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

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Math Expert
Joined: 02 Sep 2009
Posts: 47920
A survey was sent to 80 customers, 7 of whom responded. Then the surve  [#permalink]

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18 Nov 2014, 08:29
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Difficulty:

65% (hard)

Question Stats:

56% (01:32) correct 44% (01:28) wrong based on 237 sessions

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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.

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

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18 Nov 2014, 22:36
5
Rate of first survey = 7/80
Rate of second survey = 9/63

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

##### General Discussion
Manager
Joined: 10 Sep 2014
Posts: 98
Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve  [#permalink]

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18 Nov 2014, 08:59
I wrote down (9/63) - (7/80) and then cross multiplied to get 279/5040 which I reduced down to about 6/112 so it looks like there was a 5% difference. Answer B!
Manager
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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve  [#permalink]

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18 Nov 2014, 21:56
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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18 Nov 2014, 23:57
3

$$\frac{\frac{9}{63} - \frac{7}{80}}{\frac{7}{80}} * 100$$

$$= \frac{31}{560} * \frac{80}{7} * 100 = \frac{3100}{49} \approx{63%}$$
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Math Expert
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Posts: 47920
Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve  [#permalink]

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19 Nov 2014, 08:02
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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06 Apr 2016, 22:30
1
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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Save up to $1,000 on GMAT prep through 8/20! Learn more here > GMAT self-study has never been more personalized or more fun. Try ORION Free! Target Test Prep Representative Status: Head GMAT Instructor Affiliations: Target Test Prep Joined: 04 Mar 2011 Posts: 2727 Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink] ### Show Tags 26 Jan 2018, 10:36 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%. Answer: E _________________ Jeffery Miller Head of GMAT Instruction GMAT Quant Self-Study Course 500+ lessons 3000+ practice problems 800+ HD solutions Intern Joined: 01 Jan 2016 Posts: 21 Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink] ### Show Tags 09 May 2018, 11:09 amitshri15 wrote: Rate of first survey = 7/80 Rate of second survey = 9/63 % Response rate increase (9/63-7/80)/(7/80) = 63% Answer is E = 63% Are you doing this math in your head? Veritas Prep GMAT Instructor Joined: 16 Oct 2010 Posts: 8184 Location: Pune, India Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve [#permalink] ### Show Tags 10 May 2018, 23:33 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% Answer is E = 63% Are you doing this math in your head? 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 $$\frac{31}{50}* 100 = 62%$$ _________________ Karishma Veritas Prep GMAT Instructor Save up to$1,000 on GMAT prep through 8/20! Learn more here >

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Re: A survey was sent to 80 customers, 7 of whom responded. Then the surve &nbs [#permalink] 10 May 2018, 23:33
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