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A researcher has determined that she requires a minimum of n

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A researcher has determined that she requires a minimum of n [#permalink]

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A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?

A.\(\frac{{200n}}{{100-p}}\)

B.\(\frac{{2n}}{{100-p}}\)

C.\(\frac{{200n}}{{p}}\)

D.\(\frac{{2n(100+p)}}{{100}}\)

E.\(\frac{{2n+2np}}{{100}}\)


I took some time to solve it algebraically. Have fun!
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Re: A researcher has determined that she requires a minimum of n [#permalink]

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kingflo wrote:
A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?

A.\(\frac{{200n}}{{100-p}}\)

B.\(\frac{{2n}}{{100-p}}\)

C.\(\frac{{200n}}{{p}}\)

D.\(\frac{{2n(100+p)}}{{100}}\)

E.\(\frac{{2n+2np}}{{100}}\)


I took some time to solve it algebraically. Have fun!


Say x individuals must be surveyed.

p% of the surveyed individuals fail to respond --> the number of individuals who did NOT fail to respond = \(x-x*\frac{p}{100}\).
The above must be equal to 2n, so:

\(x-x*\frac{p}{100}=2n\) --> \(x(1-\frac{p}{100})=2n\) --> \(x=\frac{200n}{100-p}\).

Answer: A.

Of course one can also use plug-in method to solve this problem.
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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 28 Jul 2013, 02:23
X - #of surveyed people

(1-P)*X>=2n --> x>=2n/(1-P)

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Re: A researcher has determined that she requires a minimum of n [#permalink]

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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 03 Jan 2016, 13:01
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suppose x is the number of people she needs to interview
out of the x, only x(100-p/100) answered.
this all is equal to n.
so n = x(100-p/100)
or x= 100n/100-p
since we need twice the number, multiply everything by 2, and get 200n/100-p.
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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 22 Jan 2016, 18:27
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Unitary method seems more comprehensible to me.

Given that p% of the surveyed individuals fail to respond.

So individual who NOT failed to respond = (100-P)%

That means,

To get (100-P) responses, 100 individual is surveyed.
For 1 response, 100 / (100-P) individual is surveyed.
For 2n responses, (100*2n) / (100-P) individual is surveyed.

Answer: (A) 200n / (100-P)
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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 09 Jul 2016, 21:01
Bunuel wrote:
kingflo wrote:
A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?

A.\(\frac{{200n}}{{100-p}}\)

B.\(\frac{{2n}}{{100-p}}\)

C.\(\frac{{200n}}{{p}}\)

D.\(\frac{{2n(100+p)}}{{100}}\)

E.\(\frac{{2n+2np}}{{100}}\)


I took some time to solve it algebraically. Have fun!


Say x individuals must be surveyed.

p% of the surveyed individuals fail to respond --> the number of individuals who did NOT fail to respond = \(x-x*\frac{p}{100}\).
The above must be equal to 2n, so:

\(x-x*\frac{p}{100}=2n\) --> \(x(1-\frac{p}{100})=2n\) --> \(x=\frac{200n}{100-p}\).

Answer: A.

Of course one can also use plug-in method to solve this problem.

The question is not hard..I got stuck because I found the wording very awkward..is the wording good enough? I'm not feeling right about this one..
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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 10 Jul 2017, 01:12
Hello from the GMAT Club BumpBot!

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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 08 Sep 2017, 12:58
A question is a little similar to https://gmatclub.com/forum/the-price-of ... 31794.html.
(the opposite similar))

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Re: A researcher has determined that she requires a minimum of n [#permalink]

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New post 09 Sep 2017, 14:54
Bunuel wrote:
kingflo wrote:
A researcher has determined that she requires a minimum of n responses to a survey for the results to be valid. If p% of the surveyed individuals fail to respond to the survey, how many individuals, in terms of n and p, must the researcher survey to produce twice the minimum required number of responses?

A.\(\frac{{200n}}{{100-p}}\)

B.\(\frac{{2n}}{{100-p}}\)

C.\(\frac{{200n}}{{p}}\)

D.\(\frac{{2n(100+p)}}{{100}}\)

E.\(\frac{{2n+2np}}{{100}}\)


I took some time to solve it algebraically. Have fun!


Say x individuals must be surveyed.

p% of the surveyed individuals fail to respond --> the number of individuals who did NOT fail to respond = \(x-x*\frac{p}{100}\).
The above must be equal to 2n, so:

\(x-x*\frac{p}{100}=2n\) --> \(x(1-\frac{p}{100})=2n\) --> \(x=\frac{200n}{100-p}\).

Answer: A.

Of course one can also use plug-in method to solve this problem.


hi

how can you equate x( 1 - p/100) with 2n ..?

say, p = 10, n = 7....
now 90 people can respond, and 2n = 14

So, 14 = 90 , how come ...?

if the question used the terms "at least", it would be somewhat clear ...

thanks in advance ..

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A researcher has determined that she requires a minimum of n [#permalink]

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New post 09 Sep 2017, 20:52
Plugin nos.
Let people surveyed be 100
10% of 100 surveyed do not respond=10
90 surveyed responded=the required no response for the survey to be valid.
Double is 180.
To get 180 you need 200 responders.
Plugin in n=90 and p=10 in the given expression.
1) Start from C

\(\frac{200n}{p}\)

\(\frac{200*90}{10}\)=1800=wrong.

2) Pick A (I checked all the answer choice but for sake of time and effort showing only 2 workings)

\(\frac{200*n}{100-p}\)

\(\frac{200*90}{100-10}\)=200=correct.

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A researcher has determined that she requires a minimum of n   [#permalink] 09 Sep 2017, 20:52
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