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# A survey was sent to 80 customers, 7 of whom responded. Then the surve

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
case 1: (7/80)=x/100
x=9%

case 2: (9/63)=y/100
y=14%

So percent increase is =(y-x)=(14-9)%=5%

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
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$$\frac{\frac{9}{63} - \frac{7}{80}}{\frac{7}{80}} * 100$$

$$= \frac{31}{560} * \frac{80}{7} * 100 = \frac{3100}{49} \approx{63%}$$
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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
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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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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
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Bunuel wrote:

Tough and Tricky questions: Percents.

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%

Kudos for a correct solution.

One can use some approximation in such questions:

Initial Response rate = (7/80)* 100 = 7*5/4 = about 9%
Redesigned Response rate = (9/63)* 100 = (1/7)*100 = 14.28% (You should remember these fraction to percent equivalents)

Increase is of about 5 on 9 which is certainly more than 50%. Only (E) satisfies.

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
Bunuel wrote:

Tough and Tricky questions: Percents.

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%

We can use the percent change formula, which is (New - Old)/Old x 100, to determine the percent increase in the response rate:

[(9/63) - (7/80)]/(7/80) x 100 =

[(1/7) - (7/80)]/(7/80) x 100 =

Multiplying the left side by 560/560, we have:

(80 - 49)/49 x 100 =

31/49 x 100

We see that 31/49 is roughly 31/50 = 62/100 = 62%

Alternate Solution:

We can approximate the initial response rate of 7/80 as roughly 7/77, or 1/11. The new response rate is 9 /63, or 1/7. We can use the percent change formula, which is (New - Old)/Old x 100, to determine the percent increase in the response rate:

(1/7 - 1/11)/1/11 x 100 =

Multiplying the expression by 77/77, we obtain:

(11 - 7)/7 x 100 =

4/7 x 100

We see that 4/7 is slightly more than ½, so 4/7 x 100 will be slightly greater than 50%.

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
amitshri15 wrote:
Rate of first survey = 7/80
Rate of second survey = 9/63

% Response rate increase (9/63-7/80)/(7/80) = 63%

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
GMAT2645 wrote:
amitshri15 wrote:
Rate of first survey = 7/80
Rate of second survey = 9/63

% Response rate increase (9/63-7/80)/(7/80) = 63%

It is not hard.

$$\frac{\frac{9}{63} - \frac{7}{80}}{\frac{7}{80}} = \frac{\frac{9}{63}}{\frac{7}{80}} - 1 = \frac{9*80}{63*7} - 1 = 80/49 - 1 = 31/49$$

In percentage terms, it is a bit more than $$\frac{31}{50}* 100 = 62%$$
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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
Because the answers are so far apart, we can do some very rough approximation.

Lets convert each survey to be out of roughly 240

first: multiply by 3/3 to get 21 / 240
second: multiply each by ~3.9/~3.9 to get somewhere in the 32 to 38 range /240

Even if we aren't great at our estimation and we pick 32, we get an increase of:

(32-21) /21 -> much closer to Option E than Option B.

If we are superb at estimation and pick more accurate numbers, we would multiply the second survey by ~3.8/~3.8, and get ~34 as the number of respondents, then see (34-21)/21 is almost exactly Option E.
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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink]
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