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

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

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22 Jul 2013, 03:55
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75% (hard)

Question Stats:

57% (01:26) correct 43% (01:42) wrong based on 483 sessions

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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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22 Jul 2013, 04:10
1
1
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:

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

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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28 Jul 2013, 01:23
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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03 Jan 2016, 12:01
2
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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22 Jan 2016, 17:27
1
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.

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

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09 Jul 2016, 20:01
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:

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

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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08 Sep 2017, 11:58
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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09 Sep 2017, 13:54
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:

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

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 ...

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

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09 Sep 2017, 19:52
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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Joined: 16 Jul 2018
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A researcher has determined that she requires a minimum of n  [#permalink]

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06 Jan 2019, 03:19
gps5441 wrote:
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.

I tried to plugin numbers too and couldn't get the right answer, may I ask you something in your approach you state that 90 people is the required number of people so that the survey is valid isn't that wrong? I mean n is the minimum number those 90 are the n-p/100 + afterwards you consider the required amount to be 180, however isn't the 200 you should actually be looking for? Still, you got the right answer...

Could you please elaborate on your approach so that I can spot my mistake?

Bunuel chetan2u maybe you could shed some light on the problem here?
A researcher has determined that she requires a minimum of n &nbs [#permalink] 06 Jan 2019, 03:19
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