we subtract the original value $$\text{Old}$$ from the increased value $$\text{New}$$, then divide the result by the original value $$\text{Old}$$. 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 $$\frac{7}{80}$$. The new response rate is $$\frac{9}{63}$$, or $$\frac{1}{7}$$. The difference is $$\frac{1}{7} - \frac{7}{80}$$. We convert to common denominators: $$\frac{80}{560} - \frac{49}{560} = \frac{31}{560}$$. Now, we divide by the original value, $$\frac{7}{80}$$. Doing so is the same as multiplying by $$\frac{80}{7}$$. This gives us $$\frac{31}{560}*\frac{80}{7} = \frac{31}{49}$$. Estimating, we can see that this fraction is slightly more than $$\frac{30}{50}$$, which is $$\frac{60}{100}$$ 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 $$= \frac{7}{80} = 0.0875 = 8.75%$$. Likewise, the new response rate $$= \frac{9}{63} = \frac{1}{7} \approx 14.3%$$. 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.

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Another faster method could be making the basis of comparison same. If 7 out of 80 have responded, how many have responded out of 100 based on 7/80 rate. This would be about (7*100)/80 = 35/4; Similarly, (9*100)/63 = 1/7. Therefore ( (1/7) - (35/4) )/ 1/7, which is about (14-8)/8, which is roughly 65%. Closest answer is 63 as we dont need to consider decimals for quick calculation. Re: S98-05   [#permalink] 17 Jan 2018, 05:46
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