nidhis.1408 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?

Since the GMAT would provide answer choices, we can plug in values.

If n=10 responses are required, then twice the minimum = 20.
If p=50% of the individuals fail to respond, then 40 individuals must be surveyed to yield 20 responses.
The question stem asks for the number of individuals who must be surveyed: 40.
This is our target.
Now we plug n=10 and p=50 into the answers to see which yields our target of 40.

Answer choice: 200n/(100-p)
200n/(100-p) = (200*10)/(100-50) = 2000/50 = 40.

Algebraically:

Let the number interviewed = i.
Since p% don't respond, the number who don't respond = (p/100)i.
Thus, the number who DO respond = i - (p/100)i.
Since this result must be equal to 2n -- twice the minimum number of required responses -- we get:

i - (p/100)i = 2n

i(1 - p/100) = 2n

i*(100-p)/100 = 2n

i = 200n/(100-p).

Hi,

I tried different approach and got wrong answer.

My understanding:

Since, we have to get number of responses equal to 2n. We consider "p%" more while taking the survey.

That comes 2n+ (2n*p)/100
= 2n((100+p)/100).

Which is option D.

Please somebody correct me.